Valid HTML 4.0! Valid CSS!
%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Graeme W. Milton",
%%%     version         = "2.01",
%%%     date            = "04 June 2018",
%%%     time            = "09:44:39 MDT",
%%%     filename        = "milton-graeme-w.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 310 JWB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 6495",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~milton",
%%%     checksum        = "61729 9891 46238 458074",
%%%     email           = "milton at math.utah.edu",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; cloaking; composite
%%%                        materials",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a very rough preliminary unreleased
%%%                        bibliography of publications by, and about,
%%%                        Graeme W. Milton.
%%%
%%%                        At version 2.01, the year coverage looked
%%%                        like this:
%%%
%%%                             1979 (   1)    1993 (   3)    2007 (   9)
%%%                             1980 (   1)    1994 (   4)    2008 (  10)
%%%                             1981 (   6)    1995 (   3)    2009 (  23)
%%%                             1982 (   6)    1996 (   1)    2010 (  12)
%%%                             1983 (   2)    1997 (   6)    2011 (  14)
%%%                             1984 (   2)    1998 (   5)    2012 (  11)
%%%                             1985 (   4)    1999 (   4)    2013 (  18)
%%%                             1986 (   5)    2000 (   3)    2014 (  16)
%%%                             1987 (   5)    2001 (   2)    2015 (  12)
%%%                             1988 (   5)    2002 (   4)    2016 (  32)
%%%                             1989 (   4)    2003 (   5)    2017 (  18)
%%%                             1990 (   4)    2004 (   4)    2018 (   3)
%%%                             1991 (   6)    2005 (   6)
%%%                             1992 (   3)    2006 (   9)
%%%
%%%                             Article:        242
%%%                             Book:             2
%%%                             InCollection:    19
%%%                             InProceedings:   21
%%%                             Misc:             3
%%%                             PhdThesis:        1
%%%                             Proceedings:      1
%%%                             TechReport:       1
%%%                             Unpublished:      1
%%%
%%%                             Total entries:  291
%%%
%%%                        Data for this bibliography have been
%%%                        collected and merged from numerous sources,
%%%                        including the author's personal bibliographic
%%%                        records, the TeX User Group and BibNet
%%%                        Project bibliography archives, the MathSciNet
%%%                        database, the Crossref database, Google
%%%                        Scholar, and many different publisher Web
%%%                        sites.
%%%
%%%                        At version 2.00 on 12 April 2018, 71 entries
%%%                        from arXiv.org where merged into this
%%%                        bibliography with abstracts and DOI values,
%%%                        labels were regenerated to correct several
%%%                        mismatches in years or three-letter
%%%                        abbreviations, and newly-exposed duplicate
%%%                        entries were merged.  In addition, ORCID
%%%                        numbers have been added to all entries where
%%%                        GWM is an author or editor.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
%%% ====================================================================
%%% Preamble material for TeX/LaTeX:
@Preamble{
    "\ifx \bblindex     \undefined \def \bblindex   #1{} \fi" #
    "\ifx \bbljournal   \undefined \def \bbljournal #1{{\em #1}\index{#1@{\em #1}}} \fi" #
    "\ifx \bblnumber    \undefined \def \bblnumber  #1{{\bf #1}} \fi" #
    "\ifx \bblvolume    \undefined \def \bblvolume  #1{{\bf #1}} \fi" #
    "\ifx \booktitle    \undefined \def \booktitle  #1{{{\em #1}}} \fi" #
    "\ifx \mathbb       \undefined \def \mathbb     #1{{\bf #1}} \fi"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-gwm =   "Graeme W. Milton,
                    University of Utah,
                    Department of Mathematics,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    e-mail: \path|milton@math.utah.edu| (Internet),
                    URL: \path|http://www.math.utah.edu/~milton/|"}

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Institution abbreviations:
@String{inst-CORNELL            = "Cornell University"}
@String{inst-CORNELL:adr        = "Ithaca, New York."}

%%% ====================================================================
%%% Journal abbreviations: These are INTENTIONALLY given as full journal
%%% names, because abbreviations are often obscure, and sometimes, also
%%% ambiguous.
@String{j-AIP-CONF-PROC         = "AIP Conference Proceedings"}

@String{j-ANAL-MATH-PHYS        = "Analysis and Mathematical Physics"}

@String{j-APPL-PHYS             = "Applied Physics"}

@String{j-APPL-PHYS-A           = "Applied Physics A: Materials Science \&
                                  Processing"}

@String{j-APPL-PHYS-LET         = "Applied Physics Letters"}

@String{j-ARCH-RAT-MECH-ANAL    = "Archive for Rational Mechanics and
                                  Analysis"}

@String{j-ASYMPTOT-ANAL         = "Asymptotic Analysis"}

@String{j-C-R-MEC               = "Comptes Rendus M{'e}canique"}

@String{j-C-R-PHYS              = "Comptes Rendus Physique"}

@String{j-CALC-VAR-PARTIAL-DIFFER-EQU = "Calculus of Variations and Partial
                                  Differential Equations"}

@String{j-CAN-J-PHYS            = "Canadian Journal of Physics = Journal
                                  canadien de physique"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMMUN-MATH-PHYS      = "Communications in Mathematical Physics"}

@String{j-COMMUN-MATH-SCI       = "Communications in Mathematical Sciences"}

@String{j-DOC-MATH              = "Documenta Mathematica"}

@String{j-EPJ-APPL-PHYS         = "European Physical Journal. Applied Physics"}

@String{j-EUR-J-MECH-A-SOLIDS   = "European Journal of Mechanics, A, Solids"}

@String{j-EUROPHYS-LETT         = "Europhysics Letters"}

@String{j-GEOPHYSICS            = "Geophysics"}

@String{j-INT-J-ENG-SCI         = "International journal of engineering science"}

@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical Methods
                                  in Engineering"}

@String{j-INVERSE-PROBLEMS      = "Inverse Problems"}

@String{j-J-APPL-MECH           = "Journal of Applied Mechanics"}

@String{j-J-APPL-PHYS           = "Journal of Applied Physics"}

@String{j-J-CHEM-PHYS           = "Journal of Chemical Physics"}

@String{j-J-ELAST               = "Journal of Elasticity"}

@String{j-J-ENG-MATER-TECHNOL   = "Journal of Engineering Materials and
                                  Technology"}

@String{j-J-FLUID-MECH          = "Journal of Fluid Mechanics"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-J-MATH-PURES-APPL     = "Journal de Math{\'e}matiques Pures et
                                  Appliqu{\'e}es"}

@String{j-J-MECH-PHYS-SOLIDS    = "Journal of the Mechanics and Physics of
                                  Solids"}

@String{j-J-PHYS-D              = "Journal of Physics D: Applied Physics"}

@String{j-J-REINF-PLAST-COMPOS  = "Journal of Reinforced Plastics and
                                  Composites"}

@String{j-J-STAT-PHYS           = "Journal of Statistical Physics"}

@String{j-MATER-RES-SOC-SYMP-PROC = "Materials Research Society Symposium
                                  Proceedings"}

@String{j-MATH-MECH-COMPLEX-SYST = "Mathematics and Mechanics of Complex
                                  Systems"}

@String{j-MATH-MODEL-NUM-ANA    = "Mathematical modelling and numerical analysis
                                   = Modelisation math{\'e}matique et
                                   analyse num{\'e}rique: $M^2AN$"}

@String{j-MECH-MATER            = "Mechanics of Materials: An International
                                  Journal"}

@String{j-METHODS-APPL-ANAL     = "Methods and Applications of Analysis"}

@String{j-MULTISCALE-MODELING-SIMUL = "Multiscale Modeling \& Simulation"}

@String{j-NATURE                = "Nature"}

@String{j-NETW-HETEROG-MEDIA    = "Networks and Heterogeneous Media (NHM)"}

@String{j-NEW-J-PHYS            = "New Journal of Physics"}

@String{j-OPT-EXPRESS           = "Optics Express"}

@String{j-PHYS-REV-B-CMMP       = "Physical Review B: Condensed Matter and
                                  Materials Physics"}

@String{j-PHYS-REV-LET          = "Physical Review Letters"}

@String{j-PHYS-STATUS-SOLIDI    = "Physica Status Solidi"}

@String{j-PHYS-STATUS-SOLIDI-B-BASIC-RES = "Physica Status Solidi. B, Basic
                                  Research"}

@String{j-PHYS-TODAY            = "Physics Today"}

@String{j-PHYSICA-A             = "Physica A"}

@String{j-PHYSICA-B             = "Physica. B, Condensed Matter"}

@String{j-PHYSICA-D             = "Physica. D, Nonlinear Phenomena"}

@String{j-PROC-R-SOC-EDINB      = "Proceedings of the Royal Society of
                                  Edinburgh"}

@String{j-PROC-R-SOC-EDINB-SECT-A-MATH = "Proceedings of the Royal Society of
                                  Edinburgh. Section A, Mathematical and
                                  Physical Sciences"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
                                  Society of London. Series A,
                                  Mathematical and physical sciences"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI = "Proceedings of the Royal
                                  Society A: Mathematical, Physical, \&
                                  Engineering Sciences"}

@String{j-QUART-APPL-MATH       = "Quarterly of Applied Mathematics"}

@String{j-RHEOL-ACTA            = "Rheologica Acta"}

@String{j-SIAM-J-APPL-DYN-SYST  = "SIAM Journal on Applied Dynamical Systems"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-WAVE-MOTION           = "Wave motion"}

%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-AIP                 = "American Institute of Physics"}
@String{pub-AIP:adr             = "Woodbury, New York"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-ASME                = "American Society of Mechanical Engineers"}
@String{pub-ASME:adr            = "United Engineering Center, 345 E. 47th St.,
                                    New York, NY 10017, USA"}

@String{pub-BIRKHAUSER          = "Birkh{\"a}user Verlag"}
@String{pub-BIRKHAUSER:adr      = "Basel, Switzerland"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-ELSEVIER            = "Elsevier"}
@String{pub-ELSEVIER:adr        = "Amsterdam, The Netherlands"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-IOS                 = "IOS Press"}
@String{pub-IOS:adr             = "Amsterdam, The Netherlands"}

@String{pub-LONGMAN             = "Longman Scientific and Technical"}
@String{pub-LONGMAN:adr         = "Harlow, Essex, UK"}

@String{pub-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PLENUM              = "Plenum Press"}
@String{pub-PLENUM:adr          = "New York~/ London"}

@String{pub-SIAM                = "SIAM Press"}
@String{pub-SIAM:adr            = "Philadelphia"}

@String{pub-SV                  = "Springer-Verlag"}
@String{pub-SV:adr              = "Berlin~/ Heidelberg~/
                                  London~/ etc."}

%%% ====================================================================
%%% Bibliography entries, sorted in rough publication order with
%%% ``bibsort --byyear'':
@TechReport{Milton:1979:TST,
  author =       "Graeme W. Milton",
  title =        "Theoretical studies of the transport properties of
                 inhomogeneous media",
  type =         "Unpublished report",
  number =       "TP/79/1",
  institution =  "University of Sydney",
  address =      "Sydney, Australia",
  pages =        "1--65",
  year =         "1979",
  DOI =          "https://doi.org/10.13140/RG.2.1.2184.8482",
  bibdate =      "Sun Jul 5 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:1980:BCD,
  author =       "Graeme W. Milton",
  title =        "Bounds on the complex dielectric constant of a
                 composite material",
  journal =      j-APPL-PHYS-LET,
  volume =       "37",
  number =       "3",
  pages =        "300--302",
  day =          "1",
  month =        aug,
  year =         "1980",
  CODEN =        "APPLAB",
  DOI =          "https://doi.org/10.1063/1.91895",
  ISSN =         "0003-6951 (print), 1077-3118 (electronic), 1520-8842",
  ISSN-L =       "0003-6951",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics Letters",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/apl",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0272; GWM0697",
  originalref =  "Milton G. W. 1980 Bounds on the complex dielectric
                 constant of a composite material. {\em Appl. Phys.
                 Lett.} {\bf 37}, 300--302.",
  texsource =    "l-lec4.tex; l-lec15.tex",
  xxURL =        "http://scitation.aip.org/content/aip/journal/apl/37/3/10.1063/1.91895",
}

@Article{McPhedran:1981:BET,
  author =       "Ross C. McPhedran and Graeme W. Milton",
  title =        "Bounds and exact theories for the transport properties
                 of inhomogeneous media",
  journal =      j-APPL-PHYS-A,
  volume =       "26",
  number =       "4",
  pages =        "207--220",
  month =        dec,
  year =         "1981",
  CODEN =        "APSFDB",
  DOI =          "https://doi.org/10.1007/BF00617840",
  ISSN =         "0721-7250",
  ISSN-L =       "0721-7250",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics A: Materials Science \& Processing",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/339",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0469",
  originallab =  "GWM0370",
  originallab =  "GWM0129",
  originalref =  "McPhedran R. C. and Milton G. W. 1981 Bounds and exact
                 theories for the transport properties of inhomogeneous
                 media. {\em Appl. Phys. A} {\bf 26}, 207--220.",
  texsource =    "l-lec19.tex",
  texsource =    "l-lec17.tex",
  texsource =    "l-lec10.tex",
}

@Article{Milton:1981:BCP,
  author =       "Graeme W. Milton",
  title =        "Bounds on the complex permittivity of a two-component
                 composite material",
  journal =      j-J-APPL-PHYS,
  volume =       "52",
  number =       "8",
  pages =        "5286--5293",
  day =          "1",
  month =        aug,
  year =         "1981",
  CODEN =        "JAPIAU",
  DOI =          "https://doi.org/10.1063/1.329385",
  ISSN =         "0021-8979 (print), 1089-7550 (electronic), 1520-8850",
  ISSN-L =       "0021-8979",
  bibdate =      "Sat Nov 28 20:27:56 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/jap/52/8/10.1063/1.329385",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of Applied Physics",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/jap/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0736",
  originallab =  "GWM0698",
  originallab =  "GWM0473",
  originallab =  "GWM0197",
  originalref =  "Milton G. W. 1981 Bounds on the complex permittivity
                 of a two-component composite material, {\em J. Appl.
                 Phys.} {\bf 52}, 5286--5293.",
  originalref-2 = "Milton G. W. 1981a Bounds on the complex permittivity
                 of a two-component composite material. {\em J. Appl.
                 Phys.} {\bf 52}, 5286--5293.",
  texsource =    "l-lec5.tex",
  texsource =    "l-lec4.tex",
  texsource =    "l-lec19.tex",
  texsource =    "l-lec12.tex",
  xxURL =        "http://scitation.aip.org/content/aip/journal/apl/37/3/10.1063/1.91895",
}

@Article{Milton:1981:BEE,
  author =       "Graeme W. Milton",
  title =        "Bounds on the electromagnetic, elastic, and other
                 properties of two-component composites",
  journal =      j-PHYS-REV-LET,
  volume =       "46",
  number =       "8",
  pages =        "542--545",
  day =          "23",
  month =        feb,
  year =         "1981",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.46.542",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0475",
  originallab =  "GWM0374",
  originallab =  "GWM0327",
  originallab =  "GWM0214",
  originallab =  "GWM0133",
  originalref =  "Milton G. W. 1981c Bounds on the electromagnetic,
                 elastic, and other properties of two-component
                 composites, {\em Phys. Rev. Lett.} {\bf 46},
                 542--545.",
  originalref-2 = "Milton G. W. 1981b Bounds on the electromagnetic,
                 elastic, and other properties of two-component
                 composites, {\em Phys. Rev. Lett.} {\bf 46},
                 542--545.",
  originalref-3 = "Milton G. W. 1981 Bounds on the electromagnetic,
                 elastic, and other properties of two-component
                 composites, {\em Phys. Rev. Lett.} {\bf 46},
                 542--545.",
  texsource =    "l-lec19.tex",
  texsource =    "l-lec17.tex",
  texsource =    "l-lec16.tex",
  texsource =    "l-lec13.tex",
  texsource =    "l-lec10.tex",
}

@Article{Milton:1981:BTO,
  author =       "Graeme W. Milton",
  title =        "Bounds on the transport and optical properties of a
                 two-component composite material",
  journal =      j-J-APPL-PHYS,
  volume =       "52",
  number =       "8",
  pages =        "5294--5304",
  month =        aug,
  year =         "1981",
  CODEN =        "JAPIAU",
  DOI =          "https://doi.org/10.1063/1.329386",
  ISSN =         "0021-8979 (print), 1089-7550 (electronic), 1520-8850",
  ISSN-L =       "0021-8979",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/jap/52/8/10.1063/1.329386",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of Applied Physics",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/jap/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0547",
  originallab =  "GWM0474",
  originallab =  "GWM0373",
  originallab =  "GWM0198",
  originalref =  "Milton G. W. 1981 Bounds on the transport and optical
                 properties of a two-component composite material. {\em
                 J. Appl. Phys.} {\bf 52}, 5294--5304.",
  originalref-2 = "Milton G. W. 1981b Bounds on the transport and
                 optical properties of a two-component composite
                 material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.",
  originalref-3 = "Milton G. W. 1981b Bounds on the transport and
                 optical properties of a two-component composite
                 material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.",
  originalref-4 = "Milton G. W. 1981a Bounds on the transport and
                 optical properties of a two-component composite
                 material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.",
  texsource =    "l-lec20.tex",
  texsource =    "l-lec19.tex",
  texsource =    "l-lec17.tex",
  texsource =    "l-lec12.tex",
}

@Article{Milton:1981:CBT,
  author =       "Graeme W. Milton",
  title =        "Concerning bounds on the transport and mechanical
                 properties of multicomponent composite materials",
  journal =      j-APPL-PHYS,
  volume =       "A26",
  number =       "2",
  pages =        "125--130",
  year =         "1981",
  CODEN =        "APAMFC",
  DOI =          "https://doi.org/10.1007/BF00616659",
  ISSN =         "0947-8396 (print), 1432-0630 (electronic)",
  ISSN-L =       "0947-8396",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics",
  journal-URL =  "http://link.springer.com/journal/339",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0326",
  originalref =  "Milton G. W. 1981a Concerning bounds on the transport
                 and mechanical properties of multicomponent composite
                 materials. {\em Appl. Phys.} {\bf A26}, 125--130.",
  texsource =    "l-lec16.tex",
}

@Article{Milton:1981:TPA,
  author =       "Graeme W. Milton and Ross C. McPhedran and D. R.
                 McKenzie",
  title =        "Transport properties of arrays of intersecting
                 cylinders",
  journal =      j-APPL-PHYS,
  volume =       "25",
  number =       "1",
  pages =        "23--30",
  year =         "1981",
  CODEN =        "APAMFC",
  DOI =          "https://doi.org/10.1007/BF00935387",
  ISSN =         "0947-8396 (print), 1432-0630 (electronic)",
  ISSN-L =       "0947-8396",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics",
  journal-URL =  "http://link.springer.com/journal/339",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0478",
  originalref =  "Milton G. W., McPhedran R. C., and McKenzie D. R. 1981
                 Transport properties of arrays of intersecting
                 cylinders. {\em Appl. Phys.} {\bf 25}, 23--30.",
  texsource =    "l-lec19.tex",
  xxURL =        "http://link.springer.com/article/10.1007/BF00935387",
}

@Article{McPhedran:1982:ESI,
  author =       "Ross C. McPhedran and D. R. McKenzie and Graeme W.
                 Milton",
  title =        "Extraction of structural information from measured
                 transport properties of composites",
  journal =      j-APPL-PHYS-A,
  volume =       "29",
  number =       "1",
  pages =        "19--27",
  month =        sep,
  year =         "1982",
  CODEN =        "APSFDB",
  DOI =          "https://doi.org/10.1007/BF00618111",
  ISSN =         "0721-7250",
  ISSN-L =       "0721-7250",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00618111",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics A: Materials Science \& Processing",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/339",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0470",
  originalref =  "McPhedran R. C., McKenzie D. R., and Milton G. W. 1982
                 Extraction of structural information from measured
                 transport properties of composites. {\em Appl. Phys. A}
                 {\bf 29}, 19--27.",
  texsource =    "l-lec19.tex",
}

@Article{Milton:1982:BET,
  author =       "Graeme W. Milton",
  title =        "Bounds on the elastic and transport properties of
                 two-component composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "30",
  number =       "3",
  pages =        "177--191",
  year =         "1982",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/0022-5096(82)90022-9",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "73K20",
  MRnumber =     "666510 (83g:73058)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0022509682900229",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0476",
  originallab =  "GWM0375",
  originallab =  "GWM0134",
  originalref =  "Milton G. W. 1982 Bounds on the elastic and transport
                 properties of two-component composites, {J. Mech. Phys.
                 Solids} {\bf 30}, 177--191.",
  originalref-2 = "Milton G. W. 1982 Bounds on the elastic and transport
                 properties of two-component composites. {\em J. Mech.
                 Phys. Solids} {\bf 30}, 177--191.",
  texsource =    "l-lec19.tex",
  texsource =    "l-lec17.tex",
  texsource =    "l-lec10.tex",
}

@InProceedings{Milton:1982:CTM,
  author =       "Graeme W. Milton and Ross C. McPhedran",
  editor =       "Robert Burridge and Stephen Childress and George C.
                 Papanicolaou",
  booktitle =    "Macroscopic Properties of Disordered Media:
                 Proceedings of a Conference Held at the Courant
                 Institute, June 1--3, 1981",
  title =        "A comparison of two methods for deriving bounds on the
                 effective conductivity of composites",
  volume =       "154",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "vi + 307",
  pages =        "183--193",
  year =         "1982",
  ISBN =         "0-387-11202-2",
  ISBN-13 =      "978-0-387-11202-2",
  LCCN =         "QA911 .M32 1981",
  MRclass =      "73-06",
  MRnumber =     "674958 (83m:73005)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Lecture Notes in Physics",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0479",
  originalref =  "Milton G. W. and McPhedran R. C. 1982 A comparison of
                 two methods for deriving bounds on the effective
                 conductivity of composites. In {\em Macroscopic
                 Properties of Disordered Media}, ed. by R. Burridge, S.
                 Childress, and G. Papanicolaou, {\em Lecture notes in
                 physics}, {\bf 154}, pp. 183--193, Springer Verlag.",
  rest =         "Springer Verlag",
  texsource =    "l-lec19.tex",
}

@Article{Milton:1982:NBE,
  author =       "Graeme W. Milton and N. Phan-Thien",
  title =        "New bounds on effective elastic moduli of
                 two-component materials",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "380",
  number =       "1779",
  pages =        "305--331",
  year =         "1982",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1982.0044",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0376",
  originallab =  "GWM0333",
  originalref =  "Milton G. W. and Phan-Thien N. 1982 New bounds on
                 effective elastic moduli of two-component materials.
                 {\em Proc. Roy. Soc. Lond. A} {\bf 380}, 305--331.",
  texsource =    "l-lec17.tex",
  texsource =    "l-lec16.tex",
}

@Article{Phan-Thien:1982:NBE,
  author =       "N. Phan-Thien and Graeme W. Milton",
  title =        "New bounds on the effective thermal conductivity of
                 {$N$}-phase materials",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "380",
  number =       "1779",
  pages =        "333--348",
  year =         "1982",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1982.0045",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0377",
  originalref =  "Phan-Thien N. and Milton G. W. 1982 New bounds on the
                 effective thermal conductivity of $N$-phase materials.
                 {\em Proc. Roy. Soc. Lond. A} {\bf 380}, 333--348.",
  texsource =    "l-lec17.tex",
}

@Article{Phan-Thien:1982:PUB,
  author =       "N. Phan-Thien and Graeme W. Milton",
  title =        "A possible use of bounds on effective moduli of
                 composites",
  journal =      j-J-REINF-PLAST-COMPOS,
  volume =       "1",
  number =       "2",
  pages =        "107--114",
  month =        apr,
  year =         "1982",
  CODEN =        "JRPCDW",
  DOI =          "https://doi.org/10.1177/07316844820010020",
  ISSN =         "0731-6844 (print), 1530-7964 (electronic)",
  ISSN-L =       "0731-6844",
  bibdate =      "Fri Aug 12 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://jrp.sagepub.com/content/1/2/107.abstract",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of Reinforced Plastics and Composites",
  journal-URL =  "http://jrp.sagepub.com/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:1983:CFD,
  author =       "Graeme W. Milton and Michael E. Fisher",
  title =        "Continuum fluids with a discontinuity in the
                 pressure",
  journal =      j-J-STAT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "413--438",
  month =        aug,
  year =         "1983",
  CODEN =        "JSTPSB",
  DOI =          "https://doi.org/10.1007/BF01012719",
  ISSN =         "0022-4715 (print), 1572-9613 (electronic)",
  ISSN-L =       "0022-4715",
  MRclass =      "82A25 (82A05)",
  MRnumber =     "715034 (85e:82031)",
  MRreviewer =   "O. Penrose",
  bibdate =      "Thu Aug 28 18:33:54 MDT 2014",
  bibsource =    "http://link.springer.com/journal/10955;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=32&issue=2;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01012719",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
  journal-URL =  "http://link.springer.com/journal/10955",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Phan-Thien:1983:NTO,
  author =       "N. Phan-Thien and Graeme W. Milton",
  title =        "New third-order bounds on the effective moduli of
                 {$N$}-phase composites",
  journal =      j-QUART-APPL-MATH,
  volume =       "41",
  number =       "1",
  pages =        "59--74",
  year =         "1983",
  CODEN =        "QAMAAY",
  ISSN =         "0033-569X (print), 1552-4485 (electronic)",
  ISSN-L =       "0033-569X",
  MRclass =      "73K20 74A40 74A20",
  MRnumber =     "700661 (84i:73058)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  ZMnumber =     "0513.73004",
  acknowledgement = ack-gwm,
  fjournal =     "Quarterly of Applied Mathematics",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J641;
                 http://www.ams.org/journals/qam",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0135",
  originalref =  "Phan-Thien N. and Milton G. W. 1983 New third-order
                 bounds on the effective moduli of N-phase composites.
                 {\em Quart. Appl. Math.} {\bf 41}, 59--74.",
  remark =       "AMS journal Web site has data only for 2005--date, so
                 no DOI or URL is known. Not found in JSTOR either.",
  texsource =    "l-lec10.tex",
}

@InProceedings{Milton:1984:CEEa,
  author =       "Graeme W. Milton",
  editor =       "D. L. Johnson and P. N. Sen",
  booktitle =    "Physics and Chemistry of Porous Media: Papers from a
                 Symposium Held at Schlumberger--Doll Research, Oct.
                 24--25, 1983",
  title =        "Correlation of the electromagnetic and elastic
                 properties of composities and microgeometries
                 corresponding with effective medium approximations",
  journal =      j-AIP-CONF-PROC,
  volume =       "107",
  publisher =    pub-AIP,
  address =      pub-AIP:adr,
  bookpages =    "223",
  pages =        "52--65",
  year =         "1984",
  CODEN =        "APCPCS",
  DOI =          "https://doi.org/10.1063/1.34305",
  ISBN =         "0-88318-306-4",
  ISBN-13 =      "978-0-88318-306-9",
  ISSN =         "0094-243X (print), 1551-7616 (electronic), 1935-0465",
  ISSN-L =       "0094-243X",
  LCCN =         "TA418.9.P6 P46 1983",
  bibdate =      "Sat Nov 28 20:27:56 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.34305",
  acknowledgement = ack-nhfb,
  fjournal =     "AIP Conference Proceedings",
  journal-URL =  "http://scitation.aip.org/content/aip/proceeding/aipcp",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Conference date: 24--25 October 1983. Location:
                 Schlumberger- Doll Research",
}

@InProceedings{Milton:1984:CEEb,
  author =       "Graeme W. Milton",
  editor =       "D. L. Johnson and P. N. Sen",
  booktitle =    "Physics and Chemistry of Porous Media: Papers from a
                 Symposium Held at Schlumberger--Doll Research, Oct.
                 24--25, 1983",
  title =        "Correlation of the electromagnetic and elastic
                 properties of composites and microgeometries
                 corresponding with effective medium theory",
  journal =      j-AIP-CONF-PROC,
  volume =       "107",
  publisher =    pub-AIP,
  address =      pub-AIP:adr,
  bookpages =    "223",
  pages =        "66--77",
  year =         "1984",
  CODEN =        "APCPCS",
  DOI =          "https://doi.org/10.1063/1.34306",
  ISBN =         "0-88318-306-4",
  ISBN-13 =      "978-0-88318-306-9",
  ISSN =         "0094-243X (print), 1551-7616 (electronic), 1935-0465",
  ISSN-L =       "0094-243X",
  LCCN =         "TA418.9.P6 P46 1983",
  bibdate =      "Sat Nov 28 20:27:56 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "AIP Conference Proceedings",
  URL =          "http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.34306",
  acknowledgement = ack-gwm # "\slash " # ack-nhfb,
  fjournal =     "AIP Conference Proceedings",
  journal-URL =  "http://scitation.aip.org/content/aip/proceeding/aipcp",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0781",
  originallab =  "GWM0406",
  originalref =  "Milton G. W. 1984 Correlation of the electromagnetic
                 and elastic properties of composites and
                 microgeometries corresponding with effective medium
                 theory. In {\em Physics and Chemistry of Porous Media},
                 pp. 66--77, ed. by D. L. Johnson and P. N. Sen,
                 American Institute of Physics, New York.",
  originalref-2 = "Milton G. W. 1984 Correlation of the electromagnetic
                 and elastic properties of composites and
                 microgeometries corresponding with effective medium
                 approximations. In {\em Physics and Chemistry of Porous
                 Media} D. L. Johnson and P. N. Sen, eds., Am. Inst.
                 Phys., New York, pp. 66--77.",
  remark =       "Conference date: 24--25 October 1983. Location:
                 Schlumberger- Doll Research",
  rest =         "ed. by D. L. Johnson and P. N. Sen, American Institute
                 of Physics, New York",
  texsource =    "l-lec6.tex",
  texsource =    "l-lec18.tex",
  xxtitle =      "Correlation of the electromagnetic and elastic
                 properties of composites and microgeometries
                 corresponding with effective medium approximations",
}

@Article{Berryman:1985:NCV,
  author =       "James G. Berryman and Graeme W. Milton",
  title =        "Normalization constraint for variational bounds on
                 fluid permeability",
  journal =      j-J-CHEM-PHYS,
  volume =       "83",
  number =       "2",
  pages =        "754--760",
  day =          "15",
  month =        jul,
  year =         "1985",
  CODEN =        "JCPSA6",
  DOI =          "https://doi.org/10.1063/1.449489",
  ISSN =         "0021-9606 (print), 1089-7690 (electronic)",
  ISSN-L =       "0021-9606",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/jcp/83/2/10.1063/1.449489",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Chemical Physics",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/jcp/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:1985:CPA,
  author =       "Graeme W. Milton",
  title =        "The coherent potential approximation is a realizable
                 effective medium scheme",
  journal =      j-COMMUN-MATH-PHYS,
  volume =       "99",
  number =       "4",
  pages =        "463--500",
  year =         "1985",
  CODEN =        "CMPHAY",
  DOI =          "https://doi.org/10.1007/BF01215906",
  ISSN =         "0010-3616 (print), 1432-0916 (electronic)",
  ISSN-L =       "0010-3616",
  MRclass =      "82A57 (73B99 82A42)",
  MRnumber =     "796009 (86i:82054)",
  MRreviewer =   "B. Derrida",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01215906;
                 http://projecteuclid.org/euclid.cmp/1103942837",
  acknowledgement = ack-gwm,
  fjournal =     "Communications in Mathematical Physics",
  journal-URL =  "http://link.springer.com/journal/220",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0782",
  originalref =  "Milton G. W. 1985a The coherent potential
                 approximation is a realizable effective medium scheme.
                 {\em Comm. Math. Phys.} {\bf 99}, 463--500.",
  texsource =    "l-lec6.tex",
  xxURL =        "http://projecteuclid.org/euclid.cmp/1103942837",
}

@PhdThesis{Milton:1985:SEM,
  author =       "Graeme W. Milton",
  title =        "Some exotic models in statistical physics. {I}. {The}
                 coherent potential approximation is a realizable
                 effective medium scheme. {II}. {Anomalous} first-order
                 transitions",
  type =         "{Ph.D.} thesis",
  school =       inst-CORNELL,
  address =      inst-CORNELL:adr,
  pages =        "x + 164",
  year =         "1985",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://search.proquest.com/dissertations/docview/303393850/",
  acknowledgement = ack-gwm,
  advisor =      "Michael Ellis Fisher",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0783",
  originalref =  "Milton G. W. 1985b Some exotic models in statistical
                 physics. I The coherent potential approximation is a
                 realizable effective medium scheme. II Anomalous
                 first-order transitions. {\em PhD Thesis} Cornell
                 University.",
  rest =         "Cornell University",
  texsource =    "l-lec6.tex",
}

@InProceedings{Milton:1985:TCC,
  author =       "Graeme W. Milton and Kenneth M. Golden",
  editor =       "T. Ashworth and D. R. Smith",
  booktitle =    "Thermal Conductivity",
  title =        "Thermal conduction in composites",
  volume =       "18",
  publisher =    pub-PLENUM,
  address =      pub-PLENUM:adr,
  bookpages =    "xix + 764",
  pages =        "571--582",
  year =         "1985",
  ISBN =         "0-306-41918-1",
  ISBN-13 =      "978-0-306-41918-8",
  LCCN =         "QC 320.8 I58 1983",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0550",
  originallab =  "GWM0217",
  originalref =  "Milton G. W. and Golden K. 1985 Thermal conduction in
                 composites. In {\em Thermal Conductivity} {\bf 18}, ed.
                 by T. Ashworth and D. R. Smith, pp. 571-582, Plenum
                 Press, New York.",
  originalref-2 = "Milton G. W. and Golden K. 1985 Thermal conduction in
                 composites. In {\em Thermal Conductivity} {\bf 18}, ed.
                 by T. Ashworth and D. R. Smith (Plenum Press, New
                 York). pp. 571--582.",
  rest =         "Plenum Press, New York",
  texsource =    "l-lec20.tex",
  texsource =    "l-lec13.tex",
  xxnote =       "Proceedings of the Eighteenth International
                 Conductivity Conference, hosted and organized by the
                 South Dakota School of Mines and Technology, sponsored
                 by RE\slash SPEC Inc. of Rapid City and CINDAS\slash
                 Purdue University, Held October 3--5, 1983, in Rapid
                 City, South Dakota.",
}

@Article{Fisher:1986:CFO,
  author =       "Michael E. Fisher and Graeme W. Milton",
  title =        "Classifying first-order phase transitions",
  journal =      j-PHYSICA-A,
  volume =       "138",
  number =       "1--2",
  pages =        "22--54",
  month =        sep,
  year =         "1986",
  CODEN =        "PHYSAG",
  DOI =          "https://doi.org/10.1016/0378-4371(86)90172-X",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "82A25 (82A97)",
  MRnumber =     "865235 (87k:82052)",
  MRreviewer =   "V. A. Zagrebnov",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037843718690172X",
  fjournal =     "Physica A. Statistical and Theoretical Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Kohn:1986:BEC,
  author =       "Robert V. Kohn and Graeme W. Milton",
  editor =       "J. L. Ericksen and David Kinderlehrer and Robert V.
                 Kohn and Jacques-Louis Lions",
  booktitle =    "{Homogenization and Effective Moduli of Materials and
                 Media: Papers presented at a Workshop on Homogenization
                 of Differential Equations and the Determination of
                 Effective Moduli of Materials and Media, Primarily in
                 the Context of Continuum Theory; Minneapolis, MN,
                 October 22--October 26, 1984}",
  title =        "On bounding the effective conductivity of anisotropic
                 composites",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 263",
  pages =        "97--125",
  year =         "1986",
  DOI =          "https://doi.org/10.1007/978-1-4613-8646-9_5",
  ISBN =         "0-387-96306-5",
  ISBN-13 =      "978-0-387-96306-8",
  LCCN =         "QA808.2 .H661 1986",
  MRclass =      "78A25",
  MRnumber =     "859413 (87k:78005)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "The IMA Volumes in Mathematics and its Applications",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4613-8646-9_5",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0319",
  originalref =  "Kohn R. V. and Milton G. W. 1986 On bounding the
                 effective conductivity of anisotropic composites. In
                 {\em Homogenization and Effective Moduli of Materials
                 and Media}, ed. by J. L. Ericksen, D. Kinderlehrer, R.
                 Kohn, and J.-L. Lions., {\em The IMA volumes in
                 mathematics and its applications} {\bf 1}, pp. 97--125,
                 Springer-Verlag.",
  rest =         "Springer-Verlag",
  texsource =    "l-lec16.tex",
}

@InProceedings{Milton:1986:APLG,
  author =       "Graeme W. Milton",
  editor =       "George C. Papanicolaou",
  booktitle =    "Advances in Multiphase Flow and Related Problems:
                 Proceedings of the Workshop on Cross Disciplinary
                 Research in Multiphase Flow, Leesburg, Virginia, June
                 2--4, 1986",
  title =        "A proof that laminates generate all possible effective
                 conductivity functions of two-dimensional, two-phase
                 media",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  bookpages =    "x + 295",
  pages =        "136--146",
  year =         "1986",
  ISBN =         "0-89871-212-2",
  ISBN-13 =      "978-0-89871-212-4",
  LCCN =         "QA922 .W671 1986",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0200",
  originalref =  "Milton G. W. 1986b A proof that laminates generate all
                 possible effective conductivity functions of
                 two-dimensional, two-phase media. In {\em Advances in
                 multiphase flow and related problems}, ed. G.
                 Papanicolaou {\em S.I.A.M., Philadelphia}, 136--146.",
  texsource =    "l-lec12.tex",
  xxkey =        "xx1986b",
  xxtitle =      "Proof that laminates generate all possible effective
                 conductivity functions of two-dimensional, two-phase
                 media",
}

@InCollection{Milton:1986:MPC,
  author =       "Graeme W. Milton",
  editor =       "J. L. Ericksen and David Kinderlehrer and Robert V.
                 Kohn and Jacques-Louis Lions",
  booktitle =    "{Homogenization and Effective Moduli of Materials and
                 Media: Papers presented at a Workshop on Homogenization
                 of Differential Equations and the Detemination of
                 Effective Moduli of Materials and Media, Primarily in
                 the Context of Continuum Theory; Minneapolis, MN,
                 October 22--October 26, 1984}",
  title =        "Modeling the properties of composites by laminates",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 263",
  pages =        "150--174",
  year =         "1986",
  DOI =          "https://doi.org/10.1007/978-1-4613-8646-9_7",
  ISBN =         "0-387-96306-5",
  ISBN-13 =      "978-0-387-96306-8",
  LCCN =         "QA808.2 .H661 1986",
  MRclass =      "73-02 (76-02 78-02) 73K20",
  MRnumber =     "859409 (87i:73006); 859415",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "The IMA Volumes in Mathematics and its Applications",
  acknowledgement = ack-gwm,
  book-DOI =     "https://doi.org/10.1007/978-1-4613-8646-9",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0737",
  originallab =  "GWM0548",
  originallab =  "GWM0328",
  originallab =  "GWM0199",
  originalref =  "Milton G. W. 1986 Modeling the properties of
                 composites by laminates. In {\em Homogenization and
                 Effective Moduli of Materials and Media}, ed. by J. L.
                 Ericksen, D. Kinderlehrer, R. Kohn, and J.-L. Lions.,
                 {\em The IMA volumes in mathematics and its
                 applications} {\bf 1}, pp. 150--174, Springer-Verlag.",
  originalref-2 = "Milton G. W. 1986a Modeling the properties of
                 composites by laminates. In {\em Homogenization and
                 Effective Moduli of Materials and Media}, ed. by J. L.
                 Ericksen, D. Kinderlehrer, R. Kohn, and J.-L. Lions.,
                 {\em The IMA volumes in mathematics and its
                 applications} {\bf 1}, pp. 150--174, Springer-Verlag.",
  rest =         "Springer-Verlag",
  rest =         "{\em The IMA volumes in mathematics and its
                 applications}",
  texsource =    "l-lec5.tex",
  texsource =    "l-lec20.tex",
  texsource =    "l-lec16.tex",
  texsource =    "l-lec12.tex",
  xxkey =        "xx1986a",
  xxtitle =      "Modelling the properties of composites by laminates",
}

@Article{Stroud:1986:AMD,
  author =       "D. Stroud and Graeme W. Milton and B. R. De",
  title =        "Analytical model for the dielectric response of
                 brine-saturated rocks",
  journal =      j-PHYS-REV-B-CMMP,
  volume =       "34",
  number =       "8",
  pages =        "5145--5153",
  day =          "15",
  month =        oct,
  year =         "1986",
  CODEN =        "PRBMDO",
  DOI =          "https://doi.org/10.1103/PhysRevB.34.5145",
  ISSN =         "1098-0121",
  ISSN-L =       "1098-0121",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevB.34.5145",
  fjournal =     "Physical Review B: Condensed Matter and Materials
                 Physics",
  journal-URL =  "http://prb.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Fisher:1987:ECF,
  author =       "Michael E. Fisher and Graeme W. Milton",
  title =        "Erratum: ``{Classifying} first-order phase
                 transitions'' [{Phys}.\ {A} {\bf 138} (1986), no.\ 1,
                 22--54; {MR0865235} (87k:82052)]",
  journal =      j-PHYSICA-A,
  volume =       "142",
  number =       "1-3",
  pages =        "649",
  year =         "1987",
  CODEN =        "PHYSAG",
  DOI =          "https://doi.org/10.1016/0378-4371(87)90048-3",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "82A25 (82A97)",
  MRnumber =     "897288 (88h:82027)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  fjournal =     "Physica A. Statistical and Theoretical Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Francfort:1987:OBC,
  author =       "G. A. Francfort and Graeme W. Milton",
  title =        "Optimal bounds for conduction in two-dimensional,
                 multiphase, polycrystalline media",
  journal =      j-J-STAT-PHYS,
  volume =       "46",
  number =       "1--2",
  pages =        "161--177",
  month =        jan,
  year =         "1987",
  CODEN =        "JSTPSB",
  DOI =          "https://doi.org/10.1007/BF01010338",
  ISSN =         "0022-4715 (print), 1572-9613 (electronic)",
  ISSN-L =       "0022-4715",
  MRclass =      "78A25",
  MRnumber =     "887243 (88m:78003)",
  bibdate =      "Thu Aug 28 18:38:02 MDT 2014",
  bibsource =    "http://link.springer.com/journal/10955;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=46&issue=1;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01010338",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
  journal-URL =  "http://link.springer.com/journal/10955",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0264",
  originalref =  "Francfort G. A. and Milton G. W. 1987 Optimal bounds
                 for conduction in two-dimensional, multiphase,
                 polycrystalline media. {\em J. Stat. Phys.} {\bf 46},
                 161--177.",
  texsource =    "l-lec15.tex",
}

@Article{McPhedran:1987:TPT,
  author =       "Ross C. McPhedran and Graeme W. Milton",
  title =        "Transport properties of touching cylinder pairs and of
                 the square array of touching cylinders",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "411",
  number =       "1841",
  pages =        "313--326",
  day =          "8",
  month =        jun,
  year =         "1987",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1987.0069",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  bibdate =      "Wed Jun 8 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/411/1841/313",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:1987:MCEa,
  author =       "Graeme W. Milton",
  title =        "Multicomponent composites, electrical networks and new
                 types of continued fraction. {I}",
  journal =      j-COMMUN-MATH-PHYS,
  volume =       "111",
  number =       "2",
  pages =        "281--327",
  year =         "1987",
  CODEN =        "CMPHAY",
  DOI =          "https://doi.org/10.1007/BF01217763",
  ISSN =         "0010-3616 (print), 1432-0916 (electronic)",
  ISSN-L =       "0010-3616",
  MRclass =      "82A55 (73B99)",
  MRnumber =     "899853 (89b:82084)",
  MRreviewer =   "V. Mastrangelo",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://projecteuclid.org/euclid.cmp/1104159541",
  acknowledgement = ack-gwm,
  fjournal =     "Communications in Mathematical Physics",
  journal-URL =  "http://link.springer.com/journal/220",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0556",
  originallab =  "GWM0215",
  originalref =  "Milton G. W. 1987a Multicomponent composites,
                 electrical networks and new types of continued fraction
                 I. {\em Comm. Math. Phys.} {\bf 111}, 281--327.",
  originalref-2 = "Milton G. W. 1987 Multicomponent composites,
                 electrical networks and new types of continued fraction
                 I. {\em Comm. Math. Phys.} {\bf 111}, 281--327.",
  texsource =    "l-lec21.tex",
  texsource =    "l-lec13.tex",
}

@Article{Milton:1987:MCEb,
  author =       "Graeme W. Milton",
  title =        "Multicomponent composites, electrical networks and new
                 types of continued fraction. {II}",
  journal =      j-COMMUN-MATH-PHYS,
  volume =       "111",
  number =       "3",
  pages =        "329--372",
  year =         "1987",
  CODEN =        "CMPHAY",
  DOI =          "https://doi.org/10.1007/BF01238903",
  ISSN =         "0010-3616 (print), 1432-0916 (electronic)",
  ISSN-L =       "0010-3616",
  MRclass =      "82A55 (73B99 73F99 94C05)",
  MRnumber =     "900499 (89b:82085)",
  MRreviewer =   "V. Mastrangelo",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://projecteuclid.org/euclid.cmp/1104159635",
  acknowledgement = ack-gwm,
  fjournal =     "Communications in Mathematical Physics",
  journal-URL =  "http://link.springer.com/journal/220",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0557",
  originallab =  "GWM0273",
  originalref =  "Milton G. W. 1987b Multicomponent composites,
                 electrical networks and new types of continued fraction
                 II. {\em Comm. Math. Phys.} {\bf 111}, 329--372.",
  originalref-2 = "Milton G. W. 1987 Multicomponent composites,
                 electrical networks and new types of continued fraction
                 II. {\em Comm. Math. Phys.} {\bf 111}, 329--372.",
  texsource =    "l-lec21.tex",
  texsource =    "l-lec15.tex",
}

@Article{Avellaneda:1988:ECP,
  author =       "M. Avellaneda and Andrej V. Cherkaev and K. A. Lurie
                 and Graeme W. Milton",
  title =        "On the effective conductivity of polycrystals and a
                 three-dimensional phase-interchange inequality",
  journal =      j-J-APPL-PHYS,
  volume =       "63",
  number =       "10",
  pages =        "4989--5003",
  year =         "1988",
  CODEN =        "JAPIAU",
  DOI =          "https://doi.org/10.1063/1.340445",
  ISSN =         "0021-8979 (print), 1089-7550 (electronic), 1520-8850",
  ISSN-L =       "0021-8979",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/jap/63/10/10.1063/1.340445",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of Applied Physics",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/jap/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0676",
  originallab =  "GWM0421",
  originallab =  "GWM0389",
  originallab =  "GWM0257",
  originalref =  "Avellaneda M., Cherkaev A. V., Lurie K. A., and Milton
                 G. W. 1988 On the effective conductivity of
                 polycrystals and a three-dimensional phase-interchange
                 inequality. {\em J. Appl. Phys.} {\bf 63},
                 4989--5003.",
  texsource =    "l-lec4.tex",
  texsource =    "l-lec18.tex",
  texsource =    "l-lec15.tex",
}

@Article{Berryman:1988:MRC,
  author =       "James G. Berryman and Graeme W. Milton",
  title =        "Microgeometry of random composites and porous media",
  journal =      j-J-PHYS-D,
  volume =       "21",
  number =       "1",
  pages =        "87--94",
  year =         "1988",
  CODEN =        "JPAPBE",
  DOI =          "https://doi.org/10.1088/0022-3727/21/1/013",
  ISSN =         "0022-3727 (print), 1361-6463 (electronic)",
  ISSN-L =       "0022-3727",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://iopscience.iop.org/0022-3727/21/1/013",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of Physics D: Applied Physics",
  journal-URL =  "http://iopscience.iop.org/0022-3727/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0391",
  originallab =  "GWM0349",
  originalref =  "Berryman J. G. and Milton G. W. 1988 Microgeometry of
                 random composites and porous media. {\em J. Phys. D:
                 Appl. Phys.} {\bf 21}, 87--94.",
  texsource =    "l-lec18.tex",
  texsource =    "l-lec17.tex",
  xxURL =        "http://iopscience.iop.org/article/10.1088/0022-3727/21/1/013/",
}

@Article{McPhedran:1988:ASC,
  author =       "Ross C. McPhedran and L. Poladian and Graeme W.
                 Milton",
  title =        "Asymptotic studies of closely spaced, highly
                 conducting cylinders",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "415",
  number =       "1848",
  pages =        "185--196",
  year =         "1988",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1988.0009",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0831",
  originalref =  "McPhedran R. C., Poladian L., and Milton G. W. 1988
                 Asymptotic studies of closely spaced, highly conducting
                 cylinders. {\em Proc. Roy. Soc. Lond. A} {\bf 415},
                 185--196.",
  texsource =    "l-lec7.tex",
}

@Article{Milton:1988:CHE,
  author =       "Graeme W. Milton",
  title =        "Classical {Hall}-effect in two-dimensional composites:
                 a characterization of the set of realizable effective
                 conductivity tensors",
  journal =      j-PHYS-REV-B-CMMP,
  volume =       "38",
  number =       "16",
  pages =        "11296--11303",
  day =          "1",
  month =        dec,
  year =         "1988",
  CODEN =        "PRBMDO",
  DOI =          "https://doi.org/10.1103/PhysRevB.38.11296",
  ISSN =         "1098-0121",
  ISSN-L =       "1098-0121",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.aps.org/prb/abstract/10.1103/PhysRevB.38.11296",
  acknowledgement = ack-gwm,
  fjournal =     "Physical Review B: Condensed Matter and Materials
                 Physics",
  journal-URL =  "http://prb.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0530",
  originalref =  "Milton G. W. 1988 Classical Hall-effect in
                 two-dimensional composites: a characterization of the
                 set of realizable effective conductivity tensors. {\em
                 Phys. Rev. B} {\bf 38}, 11296--11303.",
  texsource =    "l-lec2.tex",
}

@Article{Milton:1988:VBE,
  author =       "Graeme W. Milton and Robert V. Kohn",
  title =        "Variational bounds on the effective moduli of
                 anisotropic composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "36",
  number =       "6",
  pages =        "597--629",
  year =         "1988",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/0022-5096(88)90001-4",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "73C40 (73C30 73C60 73K20 73R05)",
  MRnumber =     "969257 (90h:73015)",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0022509688900014",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0895",
  originallab =  "GWM0739",
  originallab =  "GWM0331",
  originalref =  "Milton G. W. and Kohn R. V., 1988 Variational bounds
                 on the effective moduli of anisotropic composites. {\em
                 J. Mech. Phys. Solids} {\bf 36}, 597--629.",
  texsource =    "l-lec9.tex",
  texsource =    "l-lec5.tex",
  texsource =    "l-lec16.tex",
}

@InProceedings{Avellaneda:1989:BEE,
  author =       "M. Avellaneda and Graeme W. Milton",
  editor =       "David Hui and Thomas J. Kozik",
  booktitle =    "{Composite material technology 1989: presented at the
                 twelfth Annual Energy-Sources Technology Conference and
                 Exhibition, Houston, Texas January 22--25, 1989}",
  title =        "Bounds on the effective elasticity tensor of
                 composites based on two point correlations",
  volume =       "PD-24",
  publisher =    pub-ASME,
  address =      pub-ASME:adr,
  bookpages =    "vi + 215",
  pages =        "89--93",
  year =         "1989",
  LCCN =         "TA 418.9.C6 C56 1989",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Petroleum Division",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0723",
  texsource =    "l-lec5.tex",
  xxaddress =    "Houston, Texas",
  xxpublisher =  "American Society of Mechanical Engineers, Petroleum
                 Division",
}

@Article{Avellaneda:1989:CPP,
  author =       "Marco Avellaneda and A. V. Cherkaev and K. A. Lurie
                 and Graeme Milton",
  title =        "On the conductivity of polycrystals and a
                 phase-interchange inequality",
  journal =      j-PHYSICA-A,
  volume =       "157",
  number =       "1",
  pages =        "148--153",
  month =        may,
  year =         "1989",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/0378-4371(89)90291-4",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Sat Nov 28 18:44:37 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0378437189902914",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Avellaneda:1989:OBE,
  author =       "Marco Avellaneda and Graeme W. Milton",
  title =        "Optimal Bounds on the Effective Bulk Modulus of
                 Polycrystals",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "824--837",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/0149048",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "73K20 (73B27 73V25)",
  MRnumber =     "997923 (91e:73088)",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  URL =          "http://epubs.siam.org/doi/pdf/10.1137/0149048",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  bibno =        "64947",
  catcode =      "G.1.8; J.2; G.1.2; G.1.6",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Difference
                 methods; J.2 Physics; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.6 Optimization;
                 G.1.6 Constrained optimization",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Difference methods; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09716",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0419",
  originallab =  "GWM0388",
  originallab =  "GWM0258",
  originalref =  "Avellaneda M. and Milton G. W. 1989 Optimal bounds on
                 the effective bulk modulus of polycrystals. {\em SIAM
                 J. Appl. Math.} {\bf 49}, 824--837.",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
  texsource =    "l-lec18.tex",
  texsource =    "l-lec15.tex",
}

@InProceedings{Tartar:1989:MSA,
  author =       "Luc Tartar",
  editor =       "Robert V. Kohn and Graeme W. Milton",
  booktitle =    "{Proceedings of the SIAM Workshop on Random Media and
                 Composites, Leesburg, Virginia, December 7--10, 1988}",
  title =        "{$H$}-measures and small amplitude homogenization",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  bookpages =    "214",
  pages =        "89--99",
  year =         "1989",
  ISBN =         "0-89871-246-7",
  ISBN-13 =      "978-0-89871-246-9",
  LCCN =         "TA401.3 .S53 1988",
  MRclass =      "00B25 (35-06 73-06 73B27 73B99 73K20 82B44 82C44)",
  MRnumber =     "1059286 (91b:00052)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0091",
  originalref =  "Tartar L. 1989 $H$-measures and small amplitude
                 homogenization. In {\em Random Media and Composites},
                 ed. by R. V. Kohn and G. W. Milton, pp. 89--99, Society
                 for Industrial and Applied Mathematics.",
  rest =         "Society for Industrial and Applied Mathematics",
  texsource =    "l-lec10.tex",
}

@Article{McPhedran:1990:ITP,
  author =       "Ross C. McPhedran and Graeme W. Milton",
  title =        "Inverse transport problems for composite media",
  journal =      j-MATER-RES-SOC-SYMP-PROC,
  volume =       "195",
  number =       "??",
  pages =        "257--274",
  year =         "1990",
  CODEN =        "MRSPDH",
  DOI =          "https://doi.org/10.1557/PROC-195-257",
  ISSN =         "1946-4274",
  ISSN-L =       "1946-4274",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.cambridge.org/abstract_S1946427400554219",
  acknowledgement = ack-gwm,
  fjournal =     "Materials Research Society Symposium Proceedings",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=OPL",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0471",
  originalref =  "McPhedran R. C. and Milton G. W. 1990 Inverse
                 transport problems for composite media. {\em Mat. Res.
                 Soc. Symp. Proc.} {\bf 195}, 257--274.",
  texsource =    "l-lec19.tex",
}

@InCollection{Milton:1990:BRT,
  author =       "Graeme W. Milton",
  editor =       "G{\'e}rard A. Maugin",
  booktitle =    "{Continuum models and discrete systems: [contains the
                 texts of most of the short contributions presented at
                 the Sixth International Symposium on Continuum Models
                 and Discrete Systems \ldots{} held on the campus of the
                 University of Bourgogne, Dijon, France, from June 25 to
                 June 29, 1989] Vol. 1}",
  title =        "A brief review of the translation method for bounding
                 effective elastic tensors of composites",
  volume =       "1",
  publisher =    pub-LONGMAN,
  address =      pub-LONGMAN:adr,
  bookpages =    "324",
  pages =        "60--74",
  year =         "1990",
  ISBN =         "0-582-05121-5",
  ISBN-13 =      "978-0-582-05121-8",
  MRclass =      "73K20 (73B27 73V25)",
  MRnumber =     "1100723 (92d:73035)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Interaction of Mechanics and Mathematics Series,
                 Longman, Essex",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0408",
  originalref =  "Milton G. W. 1990 A brief review of the translation
                 method for bounding effective elastic tensors of
                 composites. In {\em Continuum Models and Discrete
                 Systems}, pp. 60--74, ed. by G. A. Maugin, Volume 1,
                 Interaction of Mechanics and Mathematics Series,
                 Longman, Essex.",
  rest =         "ed. by G. A. Maugin, Volume 1, Interaction of
                 Mechanics and Mathematics Series, Longman, Essex",
  texsource =    "l-lec18.tex",
}

@Article{Milton:1990:CSP,
  author =       "Graeme W. Milton",
  title =        "On characterizing the set of possible effective
                 tensors of composites: {The} variational method and the
                 translation method",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "43",
  number =       "1",
  pages =        "63--125",
  year =         "1990",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160430104",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "73B27 (49S05 73K20)",
  MRnumber =     "1024190 (91c:73006)",
  MRreviewer =   "John M. Ball",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430104/full",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0894",
  originallab =  "GWM0871",
  originallab =  "GWM0738",
  originallab =  "GWM0407",
  originallab =  "GWM0329",
  originallab =  "GWM0274",
  originalref =  "Milton G. W. 1990 On characterizing the set of
                 possible effective tensors of composites: The
                 variational method and the translation method. {\em
                 Comm. of Pure and Appl. Math} {\bf XLIII}, 63--125.",
  originalref-2 = "Milton G. W. 1990 On characterizing the set of
                 possible effective tensors of composites: the
                 variational method and the translation method. {\em
                 Comm. Pure Appl. Math.} {\bf 43}, 63--125.",
  texsource =    "l-lec9.tex",
  texsource =    "l-lec5.tex",
  texsource =    "l-lec18.tex",
  texsource =    "l-lec16.tex",
  texsource =    "l-lec15.tex",
  xxURL =        "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430104/",
  xxvolume =     "XLIII",
}

@Article{Milton:1990:RCF,
  author =       "Graeme W. Milton and Kenneth M. Golden",
  title =        "Representations for the conductivity functions of
                 multicomponent composites",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "43",
  number =       "5",
  pages =        "647--671",
  year =         "1990",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160430504",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "78A30",
  MRnumber =     "1057234 (91c:78009)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Communications on Pure and Applied Mathematics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0559",
  originallab =  "GWM0275",
  originallab =  "GWM0201",
  originallab =  "GWM0086",
  originalref =  "Milton G. W. and Golden K. 1990 Representations for
                 the conductivity functions of multicomponent
                 composites. {\em Comm. Pure Appl. Math.} {\bf XLIII},
                 647--671.",
  originalref-2 = "Milton G. W. and Golden K. 1990 Representations for
                 the conductivity functions of multicomponent
                 composites. {\em Comm. Pure Appl. Math.} {\bf 43},
                 647-671.",
  texsource =    "l-lec21.tex",
  texsource =    "l-lec15.tex",
  texsource =    "l-lec12.tex",
  texsource =    "l-lec10.tex",
  xxURL =        "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430504/",
  xxvolume =     "XLIII",
}

@Article{Berryman:1991:ERG,
  author =       "James G. Berryman and Graeme W. Milton",
  title =        "Exact results for generalized {Gassman}'s equations in
                 composite porous media with two constituents",
  journal =      j-GEOPHYSICS,
  volume =       "56",
  number =       "12",
  pages =        "1950--1960",
  month =        dec,
  year =         "1991",
  CODEN =        "GPYSA7",
  DOI =          "https://doi.org/10.1190/1.1443006",
  ISSN =         "0016-8033 (print), 1942-2156 (electronic)",
  ISSN-L =       "0016-8033",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://library.seg.org/doi/abs/10.1190/1.1443006",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Geophysics",
  journal-URL =  "http://library.seg.org/loi/gpysa7",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0623",
  originalref =  "Berryman J. G. and Milton G. W. 1991 Exact results for
                 generalized Gassman's equations in composite porous
                 media with two constituents. {\em Geophysics} {\bf 56},
                 1950--1960.",
  texsource =    "l-lec3.tex",
  xxURL =        "http://library.seg.org/doi/abs/10.1190/1.1443006",
}

@Unpublished{Kublanov:1991:REE,
  author =       "L. Kublanov and Graeme W. Milton",
  title =        "Rigorous estimates for the elastic moduli for a
                 two-dimensional two-phase material",
  pages =        "????",
  year =         "1991",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Unpublished manuscript.",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0367",
  originalref =  "Kublanov L. and Milton G. W. 1991 Rigorous estimates
                 for the elastic moduli for a two-dimensional two-phase
                 material. {\em Unpublished manuscript}.",
  texsource =    "l-lec17.tex",
}

@InProceedings{Milton:1991:EMC,
  author =       "Robert V. Kohn and Graeme W. Milton",
  editor =       "Shun-Chin Chou",
  booktitle =    "Proceedings of [the] 12th Army Symposium on Solid
                 Mechanics: Synergism of Mechanics. Mathematics, and
                 Materials: 4--7 November 1991, Plymouth,
                 Massachusetts",
  title =        "Extremal Microstructures for Composite Materials",
  publisher =    "Defense Technical Information Center",
  address =      "Ft. Belvoir, VA 22060-5606, USA",
  bookpages =    "viii + 644",
  pages =        "75--84",
  year =         "1991",
  LCCN =         "TA349 .P6 1991",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA326997#page=74",
  acknowledgement = ack-nhfb,
  book-URL =     "http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA326997",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InProceedings{Milton:1991:FER,
  author =       "Graeme W. Milton",
  editor =       "Gianni {Dal Maso} and Gianfausto F. Dell'Antonio",
  booktitle =    "Composite Media and Homogenization Theory: Proceedings
                 of the Workshop on Composite Media and Homogenization
                 Theory Held in Trieste, Italy, from January 15 to 26,
                 1990",
  title =        "The field equation recursion method",
  volume =       "5",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  bookpages =    "xiv + 258",
  pages =        "223--245",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4684-6787-1_13",
  ISBN =         "0-8176-3511-4, 3-7643-3511-4",
  ISBN-13 =      "978-0-8176-3511-4, 978-3-7643-3511-3",
  LCCN =         "QA808.2 .C665 1991",
  MRclass =      "73-06 (00B25 49J45 73B27 73K20 76S05) 78A25",
  MRnumber =     "1145753 (93b:73007); 1145740 (92h:73002)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Progress in Nonlinear Differential Equations and Their
                 Applications",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4684-6787-1_13",
  acknowledgement = ack-gwm,
  book-DOI =     "https://doi.org/10.1007/978-1-4684-6787-1",
  book-URL =     "http://link.springer.com/book/10.1007/978-1-4684-6787-1",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0558",
  originallab =  "GWM0549",
  originallab =  "GWM0409",
  originallab =  "GWM0216",
  originalref =  "Milton G. W. 1991b The field equation recursion
                 method. In {\em Composite Media and Homogenization
                 Theory}, ed. by G. Dal Maso and G. F. Dell'Antonio,
                 {\em Progress in Nonlinear Differential Equations and
                 Their Applications} {\bf 5}, pp. 223--245,
                 Birkh{\"a}user.",
  originalref-2 = "Milton G. W. 1991 The field equation recursion
                 method. In {\em Composite Media and Homogenization
                 Theory}, ed. by G. Dal Maso and G. F. Dell'Antonio,
                 {\em Progress in Nonlinear Differential Equations and
                 Their Applications} {\bf 5}, pp. 223--245,
                 Birkh{\"a}user.",
  originalref-3 = "Milton G. W. 1991 The field equation recursion
                 method. In {\em Composite Media and Homogenization
                 Theory}, pp. 223--245, ed. by G. Dal Maso and G. F.
                 Dell'Antonio, {\em Progress in Nonlinear Differential
                 Equations and Their Applications} {\bf 5},
                 Birkh{\"a}user.",
  rest =         "Birkh{\"a}user",
  texsource =    "l-lec21.tex",
  texsource =    "l-lec20.tex",
  texsource =    "l-lec18.tex",
  texsource =    "l-lec13.tex",
  xxbooktitle =  "Composite Media and Homogenization Theory: An
                 International Centre for Theoretical Physics workshop,
                 Trieste, Italy, January 1990",
}

@Article{Nesi:1991:PCM,
  author =       "Vincenzo Nesi and Graeme W. Milton",
  title =        "Polycrystalline configurations that maximize
                 electrical resistivity",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "39",
  number =       "4",
  pages =        "525--542",
  year =         "1991",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/0022-5096(91)90039-Q",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "73R05 (73B99 73K20 73V25 78A25 82D25)",
  MRnumber =     "1106125 (93a:73070)",
  MRreviewer =   "Philippe Boulanger",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002250969190039Q",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0607",
  originallab =  "GWM0433",
  originalref =  "Nesi V. and Milton G. W. 1991 Polycrystalline
                 configurations that maximize electrical resistivity.
                 {\em J. Mech. Phys. Solids} {\bf 39}, 525--542.",
  texsource =    "l-lec23.tex",
  texsource =    "l-lec18.tex",
  xxURL =        "http://www.sciencedirect.com/science/article/pii/002250969190039Q",
}

@Article{Smereka:1991:BFR,
  author =       "Peter Smereka and Graeme W. Milton",
  title =        "Bubbly flow and its relation to conduction in
                 composites",
  journal =      j-J-FLUID-MECH,
  volume =       "233",
  pages =        "65--81",
  month =        dec,
  year =         "1991",
  CODEN =        "JFLSA7",
  DOI =          "https://doi.org/10.1017/S0022112091000393",
  ISSN =         "0022-1120 (print), 1469-7645 (electronic)",
  ISSN-L =       "0022-1120",
  MRclass =      "76T05 (73B27 73K20 76D99)",
  MRnumber =     "1140079 (92i:76097)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.cambridge.org/abstract_S0022112091000393",
  fjournal =     "Journal of Fluid Mechanics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=FLM",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Berryman:1992:ERL,
  author =       "J. G. Berryman and Graeme W. Milton",
  title =        "Exact results in linear thermomechanics of fluid
                 saturated porous media",
  journal =      j-APPL-PHYS-LET,
  volume =       "61",
  number =       "17",
  pages =        "2030--??",
  day =          "26",
  month =        oct,
  year =         "1992",
  CODEN =        "APPLAB",
  DOI =          "https://doi.org/10.1063/1.108349",
  ISSN =         "0003-6951 (print), 1077-3118 (electronic), 1520-8842",
  ISSN-L =       "0003-6951",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/apl/61/17/10.1063/1.108349",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Physics Letters",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/apl",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Cherkaev:1992:IPS,
  author =       "Andrei V. Cherkaev and Konstantin A. Lurie and Graeme
                 W. Milton",
  title =        "Invariant properties of the stress in plane elasticity
                 and equivalence classes of composites",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "438",
  number =       "1904",
  pages =        "519--529",
  day =          "8",
  month =        sep,
  year =         "1992",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1992.0123",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  MRclass =      "73B27 (73C99 73K20)",
  MRnumber =     "1183894 (93g:73009)",
  bibdate =      "Thu Dec 16 15:46:41 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/438/1904/519",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0515",
  originalref =  "Cherkaev A. V., Lurie K. A., and Milton G. W. 1992
                 Invariant properties of the stress in plane elasticity
                 and equivalence classes of composites. {\em Proc. Roy.
                 Soc. London} A {\bf 438}, 519--529.",
  texsource =    "l-lec2.tex",
}

@Article{Milton:1992:CMP,
  author =       "Graeme W. Milton",
  title =        "Composite materials with {Poisson}'s ratios close to $
                 - 1 $",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "40",
  number =       "5",
  pages =        "1105--1137",
  month =        jul,
  year =         "1992",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/0022-5096(92)90063-8",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "73K20 (73B27 73C99)",
  MRnumber =     "1167758 (93c:73074)",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0576",
  originallab =  "GWM0029",
  originalref =  "Milton G. W. 1992 Composite materials with Poisson's
                 ratios close to $-1$. {\em J. Mech. Phys. Solids} {\bf
                 40}, 1105--1137.",
  texsource =    "l-lec1.tex",
  texsource =    "l-lec22.tex",
  xxURL =        "http://www.sciencedirect.com/science/article/pii/0022509692900638",
}

@Article{Gibiansky:1993:EVM,
  author =       "Leonid V. Gibiansky and Graeme W. Milton",
  title =        "On the effective viscoelastic moduli of two-phase
                 media. {I}. {Rigorous} bounds on the complex bulk
                 modulus",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "440",
  number =       "1908",
  pages =        "163--188",
  day =          "8",
  month =        jan,
  year =         "1993",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1993.0010",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  MRclass =      "73B27 (73F05 73K20 73V25)",
  MRnumber =     "1232831 (94h:73009)",
  MRreviewer =   "Bogdan Vernescu",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0304",
  originallab =  "GWM0213",
  originalref =  "Gibiansky L. V. and Milton G. W. 1993 On the effective
                 viscoelastic moduli of two-phase media. I. Rigorous
                 bounds on the complex bulk modulus. {\em Proc. Roy.
                 Soc. Lond. A} {\bf 440}, 163--188.",
  texsource =    "l-lec16.tex",
  texsource =    "l-lec13.tex",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/440/1908/163",
}

@InProceedings{Gibiansky:1993:VCE,
  author =       "Leonid V. Gibiansky and Roderic S. Lakes and Graeme W.
                 Milton",
  editor =       "J. Herskovits",
  booktitle =    "Structural Optimization 93 (Proceedings of The 1993
                 World Congress on Optimal Design of Structural
                 Systems)",
  title =        "Viscoelastic composites with extremal properties",
  volume =       "1",
  publisher =    "Federal university of Rio de Janeiro",
  address =      "Rio de Janeiro, Brazil",
  bookpages =    "xvi + 480",
  pages =        "369--376",
  year =         "1993",
  LCCN =         "TA658.8 S928 1993",
  bibdate =      "Sat May 30 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "The World Congress on Optimal Design of Structural
                 Systems Proceedings",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxISBN =       "none",
  xxisbn-13 =    "none",
}

@Article{Nicorovici:1993:TPT,
  author =       "N. A. Nicorovici and Ross C. McPhedran and Graeme W.
                 Milton",
  title =        "Transport properties of a three-phase composite
                 material: {The} square array of coated cylinders",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "442",
  number =       "1916",
  pages =        "599--620",
  day =          "8",
  month =        sep,
  year =         "1993",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1993.0124",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0832",
  originallab =  "GWM0202",
  originalref =  "Nicorovici N. A., McPhedran R. C., and Milton G. W.
                 1993 Transport properties of a three-phase composite
                 material: the square array of coated cylinders. {\em
                 Proc. Roy. Soc. Lond. A} {\bf 442}, 599--620.",
  texsource =    "l-lec7.tex",
  texsource =    "l-lec12.tex",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/442/1916/599",
}

@Article{Clark:1994:MEC,
  author =       "Karen E. Clark and Graeme W. Milton",
  title =        "Modeling the effective conductivity function of an
                 arbitrary two-dimensional polycrystal using sequential
                 laminates",
  journal =      j-PROC-R-SOC-EDINB-SECT-A-MATH,
  volume =       "124",
  number =       "4",
  pages =        "757--783",
  year =         "1994",
  CODEN =        "PEAMDU",
  DOI =          "https://doi.org/10.1017/S030821050002864X",
  ISSN =         "0308-2105 (print), 1473-7124 (electronic)",
  ISSN-L =       "0308-2105",
  MRclass =      "73B27 (82D25)",
  MRnumber =     "1298591 (96b:73005)",
  MRreviewer =   "Albert Fannjiang",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of Edinburgh. Section
                 A. Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PRM",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0179",
  originalref =  "Clark K. E. and Milton G. W. 1994 Modeling the
                 effective conductivity function of an arbitrary
                 two-dimensional polycrystal using sequential laminates,
                 {\em Proc. Roy. Soc. Edinburgh} {\bf 124A}, 757--783.",
  texsource =    "l-lec12.tex",
  xxtitle =      "Modelling the effective conductivity function of an
                 arbitrary two-dimensional polycrystal using sequential
                 laminates",
}

@Article{Francfort:1994:SCE,
  author =       "Gilles A. Francfort and Graeme W. Milton",
  title =        "Sets of conductivity and elasticity tensors stable
                 under lamination",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "47",
  number =       "3",
  pages =        "257--279",
  year =         "1994",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160470302",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "73B27 (73K20 78A25)",
  MRnumber =     "1266241 (95c:73004)",
  MRreviewer =   "J. Saint Jean Paulin",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470302/full",
  acknowledgement = ack-gwm,
  fjournal =     "Communications on Pure and Applied Mathematics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0567",
  originalref =  "Francfort G. A. and Milton G. W. 1994 Sets of
                 conductivity and elasticity tensors stable under
                 lamination. {\em Comm. Pure Appl. Math.} {\bf 47},
                 257--279.",
  texsource =    "l-lec22.tex",
}

@Article{Milton:1994:LBS,
  author =       "Graeme W. Milton",
  title =        "A link between sets of tensors stable under lamination
                 and quasiconvexity",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "47",
  number =       "7",
  pages =        "959--1003",
  year =         "1994",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160470704",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "73B27 (73K20)",
  MRnumber =     "1283879 (95k:73004)",
  MRreviewer =   "Pablo Pedregal",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470704/full",
  acknowledgement = ack-gwm,
  fjournal =     "Communications on Pure and Applied Mathematics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0577",
  originallab =  "GWM0427",
  originallab =  "GWM0410",
  originalref =  "Milton G. W. 1994 A link between sets of tensors
                 stable under lamination and quasiconvexity. {\em Comm.
                 Pure Appl. Math.} {\bf XLVII}, 959--1003.",
  originalref-2 = "Milton G. W. 1994 A link between sets of tensors
                 stable under lamination and quasiconvexity. {\em Comm.
                 Pure Appl. Math.} {\bf 47}, 959--1003.",
  texsource =    "l-lec22.tex",
  texsource =    "l-lec18.tex",
  xxURL =        "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470704/",
  xxvolume =     "XLVII",
}

@Article{Nicorovici:1994:ODP,
  author =       "N. A. Nicorovici and Ross C. McPhedran and Graeme W.
                 Milton",
  title =        "Optical and dielectric properties of partially
                 resonant composites",
  journal =      j-PHYS-REV-B-CMMP,
  volume =       "49",
  number =       "12",
  pages =        "8479--8482",
  day =          "15",
  month =        mar,
  year =         "1994",
  CODEN =        "PRBMDO",
  DOI =          "https://doi.org/10.1103/PhysRevB.49.8479",
  ISSN =         "1098-0121",
  ISSN-L =       "1098-0121",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Physical Review B: Condensed Matter and Materials
                 Physics",
  journal-URL =  "http://prb.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  texsource =    "l-lec7.tex",
  xxURL =        "http://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.8479",
}

@Article{Clark:1995:OBC,
  author =       "Karen E. Clark and Graeme W. Milton",
  title =        "Optimal bounds correlating electric, magnetic and
                 thermal properties of two-phase, two-dimensional
                 composites",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "448",
  number =       "1933",
  pages =        "161--190",
  day =          "8",
  month =        feb,
  year =         "1995",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1995.0011",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  MRclass =      "78A30 (73B27 73B30 78-08 78A25)",
  MRnumber =     "1324960 (96a:78004)",
  MRreviewer =   "David J. Bergman",
  bibdate =      "Wed Sep 12 10:43:26 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/448/1933/161",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0543",
  originalref =  "Clark K. E. and Milton G. W. 1995 Optimal bounds
                 correlating electric, magnetic and thermal properties
                 of two-phase, two-dimensional composites. {\em Proc.
                 Roy. Soc. Lond. A} {\bf 448}, 161--190.",
  texsource =    "l-lec20.tex",
  xxnote =       "OCLC ArticleFirst has both 1933 and 1934; 1934 is
                 wrong.",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/448/1933/161",
}

@Article{Milton:1995:CBP,
  author =       "Graeme W. Milton and A. B. Movchan",
  title =        "A correspondence between plane elasticity and the
                 two-dimensional real and complex dielectric equations
                 in anisotropic media",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "450",
  number =       "1939",
  pages =        "293--317",
  month =        aug,
  year =         "1995",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1995.0086",
  ISSN =         "0080-4630",
  ISSN-L =       "0080-4630",
  MRclass =      "73B40 (73C02 73K20 78A25)",
  MRnumber =     "1349509 (96i:73011)",
  MRreviewer =   "J. Saint Jean Paulin",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  abstract =     "A correspondence between the two-dimensional complex
                 dielectric equations and those of plane-strain
                 elasticity is established. Specifically, homogeneous
                 orthotropic dielectric media are shown to correspond to
                 orthotropic elastic media, and by making an affine
                 transformation of the elasticity problem, we obtain
                 correspondences between orthotropic dielectric media
                 and non-orthotropic elastic media. We also find a
                 correspondence between the elasticity problem and a
                 pair of dielectric problems in which the dielectric
                 tensors are real. These correspondences are extended to
                 certain classes of inhomogeneous media. Applied to
                 composite materials, they imply exact relations between
                 the effective tensors of associated dielectric and
                 elasticity problems.",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0718",
  originallab =  "GWM0669",
  originalref =  "Milton G. W. and Movchan A. B. 1995 A correspondence
                 between plane elasticity and the two-dimensional real
                 and complex dielectric equations in anisotropic media.
                 {\em Proc. Roy. Soc. Lond.} A{\bf 450}, 293--317.",
  originalref-2 = "Milton G. W. and Movchan A. B. 1995 A correspondence
                 between plane elasticity and the two-dimensional real
                 and complex dielectric equations in anisotropic media.
                 {\em Proc. R. Soc. Lond. A} {\bf 450}, 293--317.",
  texsource =    "l-lec4.tex",
  texsource =    "l-lec3.tex",
  xxCODEN =      "PRSLAZ",
  xxISSN =       "0370-1662",
  xxjournal =    j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  xxURL =        "http://rspa.royalsocietypublishing.org/content/450/1939/293",
}

@Article{Milton:1995:WET,
  author =       "Graeme W. Milton and Andrej V. Cherkaev",
  title =        "Which elasticity tensors are realizable?",
  journal =      j-J-ENG-MATER-TECHNOL,
  volume =       "117",
  number =       "4",
  pages =        "483--493",
  day =          "1",
  month =        oct,
  year =         "1995",
  CODEN =        "JEMTA8",
  DOI =          "https://doi.org/10.1115/1.2804743",
  ISSN =         "0094-4289 (print), 1528-8889 (electronic)",
  ISSN-L =       "0094-4289",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of engineering materials and technology",
  journal-URL =  "http://materialstechnology.asmedigitalcollection.asme.org/issues.aspx",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0578",
  originalref =  "Milton G. W. and Cherkaev A. V. 1995 Which elasticity
                 tensors are realizable? {\em ASME J. Eng. Mat. Tech.}
                 {\bf 117}, 483--493.",
  texsource =    "l-lec22.tex",
  texsource =    "l-lec01b.tex",
  xxURL =        "http://materialstechnology.asmedigitalcollection.asme.org/article.aspx?articleID=1425346",
}

@Article{Avellaneda:1996:CCP,
  author =       "M. Avellaneda and Andrej V. Cherkaev and Leonid V.
                 Gibiansky and Graeme W. Milton and M. Rudelson",
  title =        "A complete characterization of the possible bulk and
                 shear moduli of planar polycrystals",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "44",
  number =       "7",
  pages =        "1179--1218",
  month =        jul,
  year =         "1996",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/0022-5096(96)00018-X",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002250969600018X",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the mechanics and physics of solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0843",
  originallab =  "GWM0420",
  originallab =  "GWM0390",
  originalref =  "Avellaneda M., Cherkaev A. V., Gibiansky L. V., Milton
                 G. W., and Rudelson M. 1996 A complete characterization
                 of the possible bulk and shear moduli of planar
                 polycrystals. {\em J. Mech. Phys. Solids} {\bf 44},
                 1179--1218.",
  texsource =    "l-lec8.tex",
  texsource =    "l-lec18.tex",
  xxURL =        "http://www.sciencedirect.com/science/article/pii/002250969600018X",
}

@Article{Berryman:1997:VBE,
  author =       "J. G. Berryman and Graeme W. Milton",
  title =        "Variational Bounds and Effective Medium Theories for
                 Viscoelastic Composites",
  journal =      "APS March Meeting Abstracts",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "1997",
  CODEN =        "",
  ISSN =         "",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://adsabs.harvard.edu/abs/1997APS..MAR.B1510B",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://adsabs.harvard.edu",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Helsing:1997:DRC,
  author =       "Johan Helsing and Graeme W. Milton and A. B. Movchan",
  title =        "Duality relations, correspondences and numerical
                 results for planar elastic composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "45",
  number =       "4",
  pages =        "565--590",
  year =         "1997",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/S0022-5096(96)00083-X",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "73K20 (73B27 73C02 73V20)",
  MRnumber =     "1449232 (98e:73092)",
  MRreviewer =   "Leonid V. Gibiansky",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002250969600083X",
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://www.sciencedirect.com/science/article/pii/S002250969600083X",
}

@InProceedings{Milton:1997:CMM,
  author =       "Graeme W. Milton",
  editor =       "T. Tatsumi and E. Watanabe and T. Kambe",
  booktitle =    "Theoretical and Applied Mechanics 1996: Proceedings of
                 the XIXth International Congress of Theoretical and
                 Applied Mechanics, Kyoto, Japan, 25--31 August 1996",
  title =        "Composites: {A} myriad of microstructure independent
                 relations",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  bookpages =    "xxxix + 623",
  pages =        "443--459",
  year =         "1997",
  ISBN =         "0-444-82446-4",
  ISBN-13 =      "978-0-444-82446-2",
  LCCN =         "QA801 .I39 1996",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0641",
  originallab =  "GWM0055",
  originalref =  "Milton G. W. 1997 Composites: A myriad of
                 microstructure independent relations. In {\em
                 Theoretical and Applied Mechanics 1996}, pp. 443--459,
                 ed. by T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier.",
  originalref-2 = "Milton G. W. 1997 Composites: A myriad of
                 microstructure independent relations. {\em Theoretical
                 and Applied Mechanics 1996}, pp. 443--459, ed. by
                 T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier.",
  rest =         "ed. by T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier",
  texsource =    "l-lec3.tex",
  texsource =    "l-lec1.tex",
}

@Article{Milton:1997:ERC,
  author =       "Graeme W. Milton",
  title =        "Exact Relations for Composites: Towards a Complete
                 Solution",
  journal =      j-DOC-MATH,
  volume =       "Extra volume ICM 1998 III",
  pages =        "623--632",
  year =         "1997",
  ISSN =         "1431-0643",
  ISSN-L =       "1431-0635",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.mathunion.org/ICM/ICM1998.3/Main/16/Milton.MAN.ocr.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Documenta mathematica",
  journal-URL =  "http://www.math.uiuc.edu/documenta/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:1997:EVM,
  author =       "Graeme W. Milton and James G. Berryman",
  title =        "On the effective viscoelastic moduli of two-phase
                 media. {II}. {Rigorous} bounds on the complex shear
                 modulus in three dimensions",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "453",
  number =       "1964",
  pages =        "1849--1880",
  day =          "8",
  month =        sep,
  year =         "1997",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1997.0100",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "73B27 (73F05 73K20)",
  MRnumber =     "1478137 (99h:73004)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/453/1964/1849",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society. London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0330",
  originalref =  "Milton G. W. and Berryman J. G. 1997 On the effective
                 viscoelastic moduli of two-phase media. II. Rigorous
                 bounds on the complex shear modulus in three
                 dimensions. {\em Proc. Roy. Soc. Lond. A} {\bf 453},
                 1849--1880.",
  texsource =    "l-lec16.tex",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/453/1964/1849",
}

@Article{Milton:1997:FFR,
  author =       "Graeme W. Milton and David J. Eyre and Joseph V.
                 Mantese",
  title =        "Finite frequency range {Kramers--Kronig} relations:
                 {Bounds} on the dispersion",
  journal =      j-PHYS-REV-LET,
  volume =       "79",
  number =       "16",
  pages =        "3062--3065",
  day =          "20",
  month =        oct,
  year =         "1997",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.79.3062",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0477",
  originalref =  "Milton G. W., Eyre D. J., and Mantese J. V. 1997
                 Finite frequency range Kramers--Kronig relations:
                 Bounds on the dispersion. {\em Phys. Rev. Lett.} {\bf
                 79}, 3062--3065.",
  texsource =    "l-lec19.tex",
  xxURL =        "http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.79.3062",
}

@InProceedings{Berryman:1998:TIP,
  author =       "James G. Berryman",
  editor =       "Kenneth M. Golden and G. R. Grimmett and R. D. James
                 and Graeme W. Milton and P. N. Sen",
  booktitle =    "Mathematics of Multiscale Materials",
  title =        "Transversely isotropic poroelasticity arising from
                 thin isotropic layers",
  volume =       "99",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 280",
  pages =        "37--50",
  year =         "1998",
  DOI =          "https://doi.org/10.1007/978-1-4612-1728-2_3",
  ISBN =         "0-387-98528-X",
  ISBN-13 =      "978-0-387-98528-2",
  LCCN =         "TA405 .M395 1998",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "IMA Volumes in Mathematics and its Applications",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4612-1728-2_3",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0726",
  originalref =  "Berryman J. G. 1998 Transversely isotropic
                 poroelasticity arising from thin isotropic layers. In
                 {\em Mathematics of multiscale materials}, ed. by K. M.
                 Golden, G. R. Grimmett, R. D. James, G. W. Milton, and
                 P. N. Sen, IMA Volumes in mathematics and its
                 applications, {\bf 99}, pp.37--50, Springer-Verlag,
                 Berlin.",
  rest =         "Springer-Verlag, Berlin",
  texsource =    "l-lec5.tex",
}

@Article{Grabovsky:1998:ERC,
  author =       "Yury Grabovsky and Graeme W. Milton",
  booktitle =    "Proceedings of the {International} {Congress} of
                 {Mathematicians}, {Vol}. {III} ({Berlin}, 1998)",
  title =        "Exact relations for composites: towards a complete
                 solution",
  journal =      j-DOC-MATH,
  volume =       "Extra Volume ICM III",
  number =       "Extra Vol. III",
  pages =        "623--632",
  year =         "1998",
  ISSN =         "1431-0635",
  ISSN-L =       "1431-0635",
  MRclass =      "73B27 (35B27 49J45)",
  MRnumber =     "1648193 (99j:73008)",
  MRreviewer =   "David J. Bergman",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.math.uiuc.edu/documenta/xvol-icm/16/Milton.MAN.ps.gz",
  acknowledgement = ack-gwm,
  fjournal =     "Documenta Mathematica",
  journal-URL =  "http://www.math.uiuc.edu/documenta/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0848",
  originalref =  "Grabovsky Y., and Milton G. W. 1998b Exact relations
                 for composites: towards a complete solution. {\em Doc.
                 Math. J. DMV, Extra volume ICM III} 623--632.",
  texsource =    "l-lec8.tex",
  xxnote =       "ZB has: 896.35013 Grabovsky, Yury; Milton, Graeme W.
                 Exact relations for composites: Towards a complete
                 solution. (English) Doc. Math., J. DMV Extra Vol. ICM
                 III, 623-632 (1998). MSC 1991: *35B27 73B27 73S10.",
}

@Article{Grabovsky:1998:ROP,
  author =       "Yury Grabovsky and Graeme W. Milton",
  title =        "Rank one plus a null-{Lagrangian} is an inherited
                 property of two-dimensional compliance tensors under
                 homogenisation",
  journal =      j-PROC-R-SOC-EDINB-SECT-A-MATH,
  volume =       "128",
  number =       "2",
  pages =        "283--299",
  year =         "1998",
  CODEN =        "PEAMDU",
  DOI =          "https://doi.org/10.1017/S0308210500012798",
  ISSN =         "0308-2105 (print), 1473-7124 (electronic)",
  ISSN-L =       "0308-2105",
  MRclass =      "73B27 (73C02 73K20)",
  MRnumber =     "1621339 (99b:73005)",
  MRreviewer =   "Leonid V. Gibiansky",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=8240207",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society of Edinburgh. Section
                 A. Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PRM",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0847",
  originalref =  "Grabovsky Y., and Milton G. W. 1998a Rank one plus a
                 null-Lagrangian is an inherited property of
                 two-dimensional compliance tensors under
                 homogenization. {\em Proc. Roy. Soc. Edin.} {\bf 128A},
                 283--299.",
  texsource =    "l-lec8.tex",
}

@Article{Milton:1998:MCP,
  author =       "Graeme W. Milton and A. B. Movchan",
  title =        "Mapping certain planar elasticity problems to
                 antiplane ones",
  journal =      j-EUR-J-MECH-A-SOLIDS,
  volume =       "17",
  number =       "1",
  pages =        "1--11",
  year =         "1998",
  CODEN =        "EJASEV",
  DOI =          "https://doi.org/10.1016/S0997-7538(98)80060-0",
  ISSN =         "0997-7538 (print), 1873-7285 (electronic)",
  ISSN-L =       "0997-7538",
  MRclass =      "73C02 (73B27 73B40)",
  MRnumber =     "1615969 (99a:73035)",
  MRreviewer =   "Leonid V. Gibiansky",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0997753898800600",
  acknowledgement = ack-gwm,
  fjournal =     "European Journal of Mechanics. A. Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09977538",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0670",
  originalref =  "Milton G. W. and Movchan A. B. 1998 Mapping certain
                 planar elasticity problems to antiplane ones. {\em Eur.
                 J. Mech., A/Solids} {\bf 17}, 1--11.",
  texsource =    "l-lec3.tex",
  xxURL =        "http://www.sciencedirect.com/science/article/pii/S0997753898800600",
}

@InProceedings{Nesi:1998:FPS,
  author =       "V. Nesi",
  editor =       "Kenneth M. Golden and G. R. Grimmett and R. D. James
                 and Graeme W. Milton and P. N. Sen",
  booktitle =    "Mathematics of Multiscale Materials",
  title =        "Fine properties of solutions to conductivity equations
                 with applications to composites",
  volume =       "99",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 280",
  pages =        "179--208",
  year =         "1998",
  ISBN =         "0-387-98528-X",
  ISBN-13 =      "978-0-387-98528-2",
  LCCN =         "TA405 .M395 1998",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "IMA Volumes in Mathematics and its Applications",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0720",
  originalref =  "Nesi V. 1998 Fine properties of solutions to
                 conductivity equations with applications to composites.
                 In {\em Mathematics of multiscale materials}, ed. by K.
                 M. Golden, G. R. Grimmett, R. D. James, G. W. Milton,
                 and P. N. Sen, IMA Volumes in mathematics and its
                 applications, {\bf 99}, pp.179--208, Springer-Verlag,
                 Berlin.",
  rest =         "Springer-Verlag, Berlin",
  texsource =    "l-lec4.tex",
}

@Article{Eyre:1999:FNS,
  author =       "David J. Eyre and Graeme W. Milton",
  title =        "A fast numerical scheme for computing the response of
                 composites using grid refinement",
  journal =      j-EPJ-APPL-PHYS,
  volume =       "6",
  number =       "1",
  pages =        "41--47",
  month =        apr,
  year =         "1999",
  CODEN =        "EPAPFV",
  DOI =          "https://doi.org/10.1051/epjap:1999150",
  ISSN =         "1286-0042 (print), 1286-0050 (electronic)",
  ISSN-L =       "1286-0042",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.epjap.org/articles/epjap/abs/1999/04/ap8234/ap8234.html",
  acknowledgement = ack-gwm,
  fjournal =     "European Physical Journal. Applied Physics",
  journal-URL =  "http://www.epjap.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0071",
  originalref =  "Eyre D. J. and Milton G. W. 1999 A fast numerical
                 scheme for computing the response of composites using
                 grid refinement. {\em Eur. Phys. J. Applied Physics}
                 {\bf 6}, 41--47.",
  texsource =    "l-lec10.tex",
}

@Article{Gibiansky:1999:EVM,
  author =       "Leonid V. Gibiansky and Graeme W. Milton and James G.
                 Berryman",
  title =        "On the effective viscoelastic moduli of two-phase
                 media: {III}. {Rigorous} bounds on the complex shear
                 modulus in two dimensions",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "455",
  number =       "1986",
  pages =        "2117--2149",
  day =          "8",
  month =        jun,
  year =         "1999",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.1999.0395",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74Q20 (74D99 74E30)",
  MRnumber =     "1702750 (2000e:74095)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "The Royal Society of London. Proceedings. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0305",
  originalref =  "Gibiansky L. V., Milton G. W., and Berryman J. G. 1999
                 On the effective viscoelastic moduli of two-phase
                 media: III. Rigorous bounds on the complex shear
                 modulus in two dimensions. {\em Proc. Roy. Soc. Lond.
                 A} {\bf 455}, 2117--2149.",
  texsource =    "l-lec16.tex",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/455/1986/2117",
}

@Article{Milton:1999:OCB,
  author =       "Graeme W. Milton and V. Nesi",
  title =        "Optimal {$G$}-closure bounds via stability under
                 lamination",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "150",
  number =       "3",
  pages =        "191--207",
  month =        dec,
  year =         "1999",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s002050050186",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "74Q05 (49J45 74Q15)",
  MRnumber =     "1738117 (2001k:74085)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s002050050186",
  acknowledgement = ack-gwm,
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0784",
  originallab =  "GWM0579",
  originallab =  "GWM0332",
  originalref =  "Milton G. W. and Nesi V. 1999 Optimal $G$-closure
                 bounds via stability under lamination. {\em Arch. Rat.
                 Mech. Anal.} ****to appear",
  rest =         "****to appear",
  texsource =    "l-lec6.tex",
  texsource =    "l-lec22.tex",
  texsource =    "l-lec16.tex",
}

@InProceedings{Suquet:1999:NSE,
  author =       "Pierre M. Suquet and H. Moulinec",
  editor =       "Kenneth M. Golden and G. R. Grimmett and R. D. James
                 and Graeme W. Milton and P. N. Sen",
  booktitle =    "Mathematics of Multiscale Materials",
  title =        "Numerical simulation of the effective elastic
                 properties of a class of cell materials",
  volume =       "99",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 280",
  pages =        "271--280",
  year =         "1999",
  ISBN =         "0-387-98528-X",
  ISBN-13 =      "978-0-387-98528-2",
  LCCN =         "TA405.M395 1998",
  bibdate =      "Fri Mar 31 13:45:09 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "The IMA Volumes in Mathematics and its Applications",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  texsource =    "l-lec2.tex",
}

@Article{Grabovsky:2000:ERE,
  author =       "Yury Grabovsky and Graeme W. Milton and Daniel S.
                 Sage",
  title =        "Exact relations for effective tensors of composites:
                 {Necessary} conditions and sufficient conditions",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "53",
  number =       "3",
  pages =        "300--353",
  month =        mar,
  year =         "2000",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/d8k4vw",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "74Q05 (74A40 74F15 78A48 78M40)",
  MRnumber =     "1725610 (2001m:74060)",
  MRreviewer =   "Konstantin A. Lurie",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://math.cst.temple.edu/~yury/exact.pdf",
  acknowledgement = ack-gwm,
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0849",
  originalref =  "Grabovsky Y., Milton G. W., and Sage D. S. 1999(?***)
                 Exact relations for effective tensors of composites:
                 Necessary conditions and sufficient conditions. {\em
                 Comm. Pure Appl. Math.} submitted.",
  remark =       "Short punctuation-free permanent DOI supplied by
                 http://shortdoi.org on Sun Nov 22 11:04:45 2015.",
  texsource =    "l-lec8.tex",
  xxDOI =        "https://doi.org/10.1002/(SICI)1097-0312(200003)53:3<300::AID-CPA2>3.0.CO%3B2-D",
}

@Article{Milton:2000:BCN,
  author =       "Graeme W. Milton and Sergey K. Serkov",
  title =        "Bounding the current in nonlinear conducting
                 composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "48",
  number =       "6--7",
  pages =        "1295--1324",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/S0022-5096(99)00083-6",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74Q20 (74E30 78A48)",
  MRnumber =     "1766404 (2001c:74074)",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "The J. R. Willis 60th anniversary volume",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509699000836",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0428",
  originalref =  "Milton G. W. and Serkov S. K. 2000 Bounding the
                 current in nonlinear conducting composites. {\rm J.
                 Mech. Phys. Solids} to appear.",
  texsource =    "l-lec18.tex",
}

@Article{Solna:2000:BGV,
  author =       "Knut S{\o}lna and Graeme W. Milton",
  title =        "Bounds for the group velocity of electromagnetic
                 signals in two phase materials",
  journal =      j-PHYSICA-B,
  volume =       "279",
  number =       "1--3",
  pages =        "9--12",
  month =        apr,
  year =         "2000",
  CODEN =        "PHYBE3",
  DOI =          "https://doi.org/10.1016/S0921-4526(99)00654-7",
  ISSN =         "0921-4526 (print), 1873-2135 (electronic)",
  ISSN-L =       "0921-4526",
  bibdate =      "Fri Nov 5 13:45:09 MST 1999",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0921452699006547",
  acknowledgement = ack-gwm,
  fjournal =     "Physica. B, Condensed matter",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09214526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  originallab =  "GWM0837",
  originalref =  "Solna K. and Milton G. W. 1999 Bounds for the group
                 velocity of electromagnetic signals in two phase
                 materials. {\em Physica B}, ***to appear",
  rest =         "***to appear",
  texsource =    "l-lec7.tex",
}

@Article{Milton:2001:NCI,
  author =       "Graeme W. Milton and Sergey K. Serkov",
  title =        "Neutral coated inclusions in conductivity and
                 anti-plane elasticity",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "457",
  number =       "2012",
  pages =        "1973--1997",
  day =          "8",
  month =        jul,
  year =         "2001",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2001.0796",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74F15 (74E05 74Q05 78A48)",
  MRnumber =     "1852434 (2002f:74021)",
  bibdate =      "Fri Oct 20 13:45:09 MST 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/457/2012/1973",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, and Engineering Sciences",
  fjournal =     "The Royal Society of London. Proceedings. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  texsource =    "l-lec04.tex",
  xxURL =        "http://rspa.royalsocietypublishing.org/content/457/2012/1973",
}

@Article{Milton:2001:PCC,
  author =       "Graeme W. Milton",
  title =        "Proof of a conjecture on the conductivity of
                 checkerboards",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "10",
  pages =        "4873--4882",
  month =        oct,
  year =         "2001",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1385564",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "82B20 (78A48)",
  MRnumber =     "1855103 (2003a:82013)",
  MRreviewer =   "E. J. Janse van Rensburg",
  bibdate =      "Thu Mar 28 19:47:19 MST 2002",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/jmp/42/10/10.1063/1.1385564",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Eyre:2002:BIC,
  author =       "David J. Eyre and Graeme W. Milton and Roderic S.
                 Lakes",
  title =        "Bounds for interpolating complex effective moduli of
                 viscoelastic materials from measured data",
  journal =      j-RHEOL-ACTA,
  volume =       "41",
  number =       "5",
  pages =        "461--470",
  year =         "2002",
  CODEN =        "RHEAAK",
  DOI =          "https://doi.org/10.1007/s003970100172",
  ISSN =         "0035-4511 (print), 1435-1528 (electronic)",
  ISSN-L =       "0035-4511",
  bibdate =      "Mon Apr 30 13:45:09 MST 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s003970100172",
  acknowledgement = ack-gwm,
  fjournal =     "Rheologica acta",
  journal-URL =  "http://link.springer.com/journal/397",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  texsource =    "l-lec6.tex",
  texsource =    "l-lec22.tex",
}

@InCollection{Lukkassen:2002:HSR,
  author =       "Dag Lukkassen and Graeme W. Milton",
  booktitle =    "Function spaces, interpolation theory and related
                 topics ({Lund}, 2000)",
  title =        "On hierarchical structures and reiterated
                 homogenization",
  publisher =    "de Gruyter",
  address =      "Berlin, Germany",
  pages =        "355--368",
  year =         "2002",
  MRclass =      "35B27 (49J45 74Q05)",
  MRnumber =     "1943293 (2003k:35019)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2002:CMM,
  author =       "Graeme W. Milton and Knut S{\o}lna",
  title =        "Can Mixing Materials Make Electromagnetic Signals
                 Travel Faster?",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "62",
  number =       "6",
  pages =        "2064--2091 (electronic)",
  year =         "2002",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/S0036139901385084",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "78A48 (35B27 35Q60 78M40)",
  MRnumber =     "1918307 (2003i:78007)",
  MRreviewer =   "Philip Huddleston",
  bibdate =      "Fri Jul 02 09:53:22 2004",
  bibsource =    "http://epubs.siam.org/toc/smjmap/62/6;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/38508",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  texsource =    "l-lec7.tex",
  xxauthor =     "Knut S{\o}lna and Graeme W. Milton",
  xxnote =       "Check author order in PDF of original paper??",
  xxURL =        "http://epubs.siam.org/doi/abs/10.1137/S0036139901385084",
}

@Article{Benveniste:2003:NER,
  author =       "Y. Benveniste and Graeme W. Milton",
  title =        "New exact results for the effective electric, elastic,
                 piezoelectric and other properties of composite
                 ellipsoid assemblages",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "51",
  number =       "10",
  pages =        "1773--1813",
  month =        oct,
  year =         "2003",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/S0022-5096(03)00074-7",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74Q15 (74A60 74E30 78A48 78A55)",
  MRnumber =     "1993514 (2004f:74080)",
  bibdate =      "Fri Apr 15 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509603000747",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2003:EBS,
  author =       "Graeme W. Milton",
  title =        "Exact band structure for the scalar wave equation with
                 periodic complex moduli",
  journal =      j-PHYSICA-B,
  volume =       "338",
  number =       "1--4",
  pages =        "186--189",
  month =        oct,
  year =         "2003",
  CODEN =        "PHYBE3",
  DOI =          "https://doi.org/10.1016/S0921-4526(03)00484-8",
  ISSN =         "0921-4526 (print), 1873-2135 (electronic)",
  ISSN-L =       "0921-4526",
  bibdate =      "Mon Mar 31 13:45:09 MST 2003",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0921452603004848",
  fjournal =     "Physica. B, Condensed matter",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09214526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Proceedings of the Sixth International Conference on
                 Electrical Transport and Optical Properties of
                 Inhomogeneous Media Snowbird, UT, USA 15--19 July
                 2002.",
  texsource =    "l-lec7.tex",
}

@Article{Milton:2003:RAS,
  author =       "Graeme W. Milton and S. K. Serkov and A. B. Movchan",
  title =        "Realizable (Average Stress, Average Strain) Pairs in a
                 Plate with Holes",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "63",
  number =       "3",
  pages =        "987--1028",
  year =         "2003",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/S0036139901395717",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "74Q20 (74K20 74P10)",
  MRnumber =     "1969685 (2005a:74084)",
  MRreviewer =   "Yury Grabovsky",
  bibdate =      "Fri Aug 15 05:31:40 MDT 2003",
  bibsource =    "http://epubs.siam.org/toc/smjmap/63/3;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/39571",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Movchan:2003:RAS,
  author =       "A. B. Movchan and Graeme W. Milton and S. K. Serkov",
  title =        "Realizable (Average Stress, Average Strain) Pairs in a
                 Plate with Holes",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "63",
  number =       "3",
  pages =        "987--1028",
  year =         "2003",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/S0036139901395717",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Aug 15 05:31:40 MDT 2003",
  bibsource =    "http://epubs.siam.org/toc/smjmap/63/3;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/39571",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2004:CSC,
  author =       "Marc Briane and Graeme W. Milton and Vincenzo Nesi",
  title =        "Change of sign of the corrector's determinant for
                 homogenization in three-dimensional conductivity",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "173",
  number =       "1",
  pages =        "133--150",
  year =         "2004",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s00205-004-0315-8",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "49J45 (74Q05)",
  MRnumber =     "2073507 (2005i:49015)",
  MRreviewer =   "Alexander A. Pankov",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s00205-004-0315-8",
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2004:EPB,
  author =       "Graeme W. Milton",
  title =        "The exact photonic band structure for a class of media
                 with periodic complex moduli",
  journal =      j-METHODS-APPL-ANAL,
  volume =       "11",
  number =       "3",
  pages =        "413--421",
  year =         "2004",
  ISSN =         "1073-2772 (print), 1945-0001 (electronic)",
  ISSN-L =       "1073-2772",
  MRclass =      "78A48 (35P05 35Q60)",
  MRnumber =     "2214684 (2006m:78013)",
  MRreviewer =   "Alexandre Fedorov",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://projecteuclid.org/euclid.maa/1147353063",
  ajournal =     "Methods Appl. Anal.",
  fjournal =     "Methods and Applications of Analysis",
  journal-URL =  "http://www.intlpress.com/MAA/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InProceedings{Milton:2004:ERP,
  author =       "Graeme W. Milton",
  editor =       "J. S. Yang",
  booktitle =    "{The 41st annual technical meeting of the Society of
                 Engineering Science (SES-2004) held at the Cornhusker
                 Hotel in downtown Lincoln, Nebraska during October
                 10--13, 2004}",
  title =        "Exact Results for the Piezoelectric Properties of
                 Composite Ellipsoid Assemblages (keynote lecture)",
  publisher =    pub-IOS,
  address =      pub-IOS:adr,
  pages =        "??--??",
  month =        "????",
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "1383-5416 (print), 1875-8800 (electronic)",
  ISSN-L =       "1383-5416",
  LCCN =         "????",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "International journal of applied electromagnetics and
                 mechanics",
  URL =          "https://ses.confex.com/ses/2004tm/techprogram/P1230.HTM",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ses.confex.com/ses/2004tm/",
  journal-URL =  "http://ses.confex.com",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  series-URL =   "http://www.iospress.nl/journal/international-journal-of-applied-electromagnetics-and-mechanics/",
}

@InProceedings{Vinogradov:2004:BCC,
  author =       "Vladimir Vinogradov and Graeme W. Milton",
  editor =       "J. S. Yang",
  booktitle =    "{The 41st annual technical meeting of the Society of
                 Engineering Science (SES-2004) held at the Cornhusker
                 Hotel in downtown Lincoln, Nebraska during October
                 10--13, 2004}",
  title =        "Bounds on the creep of composites under hydrostatic
                 loading",
  publisher =    pub-IOS,
  address =      pub-IOS:adr,
  bookpages =    "????",
  pages =        "??--??",
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "1383-5416 (print), 1875-8800 (electronic)",
  ISSN-L =       "1383-5416",
  LCCN =         "????",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "International journal of applied electromagnetics and
                 mechanics",
  URL =          "https://ses.confex.com/ses/2004tm/techprogram/P1085.HTM",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ses.confex.com/ses/2004tm/",
  book-URL =     "https://ses.confex.com/ses/2004tm/techprogram/MEETING.HTM",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  series-URL =   "http://www.iospress.nl/journal/international-journal-of-applied-electromagnetics-and-mechanics/",
}

@Article{Camar-Eddine:2005:NLI,
  author =       "M. Camar-Eddine and Graeme W. Milton",
  title =        "Non-local interactions in the homogenization closure
                 of thermoelectric functionals",
  journal =      j-ASYMPTOT-ANAL,
  volume =       "41",
  number =       "3--4",
  pages =        "259--276",
  year =         "2005",
  CODEN =        "ASANEZ",
  ISSN =         "0921-7134 (print), 1875-8576 (electronic)",
  ISSN-L =       "0921-7134",
  MRclass =      "35Q60 (35A15 78A99)",
  MRnumber =     "2127998 (2005k:35393)",
  MRreviewer =   "Norbert Weck",
  bibdate =      "Tue Nov 14 2006",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://content.iospress.com/articles/asymptotic-analysis/asy667",
  acknowledgement = ack-gwm,
  fjournal =     "Asymptotic Analysis",
  journal-URL =  "http://content.iospress.com/journals/asymptotic-analysis",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2005:OPH,
  author =       "Graeme W. Milton",
  title =        "On Optimizing the Properties of Hierarchical Laminates
                 Using {Pontryagin}'s Maximum Principle",
  journal =      j-MULTISCALE-MODELING-SIMUL,
  volume =       "3",
  number =       "3",
  pages =        "658--679 (electronic)",
  year =         "2005",
  CODEN =        "MMSUBT",
  DOI =          "https://doi.org/10.1137/030602368",
  ISSN =         "1540-3459 (print), 1540-3467 (electronic)",
  ISSN-L =       "1540-3459",
  MRclass =      "74P10 (49K20 49N90 65K10 74N15 74Q20)",
  MRnumber =     "2136808 (2006d:74067)",
  MRreviewer =   "Yury Grabovsky",
  bibdate =      "Sat Apr 16 10:58:26 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/MMS/3/3;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siammms.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/60236",
  acknowledgement = ack-nhfb,
  fjournal =     "Multiscale Modeling and Simulation",
  journal-URL =  "http://epubs.siam.org/mms",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2005:PSQ,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici
                 and Ross C. McPhedran and Viktor A. Podolskiy",
  title =        "A proof of superlensing in the quasistatic regime, and
                 limitations of superlenses in this regime due to
                 anomalous localized resonance",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "461",
  number =       "2064",
  pages =        "3999--4034",
  day =          "8",
  month =        dec,
  year =         "2005",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2005.1570",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "78A10",
  MRnumber =     "2186014 (2006h:78001)",
  bibdate =      "Mon Dec 12 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/461/2064/3999",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Podolskiy:2005:OSMa,
  author =       "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme
                 W. Milton",
  title =        "Optimizing the {Superlens}: manipulating geometry to
                 enhance the resolution",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        sep,
  year =         "2005",
  CODEN =        "APRHCB",
  DOI =          "https://doi.org/10.1063/1.2139620",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Applied Physics Letters, v.87, p.231113
                 (2005)",
  URL =          "https://arxiv.org/abs/physics/0509067",
  abstract =     "We analyze the performance of a planar lens based on
                 realistic negative index material in a generalized
                 geometry. We demonstrate that the conventional
                 superlens design (where the lens is centered between
                 the object and the image) is not optimal from the
                 resolution point-of-view, develop an analytical
                 expression for the resolution limit of a generalized
                 lens, use it to find the optimum lens configuration,
                 and calculate the maximum absorption practical
                 nearfield superlenses may have. We demonstrate that in
                 contrast to the conventional superlens picture, planar
                 imaging is typically accompanied by excitation of
                 surface waves at both interfaces of the lens.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Optics (physics.optics); General Physics
                 (physics.gen-ph)",
}

@Article{Podolskiy:2005:OSMb,
  author =       "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme
                 W. Milton",
  title =        "Optimizing the superlens: manipulating geometry to
                 enhance the resolution",
  journal =      j-APPL-PHYS-LET,
  volume =       "87",
  number =       "23",
  pages =        "231113",
  day =          "5",
  month =        dec,
  year =         "2005",
  CODEN =        "APPLAB",
  DOI =          "https://doi.org/10.1063/1.2139620",
  ISSN =         "0003-6951 (print), 1077-3118 (electronic), 1520-8842",
  ISSN-L =       "0003-6951",
  bibdate =      "Mon Dec 12 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/apl/87/23/10.1063/1.2139620",
  acknowledgement = ack-gwm,
  fjournal =     "Applied Physics Letters",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/apl",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Vinogradov:2005:TCV,
  author =       "V. Vinogradov and Graeme W. Milton",
  title =        "The total creep of viscoelastic composites under
                 hydrostatic or antiplane loading",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "53",
  number =       "6",
  pages =        "1248--1279",
  month =        jun,
  year =         "2005",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2005.01.005",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74Q20 (74D99 74E30)",
  MRnumber =     "2137063 (2006a:74071)",
  MRreviewer =   "Sergio Guti{\'e}rrez",
  bibdate =      "Sun Jul 5 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509605000244",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Kang:2006:CPS,
  author =       "Hyeonbae Kang and Graeme W. Milton",
  booktitle =    "Inverse problems, multi-scale analysis and effective
                 medium theory",
  title =        "On conjectures of {P{\'o}lya--Szeg{\H{o}}} and
                 {Eshelby}",
  volume =       "408",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "75--80",
  year =         "2006",
  DOI =          "https://doi.org/10.1090/conm/408/07687",
  MRclass =      "35R30 (35J25)",
  MRnumber =     "2262351 (2007i:35244)",
  MRreviewer =   "Enno Pais",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Contemp. Math.",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Kang:2006:SCP,
  author =       "Hyeonbae Kang and Graeme W. Milton",
  title =        "Solutions to the conjectures of
                 {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "13",
  month =        sep,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/math/0609374",
  abstract =     "Eshelby showed that if an inclusion is of elliptic or
                 ellipsoidal shape then for any uniform elastic loading
                 the field inside the inclusion is uniform. He then
                 conjectured that the converse is true, i.e., that if
                 the field inside an inclusion is uniform for all
                 uniform loadings, then the inclusion is of elliptic or
                 ellipsoidal shape. We call this the weak Eshelby
                 conjecture. In this paper we prove this conjecture in
                 three dimensions. In two dimensions, a stronger
                 conjecture, which we call the strong Eshelby
                 conjecture, has been proved: If the field inside an
                 inclusion is uniform for a single uniform loading, then
                 the inclusion is of elliptic shape. We give an
                 alternative proof of Eshelby's conjecture in two
                 dimensions using a hodographic transformation. As a
                 consequence of the weak Eshelby's conjecture, we prove
                 in two and three dimensions a conjecture of P{\'o}lya
                 and Szeg{\H{o}} on the isoperimetric inequalities for
                 the polarization tensors. The P{\'o}lya--Szeg{\H{o}}
                 conjecture asserts that the inclusion whose electrical
                 polarization tensor has the minimal trace takes the
                 shape of a disk or a ball.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "22",
  subject =      "Analysis of PDEs (math.AP); Optimization and Control
                 (math.OC)",
}

@Article{Milton:2006:CEA,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici",
  title =        "On the cloaking effects associated with anomalous
                 localized resonance",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "462",
  number =       "2074",
  pages =        "3027--3059",
  month =        oct,
  year =         "2006",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2006.1715",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "78A55",
  MRnumber =     "2263683 (2008e:78018)",
  bibdate =      "Mon Jul 3 2006",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/462/2074/3027",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2006:CEP,
  author =       "Graeme W. Milton and Marc Briane and John R. Willis",
  title =        "On cloaking for elasticity and physical equations with
                 a transformation invariant form",
  journal =      j-NEW-J-PHYS,
  volume =       "8",
  number =       "10",
  pages =        "248",
  month =        oct,
  year =         "2006",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/8/10/248",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Mon Nov 27 2006",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://iopscience.iop.org/1367-2630/8/10/248;
                 http://iopscience.iop.org/article/10.1088/1367-2630/8/10/248/",
  abstract =     "In this paper, we investigate how the form of the
                 conventional elastodynamic equations changes under
                 curvilinear transformations. The equations get mapped
                 to a more general form in which the density is
                 anisotropic and additional terms appear which couple
                 the stress not only with the strain but also with the
                 velocity, and the momentum gets coupled not only with
                 the velocity but also with the strain. These are a
                 special case of equations which describe the
                 elastodynamic response of composite materials, and
                 which it has been argued should apply to any material
                 which has microstructure below the scale of continuum
                 modelling. If composites could be designed with the
                 required moduli then it could be possible to design
                 elastic cloaking devices where an object is cloaked
                 from elastic waves of a given frequency. To an outside
                 observer it would appear as though the waves were
                 propagating in a homogeneous medium, with the object
                 and surrounding cloaking shell invisible. Other new
                 elastodynamic equations also retain their form under
                 curvilinear transformations. The question is raised as
                 to whether all equations of microstructured continua
                 have a form which is invariant under curvilinear space
                 or space-time coordinate transformations. We show that
                 the non-local bianisotropic electrodynamic equations
                 have this invariance under space-time transformations
                 and that the standard non-local, time-harmonic,
                 electromagnetic equations are invariant under space
                 transformations.",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://stacks.iop.org/1367-2630/8/i=10/a=248",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/8/10/248/",
}

@InProceedings{Milton:2006:CSF,
  author =       "Graeme W. Milton and N. A. P. Nicorovici",
  editor =       "Anonymous",
  booktitle =    "{Photonic metamaterials: from random to periodic,
                 technical digest: June 5--8, 2006, Westin Grand Bahama
                 Island Our Lucaya Resort, Grand Island, the Bahamas}",
  title =        "Cloaking: Science Fiction or Reality?",
  publisher =    "OSA Publishing",
  address =      "Washington, DC, USA",
  pages =        "??--??",
  year =         "2006",
  DOI =          "https://doi.org/10.1364/META.2006.TuA3",
  ISBN =         "1-55752-808-X",
  ISBN-13 =      "978-1-55752-808-7",
  LCCN =         "QC759.6 .P46 2006",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.osapublishing.org/abstract.cfm?uri=META-2006-TuA3",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://osapublishing.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2006:OPL,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici
                 and Ross C. McPhedran",
  title =        "Opaque perfect lenses",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "23",
  month =        aug,
  year =         "2006",
  CODEN =        "APRHCB",
  DOI =          "https://doi.org/10.1016/j.physb.2006.12.010",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Presented at The 7th International Conference on the
                 Electrical transport and Optical Properties of
                 Inhomogeneous Media (ETOPIM7).",
  URL =          "https://arxiv.org/abs/physics/0608225",
  abstract =     "The response of the ``perfect lens'', consisting of a
                 slab of lossless material of thickness $d$ with $
                 \epsilon = \mu = - 1$ at one frequency $ \omega_0$ is
                 investigated. It is shown that as time progresses the
                 lens becomes increasingly opaque to any physical TM
                 line dipole source located a distance $ d_0 < d / 2$
                 from the lens and which has been turned on at time $ t
                 = 0$. Here a physical source is defined as one which
                 supplies a bounded amount of energy per unit time. In
                 fact the lens cloaks the source so that it is not
                 visible from behind the lens either. For sources which
                 are turned on exponentially slowly there is an exact
                 correspondence between the response of the perfect lens
                 in the long time constant limit and the response of
                 lossy lenses in the low loss limit. Contrary to the
                 usual picture where the field intensity has a minimum
                 at the front interface we find that the field diverges
                 to infinity there in the long time constant limit.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Optics (physics.optics); Classical Physics
                 (physics.class-ph)",
}

@Article{Milton:2006:SCP,
  author =       "Graeme W. Milton and H. Kang",
  title =        "Solutions to the conjectures of
                 {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2006",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/math/0609374",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Nicorovici:2006:PRT,
  author =       "N. A. Nicorovici and R. C. McPhedran and G. W. Milton
                 and L. C. Botten",
  title =        "Partial Resonances of Three-Phase Composites at Long
                 Wavelengths",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        aug,
  year =         "2006",
  CODEN =        "APRHCB",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/physics/0608247",
  abstract =     "We investigate the behaviour of a three-phase
                 composite, structured as a hexagonal array of coated
                 cylinders, when the sum of the dielectric constants of
                 the core and shell equals zero. In such cases, the
                 absorption of the composite is the same as the
                 absorption of a periodic array of solid cylinders of
                 core material and radius equal to the outer radius of
                 the original coated cylinder. When the sum of the
                 dielectric constants of the shell and matrix equals
                 zero, the composite has the same absorption as a
                 periodic array of solid cylinders of core material, and
                 radius exceeding the shell radius.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "11",
  subject =      "Optics (physics.optics); Classical Physics
                 (physics.class-ph)",
}

@InProceedings{Podolskiy:2006:OSG,
  author =       "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme
                 W. Milton",
  editor =       "Anonymous",
  booktitle =    "{CLEO/QELS 06: PhAST: Conference on Lasers and
                 Electro-optics: Quantum Electronics and Laser Science
                 Conference: Conference on Photonic Applications,
                 Systems and Technologies: technical digest CD-ROM, Long
                 Beach Convention Center, Long Beach, California, USA,
                 CLEO/QELS Conference: May 21-26, 2006: PhAST
                 Conference, May 22-25, 2006.: Lasers and Electro-optics
                 and 2006 Quantum Electronics and Laser Science
                 Conference, CLEO}",
  title =        "Optimizing the superlens geometry",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  month =        "????",
  year =         "2006",
  ISBN =         "1-55752-813-6",
  ISBN-13 =      "978-1-55752-813-1",
  LCCN =         "TA1673 .C63 2006",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.osapublishing.org/abstract.cfm?uri=QELS-2006-JWB84",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://osapublishing.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Cai:2007:NCM,
  author =       "Wenshan Cai and Uday K. Chettiar and Alexander V.
                 Kildishev and Vladimir M. Shalaev and Graeme W.
                 Milton",
  title =        "Nonmagnetic cloak with minimized scattering",
  journal =      j-APPL-PHYS-LET,
  volume =       "91",
  number =       "11",
  pages =        "111105",
  day =          "10",
  month =        sep,
  year =         "2007",
  CODEN =        "APPLAB",
  DOI =          "https://doi.org/10.1063/1.2783266",
  ISSN =         "0003-6951 (print), 1077-3118 (electronic), 1520-8842",
  ISSN-L =       "0003-6951",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://scitation.aip.org/content/aip/journal/apl/91/11/10.1063/1.2783266",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Applied Physics Letters",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/apl",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Cai:2007:NMC,
  author =       "Wenshan Cai and Uday K. Chettiar and Alexander V.
                 Kildishev and Graeme W. Milton and Vladimir M.
                 Shalaev",
  title =        "Non-Magnetic Cloak without Reflection",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        jul,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1063/1.2783266",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0707.3641",
  abstract =     "In an electromagnetic cloak based on a transformation
                 approach, reduced sets of material properties are
                 generally favored due to their easier implementation in
                 reality, although a seemingly inevitable drawback of
                 undesired reflection exists in such cloaks. Here we
                 suggest using high-order transformations to create
                 smooth moduli at the outer boundary of the cloak,
                 therefore completely eliminating the detrimental
                 scattering within the limit of geometric optics. We
                 apply this scheme to a non-magnetic cylindrical cloak
                 and demonstrate that the scattered field is reduced
                 substantially in a cloak with optimal quadratic
                 transformation as compared to its linear counterpart.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "8",
  subject =      "Optics (physics.optics)",
}

@InProceedings{Milton:2007:CNP,
  author =       "Graeme W. Milton",
  editor =       "Anonymous",
  booktitle =    "{Photonic metamaterials: from random to periodic: 4--7
                 June 2007, Jackson Hole, Wyoming, United States}",
  title =        "Cloaking: A New Phenomenon in Electromagnetism and
                 Elasticity",
  publisher =    "OSA Publishing",
  address =      "Washington, DC, USA",
  pages =        "??--??",
  year =         "2007",
  DOI =          "https://doi.org/10.1364/META.2007.TuD1",
  ISBN =         "1-55752-839-X",
  ISBN-13 =      "978-1-55752-839-1",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.osapublishing.org/abstract.cfm?uri=META-2007-TuD1",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://osapublishing.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "2",
}

@Article{Milton:2007:MNS,
  author =       "Graeme W. Milton and John R. Willis",
  title =        "On modifications of {Newton}'s second law and linear
                 continuum elastodynamics",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "463",
  number =       "2079",
  pages =        "855--880",
  month =        mar,
  year =         "2007",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2006.1795",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74Q10 (74A40 74H45 74Q99)",
  MRnumber =     "2293080 (2007m:74118)",
  MRreviewer =   "Paolo Maria Mariano",
  bibdate =      "Wed Aug 23 2006",
  bibdate =      "Sat Nov 21 09:12:03 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/463/2079/855",
  abstract =     "In this paper, we suggest a new perspective, where
                 Newton{\textquoteright}s second law of motion is
                 replaced by a more general law which is a better
                 approximation for describing the motion of seemingly
                 rigid macroscopic bodies. We confirm a finding of
                 Willis that the density of a body at a given frequency
                 of oscillation can be anisotropic. The relation between
                 the force and the acceleration is non-local (but
                 causal) in time. Conversely, for every response
                 function satisfying these properties, and having the
                 appropriate high-frequency limit, there is a model
                 which realizes that response function. In many
                 circumstances, the differences between
                 Newton{\textquoteright}s second law and the new law are
                 small, but there are circumstances, such as in
                 specially designed composite materials, where the
                 difference is enormous. For bodies which are not
                 seemingly rigid, the continuum equations of
                 elastodynamics govern behaviour and also need to be
                 modified. The modified versions of these equations
                 presented here are a generalization of the equations
                 proposed by Willis to describe elastodynamics in
                 composite materials. It is argued that these new sets
                 of equations may apply to all physical materials, not
                 just composites. The Willis equations govern the
                 behaviour of the average displacement field whereas one
                 set of new equations governs the behaviour of the
                 average-weighted displacement field, where the weighted
                 displacement field may attach zero weight to
                 {\textquoteleft}hidden{\textquoteright} areas in the
                 material where the displacement may be unobservable or
                 not defined. From knowledge of the average-weighted
                 displacement field, one obtains an approximate formula
                 for the ensemble averaged energy density. Two other
                 sets of new equations govern the behaviour when the
                 microstructure has microinertia, i.e. where there are
                 internal spinning masses below the chosen scale of
                 continuum modelling. In the first set, the average
                 displacement field is assumed to be observable, while
                 in the second set an average-weighted displacement
                 field is assumed to be observable.",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, \& Engineering Sciences",
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxyear =       "2006",
}

@Article{Milton:2007:NMMa,
  author =       "Graeme W. Milton",
  title =        "New metamaterials with macroscopic behavior outside
                 that of continuum elastodynamics",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/9/10/359",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0706.2202",
  abstract =     "Metamaterials are constructed such that, for a narrow
                 range of frequencies, the momentum density depends on
                 the local displacement gradient, and the stress depends
                 on the local velocity. In these models the momentum
                 density generally depends not only on the strain, but
                 also on the local rotation, and the stress is generally
                 not symmetric. A variant is constructed for which, at a
                 fixed frequency, the momentum density is independent of
                 the local rotation (but still depends on the strain)
                 and the stress is symmetric (but still depends on the
                 velocity). Generalizations of these metamaterials may
                 be useful in the design of elastic cloaking devices.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "14",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2007:NMMb,
  author =       "Graeme W. Milton",
  title =        "New metamaterials with macroscopic behavior outside
                 that of continuum elastodynamics",
  journal =      j-NEW-J-PHYS,
  volume =       "9",
  number =       "10",
  pages =        "359",
  year =         "2007",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/9/10/359",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Tue Nov 6 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://iopscience.iop.org/1367-2630/9/10/359",
  abstract =     "Metamaterials are constructed such that, for a narrow
                 range of frequencies, the momentum density depends on
                 the local displacement gradient and the stress depends
                 on the local acceleration. In these models the momentum
                 density generally depends not only on the strain, but
                 also on the local rotation, and the stress is generally
                 not symmetric. A variant is constructed for which, at a
                 fixed frequency, the momentum density is independent of
                 the local rotation (but still depends on the strain)
                 and the stress is symmetric (but still depends on the
                 acceleration). Generalizations of these metamaterials
                 may be useful in the design of elastic cloaking
                 devices.",
  acknowledgement = ack-gwm,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://stacks.iop.org/1367-2630/9/i=10/a=359",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/9/10/359/",
}

@Article{Milton:2007:OPL,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici
                 and Ross C. McPhedran",
  title =        "Opaque perfect lenses",
  journal =      j-PHYSICA-B,
  volume =       "394",
  number =       "2",
  pages =        "171--175",
  day =          "15",
  month =        may,
  year =         "2007",
  CODEN =        "PHYBE3",
  DOI =          "https://doi.org/10.1016/j.physb.2006.12.010",
  ISSN =         "0921-4526 (print), 1873-2135 (electronic)",
  ISSN-L =       "0921-4526",
  bibdate =      "Fri Mar 21 2008",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0921452606018941",
  acknowledgement = ack-gwm,
  fjournal =     "Physica. B, Condensed matter",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09214526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxyear =       "2006",
}

@Article{Milton:2007:RRM,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Realizable response matrices of multiterminal
                 electrical, acoustic, and elastodynamic networks at a
                 given frequency",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "7",
  month =        dec,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2007.0345",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0712.1066",
  abstract =     "We give a complete characterization of the possible
                 response matrices at a fixed frequency of n-terminal
                 electrical networks of inductors, capacitors, resistors
                 and grounds, and of n-terminal discrete linear
                 elastodynamic networks of springs and point masses,
                 both in the three-dimensional case and in the
                 two-dimensional case. Specifically we construct
                 networks which realize any response matrix which is
                 compatible with the known symmetry properties and
                 thermodynamic constraints of response matrices. Due to
                 a mathematical equivalence we also obtain a
                 characterization of the response matrices of discrete
                 acoustic networks.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "22",
  subject =      "Materials Science (cond-mat.mtrl-sci)",
}

@Article{Nicorovici:2007:QCT,
  author =       "Nicolae-Alexandru P. Nicorovici and Graeme W. Milton
                 and Ross C. McPhedran and Lindsay C. Botten",
  title =        "Quasistatic cloaking of two-dimensional polarizable
                 discrete systems by anomalous resonance",
  journal =      j-OPT-EXPRESS,
  volume =       "15",
  number =       "10",
  pages =        "6314--6323",
  day =          "14",
  month =        may,
  year =         "2007",
  CODEN =        "OPEXFF",
  DOI =          "https://doi.org/10.1364/OE.15.006314",
  ISSN =         "1094-4087",
  ISSN-L =       "1094-4087",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-10-6314",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Optics Express",
  journal-URL =  "http://opticsexpress.org/Issue.cfm",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2008:GHE,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Giant {Hall} effect in composites",
  journal =      j-MULTISCALE-MODELING-SIMUL,
  volume =       "7",
  number =       "3",
  pages =        "1405--1427",
  year =         "2008",
  CODEN =        "MMSUBT",
  DOI =          "https://doi.org/10.1137/08073189X",
  ISSN =         "1540-3459 (print), 1540-3467 (electronic)",
  ISSN-L =       "1540-3459",
  MRclass =      "35B27 (74Q15 78A55 81V70)",
  MRnumber =     "2496707 (2010m:35021)",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/08073189X",
  fjournal =     "Multiscale Modeling \& Simulation. A SIAM
                 Interdisciplinary Journal",
  journal-URL =  "http://epubs.siam.org/mms",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2008:HTD,
  author =       "M. Briane and D. Manceau and Graeme W. Milton",
  title =        "Homogenization of the two-dimensional {Hall} effect",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "339",
  number =       "2",
  pages =        "1468--1484",
  day =          "15",
  month =        mar,
  year =         "2008",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2007.07.044",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "81V70 (35B27 49J45)",
  MRnumber =     "2377101 (2008k:81378)",
  MRreviewer =   "Alain Brillard",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X07009055",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Kang:2008:IPS,
  author =       "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton",
  title =        "Inclusion Pairs Satisfying {Eshelby}'s Uniformity
                 Property",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "69",
  number =       "2",
  pages =        "577--595",
  month =        "????",
  year =         "2008",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/070691358",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "74M25 (30C20 35J25 74P99 74Q05)",
  MRnumber =     "2465857 (2009i:74077)",
  MRreviewer =   "Pham Duc Chinh",
  bibdate =      "Mon May 17 18:38:59 MDT 2010",
  bibsource =    "http://epubs.siam.org/toc/smjmap/69/2;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/070691358",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Kang:2008:SPS,
  author =       "Hyeonbae Kang and Graeme W. Milton",
  title =        "Solutions to the {P{\'o}lya--Szeg{\H{o}}} Conjecture
                 and the {Weak Eshelby Conjecture}",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "188",
  number =       "1",
  pages =        "93--116",
  month =        apr,
  year =         "2008",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s00205-007-0087-z",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "74G40 (35J55 35Q72 49Q05 74B05)",
  MRnumber =     "2379654 (2009j:74046)",
  bibdate =      "Mon Nov 7 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s00205-007-0087-z",
  acknowledgement = ack-gwm,
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2008:EC,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Electromagnetic Circuits",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        may,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0805.1079",
  abstract =     "The electromagnetic analog of an elastic spring-mass
                 network is constructed. These electromagnetic circuits
                 offer the promise of manipulating electromagnetic
                 fields in new ways, and linear electrical circuits
                 correspond to a subclass of them. They consist of thin
                 triangular magnetic components joined at the edges by
                 cylindrical dielectric components. (There are also dual
                 electromagnetic circuits consisting of thin triangular
                 dielectric components joined at the edges by
                 cylindrical magnetic components.) Some of the edges can
                 be terminal edges to which electric fields are applied.
                 The response is measured in terms of the real or
                 virtual free currents that are associated with the
                 terminal edges. The relation between the terminal
                 electric fields and the terminal free currents is
                 governed by a symmetric complex matrix $ \BW $. In the
                 case where all the terminal edges are disjoint, and the
                 frequency is fixed, a complete characterization is
                 obtained of all possible response matrices $ \BW $ both
                 in the lossless and lossy cases. This is done by
                 introducing a subclass of electromagnetic circuits,
                 called electromagnetic ladder networks. It is shown
                 that an electromagnetic ladder network, structured as a
                 cubic network, can have a macroscopic electromagnetic
                 continuum response which is non-Maxwellian, and
                 novel.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "33",
  subject =      "Classical Physics (physics.class-ph); Optics
                 (physics.optics)",
}

@Article{Milton:2008:MVP,
  author =       "Graeme W. Milton and Pierre Seppecher and Guy
                 Bouchitte",
  title =        "Minimization variational principles for acoustics,
                 elastodynamics, and electromagnetism in lossy
                 inhomogeneous bodies at fixed frequency",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        jul,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2008.0195",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Proc. R. Soc. A 465 (2009) 367-396",
  URL =          "https://arxiv.org/abs/0807.1336",
  abstract =     "The classical energy minimization principles of
                 Dirichlet and Thompson are extended as minimization
                 principles to acoustics, elastodynamics and
                 electromagnetism in lossy inhomogeneous bodies at fixed
                 frequency. This is done by building upon ideas of
                 Cherkaev and Gibiansky, who derived minimization
                 variational principles for quasistatics. In the absence
                 of free current the primary electromagnetic
                 minimization variational principles have a minimum
                 which is the time-averaged electrical power dissipated
                 in the body. The variational principles provide
                 constraints on the boundary values of the fields when
                 the moduli are known. Conversely, when the boundary
                 values of the fields have been measured, then they
                 provide information about the values of the moduli
                 within the body. This should have application to
                 electromagnetic tomography. We also derive saddle point
                 variational principles which correspond to variational
                 principles of Gurtin, Willis, and Borcea.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "32",
  subject =      "Mathematical Physics (math-ph); Materials Science
                 (cond-mat.mtrl-sci); Analysis of PDEs (math.AP);
                 Classical Physics (physics.class-ph); Optics
                 (physics.optics)",
}

@Article{Milton:2008:RRM,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Realizable response matrices of multi-terminal
                 electrical, acoustic and elastodynamic networks at a
                 given frequency",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "464",
  number =       "2092",
  pages =        "967--986",
  month =        apr,
  year =         "2008",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2007.0345",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "94C05 (74E30)",
  MRnumber =     "2379501 (2009d:94171)",
  MRreviewer =   "D. Stanomir",
  bibdate =      "Tue May 6 2008",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/464/2092/967",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2008:SFGa,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici
                 and Ross C. McPhedran and Kirill Cherednichenko and
                 Zubin Jacob",
  title =        "Solutions in folded geometries, and associated
                 cloaking due to anomalous resonance",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        apr,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/10/11/115021",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0804.3903",
  abstract =     "Solutions for the fields in a coated cylinder where
                 the core radius is bigger than the shell radius are
                 seemingly unphysical, but can be given a physical
                 meaning if one transforms to an equivalent problem by
                 unfolding the geometry. In particular the unfolded
                 material can act as an impedance matched hyperlens, and
                 as the loss in the lens goes to zero finite collections
                 of polarizable line dipoles lying within a critical
                 region surrounding the hyperlens are shown to be
                 cloaked having vanishingly small dipole moments. This
                 cloaking, which occurs both in the folded geometry and
                 the equivalent unfolded one, is due to anomalous
                 resonance, where the collection of dipoles generates an
                 anomalously resonant field, which acts back on the
                 dipoles to essentially cancel the external fields
                 acting on them.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "23",
  subject =      "Optics (physics.optics)",
}

@Article{Milton:2008:SFGb,
  author =       "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici
                 and Ross C. McPhedran and Kirill Cherednichenko and
                 Zubin Jacob",
  title =        "Solutions in folded geometries, and associated
                 cloaking due to anomalous resonance",
  journal =      j-NEW-J-PHYS,
  volume =       "10",
  number =       "11",
  pages =        "115021",
  month =        nov,
  year =         "2008",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/10/11/115021",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://stacks.iop.org/1367-2630/10/i=11/a=115021",
  abstract =     "Solutions for the fields in a coated cylinder where
                 the core radius is bigger than the shell radius are
                 seemingly unphysical, but can be given a physical
                 meaning if one transforms to an equivalent problem by
                 unfolding the geometry. In particular, the unfolded
                 material can act as an impedance matched hyperlens, and
                 as the loss in the lens goes to zero finite collections
                 of polarizable line dipoles lying within a critical
                 region surrounding the hyperlens are shown to be
                 cloaked having vanishingly small dipole moments. This
                 cloaking, which occurs both in the folded geometry and
                 the equivalent unfolded one, is due to anomalous
                 resonance, where the collection of dipoles generates an
                 anomalously resonant field, which acts back on the
                 dipoles to essentially cancel the external fields
                 acting on them.",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/10/11/115021/",
}

@Article{Vinogradov:2008:AFA,
  author =       "V. Vinogradov and Graeme W. Milton",
  title =        "An accelerated {FFT} algorithm for thermoelastic and
                 non-linear composites",
  journal =      j-INT-J-NUMER-METHODS-ENG,
  volume =       "76",
  number =       "11",
  pages =        "1678--1695",
  year =         "2008",
  CODEN =        "IJNMBH",
  DOI =          "https://doi.org/10.1002/nme.2375",
  ISSN =         "0029-5981 (print), 1097-0207 (electronic)",
  ISSN-L =       "0029-5981",
  MRclass =      "74S30 (74A40)",
  MRnumber =     "2468562 (2009m:74099)",
  MRreviewer =   "Stan Chiri{\c{t}}{\u{a}}",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  fjournal =     "International Journal for Numerical Methods in
                 Engineering",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Ammari:2009:PSE,
  author =       "Habib Ammari and Yves Capdeboscq and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton and Habib Zribi",
  title =        "Progress on the Strong {Eshelby}'s Conjecture and
                 Extremal Structures for the Elastic Moment Tensor",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        sep,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.matpur.2010.01.003",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in J. Math. Pures Appl. (9) 94(1):93--106,
                 2010",
  URL =          "https://arxiv.org/abs/0909.1969",
  abstract =     "We make progress towards proving the strong Eshelby's
                 conjecture in three dimensions. We prove that if for a
                 single nonzero uniform loading the strain inside
                 inclusion is constant and further the eigenvalues of
                 this strain are either all the same or all distinct,
                 then the inclusion must be of ellipsoidal shape. As a
                 consequence, we show that for two linearly independent
                 loadings the strains inside the inclusions are uniform,
                 then the inclusion must be of ellipsoidal shape. We
                 then use this result to address a problem of
                 determining the shape of an inclusion when the elastic
                 moment tensor (elastic polarizability tensor) is
                 extremal. We show that the shape of inclusions, for
                 which the lower Hashin--Shtrikman bound either on the
                 bulk part or on the shear part of the elastic moment
                 tensor is attained, is an ellipse in two dimensions and
                 an ellipsoid in three dimensions.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Briane:2009:GHE,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Giant {Hall} Effect in Composites",
  journal =      j-MULTISCALE-MODELING-SIMUL,
  volume =       "7",
  number =       "3",
  pages =        "1405--1427",
  month =        "????",
  year =         "2009",
  CODEN =        "MMSUBT",
  DOI =          "https://doi.org/10.1137/08073189X",
  ISSN =         "1540-3459 (print), 1540-3467 (electronic)",
  ISSN-L =       "1540-3459",
  bibdate =      "Wed May 19 17:34:41 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/MMS/7/3;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siammms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Multiscale Modeling and Simulation",
  journal-URL =  "http://epubs.siam.org/mms",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2009:HTD,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Homogenization of the three-dimensional {Hall} effect
                 and change of sign of the {Hall} coefficient",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "193",
  number =       "3",
  pages =        "715--736",
  month =        sep,
  year =         "2009",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s00205-008-0200-y",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "78A48 (35B27 35C20 74E10 74Q05)",
  MRnumber =     "2525116 (2010d:78025)",
  MRreviewer =   "Alain Brillard",
  bibdate =      "Sat Oct 31 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s00205-008-0200-y",
  acknowledgement = ack-gwm,
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{GuevaraVasquez:2009:AECa,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Active Exterior Cloaking",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        jun,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1103/PhysRevLett.103.073901",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Physical Review Letters, 103, 073901
                 (2009)",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0906.1544G;
                 https://arxiv.org/abs/0906.1544",
  abstract =     "A new method of cloaking is presented. For
                 two-dimensional quasistatics it is proven how a single
                 active exterior cloaking device can be used to shield
                 an object from surrounding fields, yet produce very
                 small scattered fields. The problem is reduced to
                 finding a polynomial which is approximately one within
                 one disk and zero within a second disk, and such a
                 polynomial is constructed. For the two-dimensional
                 Helmholtz equation, it is numerically shown that three
                 active exterior devices placed around the object
                 suffice to produce very good cloaking.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "4",
  subject =      "Mathematical Physics (math-ph); Optics
                 (physics.optics)",
}

@Article{GuevaraVasquez:2009:AECb,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Active exterior cloaking for the {$2$D} {Laplace} and
                 {Helmholtz} equations",
  journal =      j-PHYS-REV-LET,
  volume =       "103",
  number =       "7",
  pages =        "073901",
  day =          "14",
  month =        aug,
  year =         "2009",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.103.073901",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.073901",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "4",
}

@Article{GuevaraVasquez:2009:BECa,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Broadband Exterior Cloaking",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "1",
  month =        jul,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1364/OE.17.014800",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Optics Express, Vol. 17, pp. 14800-14805
                 (2009)",
  URL =          "https://arxiv.org/abs/0907.0263",
  abstract =     "It is shown how a recently proposed method of cloaking
                 is effective over a broad range of frequencies. The
                 method is based on three or more active devices. The
                 devices, while not radiating significantly, create a
                 ``quiet zone'' between the devices where the wave
                 amplitude is small. Objects placed within this region
                 are virtually invisible. The cloaking is demonstrated
                 by simulations with a broadband incident pulse.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{GuevaraVasquez:2009:BECb,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Broadband exterior cloaking",
  journal =      j-OPT-EXPRESS,
  volume =       "17",
  number =       "17",
  pages =        "14800--14805",
  day =          "17",
  month =        aug,
  year =         "2009",
  CODEN =        "OPEXFF",
  DOI =          "https://doi.org/10.1364/OE.17.014800",
  ISSN =         "1094-4087",
  ISSN-L =       "1094-4087",
  bibdate =      "Fri May 29 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://www.osapublishing.org/oe/abstract.cfm?uri=oe-17-17-14800",
  acknowledgement = ack-gwm,
  fjournal =     "Optics Express",
  journal-URL =  "http://opticsexpress.org/Issue.cfm",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{GuevaraVasquez:2009:CCS,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Complete characterization and synthesis of the
                 response function of elastodynamic networks",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        nov,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10659-010-9260-y",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Journal of Elasticity, 102, no. 1 (2011),
                 31--54, 2011",
  URL =          "https://arxiv.org/abs/0911.1501",
  abstract =     "The response function of a network of springs and
                 masses, an elastodynamic network, is the matrix valued
                 function $ W(\omega) $, depending on the frequency $
                 \omega $, mapping the displacements of some accessible
                 or terminal nodes to the net forces at the terminals.
                 We give necessary and sufficient conditions for a given
                 function $ W(\omega) $ to be the response function of
                 an elastodynamic network, assuming there is no damping.
                 In particular we construct an elastodynamic network
                 that can mimic a suitable response in the frequency or
                 time domain. Our characterization is valid for networks
                 in three dimensions and also for planar networks, which
                 are networks where all the elements, displacements and
                 forces are in a plane. The network we design can fit
                 within an arbitrarily small neighborhood of the convex
                 hull of the terminal nodes, provided the springs and
                 masses occupy an arbitrarily small volume.
                 Additionally, we prove stability of the network
                 response to small changes in the spring constants
                 and/or addition of springs with small spring
                 constants.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "23",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{McPhedran:2009:CPR,
  author =       "Ross C. McPhedran and Nicolae-Alexandru P. Nicorovici
                 and Lindsay C. Botten and Graeme W. Milton",
  title =        "Cloaking by plasmonic resonance among systems of
                 particles: cooperation or combat?",
  journal =      j-C-R-PHYS,
  volume =       "10",
  number =       "5",
  pages =        "391--399",
  month =        jun,
  year =         "2009",
  CODEN =        "CRPOBN",
  DOI =          "https://doi.org/10.1016/j.crhy.2009.03.007",
  ISSN =         "1631-0705 (print), 1878-1535 (electronic)",
  ISSN-L =       "1631-0705",
  bibdate =      "Sat Nov 28 18:44:37 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1631070509000413",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Physique",
  journal-URL =  "http://www.sciencedirect.com/science/journal/16310705",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2009:HEC,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Hybrid electromagnetic circuits",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "5",
  month =        oct,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/0910.0798",
  abstract =     "Electromagnetic circuits are the electromagnetic
                 analog at fixed frequency of mass-spring networks in
                 elastodynamics. By interchanging the roles of epsilon
                 and mu in electromagnetic circuits one obtains
                 magnetoelectric circuits. Here we show that by
                 introducing tetrahedral connectors having epsilon=mu=0
                 one can join electromagnetic and magnetoelectric
                 circuits to obtain hybrid circuits. Their response is
                 governed by a symmetric matrix with negative
                 semidefinite imaginary part. Conversely given any such
                 matrix a recipe is given for constructing a hybrid
                 circuit which has that matrix as its response matrix.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "5",
  subject =      "Optics (physics.optics)",
}

@Article{Milton:2009:MVP,
  author =       "Graeme W. Milton and Pierre Seppecher and Guy
                 Bouchitt{\'e}",
  title =        "Minimization variational principles for acoustics,
                 elastodynamics and electromagnetism in lossy
                 inhomogeneous bodies at fixed frequency",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "465",
  number =       "2102",
  pages =        "367--396",
  day =          "8",
  month =        feb,
  year =         "2009",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2008.0195",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74B05 (49S05 76Q05 78A25)",
  MRnumber =     "2471764 (2009m:74013)",
  MRreviewer =   "Sven Ivansson",
  bibdate =      "Thu May 28 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/465/2102/367",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Ammari:2010:PSE,
  author =       "Habib Ammari and Yves Capdeboscq and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton and Habib Zribi",
  title =        "Progress on the strong {Eshelby}'s conjecture and
                 extremal structures for the elastic moment tensor",
  journal =      j-J-MATH-PURES-APPL,
  volume =       "94",
  number =       "1",
  pages =        "93--106",
  year =         "2010",
  CODEN =        "JMPAAM",
  DOI =          "https://doi.org/10.1016/j.matpur.2010.01.003",
  ISSN =         "0021-7824 (print), 1776-3371 (electronic)",
  ISSN-L =       "0021-7824",
  MRclass =      "74G55 (74B05 74Q05)",
  MRnumber =     "2653981 (2011h:74049)",
  bibdate =      "Thu Apr 16 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021782410000115",
  acknowledgement = ack-gwm,
  fjournal =     "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00217824",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Benveniste:2010:EMAa,
  author =       "Y. Benveniste and Graeme W. Milton",
  title =        "The effective medium and the average field
                 approximations vis-{\`a}-vis the {Hashin--Shtrikman}
                 bounds. {I}. {The} self-consistent scheme in
                 matrix-based composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "58",
  number =       "7",
  pages =        "1026--1038",
  month =        jul,
  year =         "2010",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2010.04.014",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74A40 (74B05 74M25)",
  MRnumber =     "2642449",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509610000839",
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Benveniste:2010:EMAb,
  author =       "Y. Benveniste and Graeme W. Milton",
  title =        "The effective medium and the average field
                 approximations vis-{\`a}-vis the {Hashin--Shtrikman}
                 bounds. {II}. {The} generalized self-consistent scheme
                 in matrix-based composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "58",
  number =       "7",
  pages =        "1039--1056",
  month =        jul,
  year =         "2010",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2010.04.013",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74A40 (74B05 74M25)",
  MRnumber =     "2642450",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509610000827",
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2010:AEH,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "An Antisymmetric Effective {Hall} Matrix",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "70",
  number =       "6",
  pages =        "1810--1820",
  month =        "????",
  year =         "2010",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/09075901X",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "35B27 (35Q74 74Q15 78A48 81V70)",
  MRnumber =     "2596502 (2011b:35031)",
  MRreviewer =   "Nicolas Charalambakis",
  bibdate =      "Mon May 17 18:39:21 MDT 2010",
  bibsource =    "http://epubs.siam.org/toc/smjmap/70/6;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/09075901X",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2010:NBS,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "New Bounds on Strong Field Magneto-Transport in
                 Multiphase Columnar Composites",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "70",
  number =       "8",
  pages =        "3272--3286",
  month =        "????",
  year =         "2010",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/100798090",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "35B27 (74Q20 78A48)",
  MRnumber =     "2763504 (2012j:35015)",
  MRreviewer =   "A. K. Nandakumaran",
  bibdate =      "Fri Mar 4 09:51:08 MST 2011",
  bibsource =    "http://epubs.siam.org/toc/smjmap/70/8;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/100798090",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  onlinedate =   "December 14, 2010",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://epubs.siam.org/siap/resource/1/smjmap/v70/i8/p3272_s1",
}

@Article{GuevaraVasquez:2010:ECA,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Exterior cloaking with active sources in two
                 dimensional acoustics",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10659-010-9260-y",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Wave Motion, 48, no. 6 (2011), 515--524",
  URL =          "https://arxiv.org/abs/1009.2038",
  abstract =     "We cloak a region from a known incident wave by
                 surrounding the region with three or more devices that
                 cancel out the field in the cloaked region without
                 significantly radiating waves. Since very little waves
                 reach scatterers within the cloaked region, the
                 scattered field is small and the scatterers are for all
                 practical purposes undetectable. The devices are
                 multipolar point sources that can be determined from
                 Green's formula and an addition theorem for Hankel
                 functions. The cloaking devices are exterior to the
                 cloaked region.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2010:EC,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Electromagnetic Circuits",
  journal =      j-NETW-HETEROG-MEDIA,
  volume =       "5",
  number =       "2",
  pages =        "335--360",
  month =        jun,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3934/nhm.2010.5.335",
  ISSN =         "1556-1801 (print), 1556-181X (electronic)",
  ISSN-L =       "1556-1801",
  MRclass =      "35Q60, 78A48, 94C05",
  MRnumber =     "2661411 (2011i:94129)",
  MRreviewer =   "Alain Brillard",
  bibdate =      "Tue Sep 15 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://aimsciences.org/journals/redirecting.jsp?paperID=5217",
  acknowledgement = ack-gwm,
  fjournal =     "Networks and Heterogeneous Media (NHM)",
  journal-URL =  "http://aimsciences.org/journals/home.jsp?journalID=9",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2010:HEC,
  author =       "Graeme W. Milton and Pierre Seppecher",
  title =        "Hybrid electromagnetic circuits",
  journal =      j-PHYSICA-B,
  volume =       "405",
  number =       "14",
  pages =        "2935--2937",
  day =          "15",
  month =        jul,
  year =         "2010",
  CODEN =        "PHYBE3",
  DOI =          "https://doi.org/10.1016/j.physb.2010.01.007",
  ISSN =         "0921-4526 (print), 1873-2135 (electronic)",
  ISSN-L =       "0921-4526",
  bibdate =      "Tue Sep 15 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0921452610000098",
  acknowledgement = ack-gwm,
  fjournal =     "Physica. B, Condensed matter",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09214526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2010:MVPa,
  author =       "Graeme W. Milton and John R. Willis",
  title =        "Minimum variational principles for time-harmonic waves
                 in a dissipative medium and associated variational
                 principles of {Hashin--Shtrikman} type",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        jan,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2010.0006",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1001.2773",
  abstract =     "Minimization variational principles for linear
                 elastodynamic, acoustic, or electromagnetic
                 time-harmonic waves in dissipative media were obtained
                 by Milton, Seppecher and Bouchitt{\'e} generalizing the
                 quasistatic variational principles of Cherkaev and
                 Gibiansky. Here a further generalization is made to
                 allow for a much wider variety of boundary conditions,
                 and in particular Dirichlet and Neumann boundary
                 conditions. In addition minimization or maximization
                 principles of the Hashin--Shtrikman type, incorporating
                 ``polarization fields'', are developed.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "23",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2010:MVPb,
  author =       "Graeme W. Milton and John R. Willis",
  title =        "Minimum variational principles for time-harmonic waves
                 in a dissipative medium and associated variational
                 principles of {Hashin--Shtrikman} type",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "466",
  number =       "2122",
  pages =        "3013--3032",
  year =         "2010",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2010.0006",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74Q10",
  MRnumber =     "2684717 (2011k:74098)",
  bibdate =      "Tue Nov 1 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/early/2010/04/15/rspa.2010.0006",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2010:RMPa,
  author =       "Graeme W. Milton",
  title =        "Realizability of metamaterials with prescribed
                 electric permittivity and magnetic permeability
                 tensors",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        jan,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/12/3/033035",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1001.2761",
  abstract =     "We show that any pair of real symmetric tensors $
                 \BGve $ and $ \BGm $ can be realized as the effective
                 electric permittivity and effective magnetic
                 permeability of a metamaterial at a given fixed
                 frequency. The construction starts with two extremely
                 low loss metamaterials, with arbitrarily small
                 microstructure, whose existence is ensured by the work
                 of Bouchitt{\'e} and Bourel and Bouchitt{\'e} and
                 Schweizer, one having at the given frequency a
                 permittivity tensor with exactly one negative
                 eigenvalue, and a positive permeability tensor, and the
                 other having a positive permittivity tensor, and a
                 permeability tensor having exactly one negative
                 eigenvalue. To achieve the desired effective properties
                 these materials are laminated together in a
                 hierarchical multiple rank laminate structure, with
                 widely separated length scales, and varying directions
                 of lamination, but with the largest length scale still
                 much shorter than the wavelengths and attenuation
                 lengths in the macroscopic effective medium.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "12",
  subject =      "Optics (physics.optics)",
}

@Article{Milton:2010:RMPb,
  author =       "Graeme W. Milton",
  title =        "Realizability of metamaterials with prescribed
                 electric permittivity and magnetic permeability
                 tensors",
  journal =      j-NEW-J-PHYS,
  volume =       "12",
  number =       "3",
  pages =        "033035",
  year =         "2010",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/12/3/033035",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Wed Dec 22 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://stacks.iop.org/1367-2630/12/i=3/a=033035",
  acknowledgement = ack-gwm,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/12/3/033035/",
}

@Article{Ammari:2011:STN,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Spectral theory of a {Neumann--Poincar{\'e}}-type
                 operator and analysis of cloaking due to anomalous
                 localized resonance",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "2",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1109.0479",
  abstract =     "The aim of this paper is to give a mathematical
                 justification of cloaking due to anomalous localized
                 resonance (CALR). We consider the dielectric problem
                 with a source term in a structure with a layer of
                 plasmonic material. Using layer potentials and
                 symmetrization techniques, we give a necessary and
                 sufficient condition on the fixed source term for
                 electromagnetic power dissipation to blow up as the
                 loss parameter of the plasmonic material goes to zero.
                 This condition is written in terms of the Newtonian
                 potential of the source term. In the case of concentric
                 disks, we make the condition even more explicit. Using
                 the condition, we are able to show that for any source
                 supported outside a critical radius CALR does not take
                 place, and for sources located inside the critical
                 radius satisfying certain conditions CALR does take
                 place as the loss parameter goes to zero.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "24",
  subject =      "Analysis of PDEs (math.AP); Materials Science
                 (cond-mat.mtrl-sci); Optics (physics.optics)",
}

@Article{Benveniste:2011:EMT,
  author =       "Y. Benveniste and Graeme W. Milton",
  title =        "An effective medium theory for multi-phase
                 matrix-based dielectric composites with randomly
                 oriented ellipsoidal inclusions",
  journal =      j-INT-J-ENG-SCI,
  volume =       "49",
  number =       "1",
  pages =        "2--16",
  month =        jan,
  year =         "2011",
  CODEN =        "IJESAN",
  DOI =          "https://doi.org/10.1016/j.ijengsci.2010.06.019",
  ISSN =         "0020-7225 (print), 1879-2197 (electronic)",
  ISSN-L =       "0020-7225",
  bibdate =      "Sat Nov 28 18:44:37 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0020722510001266",
  acknowledgement = ack-nhfb,
  fjournal =     "International journal of engineering science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00207225",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2011:BSFa,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Bounds on strong field magneto-transport in
                 three-dimensional composites",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1063/1.3644377",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1105.3858",
  abstract =     "This paper deals with bounds satisfied by the
                 effective non-symmetric conductivity of
                 three-dimensional composites in the presence of a
                 strong magnetic field. On the one hand, it is shown
                 that for general composites the antisymmetric part of
                 the effective conductivity cannot be bounded solely in
                 terms of the antisymmetric part of the local
                 conductivity, contrary to the columnar case. So, a
                 suitable rank-two laminate the conductivity of which
                 has a bounded antisymmetric part together with a
                 high-contrast symmetric part, may generate an
                 arbitrarily large antisymmetric part of the effective
                 conductivity. On the other hand, bounds are provided
                 which show that the antisymmetric part of the effective
                 conductivity must go to zero if the upper bound on the
                 antisymmetric part of the local conductivity goes to
                 zero, and the symmetric part of the local conductivity
                 remains bounded below and above. Elementary bounds on
                 the effective moduli are derived assuming the local
                 conductivity and effective conductivity have transverse
                 isotropy in the plane orthogonal to the magnetic field.
                 New Hashin--Shtrikman type bounds for two-phase
                 three-dimensional composites with a non-symmetric
                 conductivity are provided under geometric isotropy of
                 the microstructure. The derivation of the bounds is
                 based on a particular variational principle
                 symmetrizing the problem, and the use of Y-tensors
                 involving the averages of the fields in each phase.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "21",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Briane:2011:BSFb,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Bounds on strong field magneto-transport in
                 three-dimensional composites",
  journal =      j-J-MATH-PHYS,
  volume =       "52",
  number =       "10",
  pages =        "103705:1--103705:118",
  month =        oct,
  year =         "2011",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.3644377",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "82D40 (35B27)",
  MRnumber =     "2894615 (2012m:82059)",
  MRreviewer =   "Alain Brillard",
  bibdate =      "Thu Oct 27 16:57:30 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v52/i10/p103705_s1",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "11 October 2011",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "18",
  xxURL =        "http://scitation.aip.org/content/aip/journal/jmp/52/10/10.1063/1.3644377",
  xxyear =       "2007",
}

@Article{GuevaraVasquez:2011:CCS,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Complete characterization and synthesis of the
                 response function of elastodynamic networks",
  journal =      j-J-ELAST,
  volume =       "102",
  number =       "1",
  pages =        "31--54",
  month =        jan,
  year =         "2011",
  CODEN =        "JELSAY",
  DOI =          "https://doi.org/10.1007/s10659-010-9260-y",
  ISSN =         "0374-3535 (print), 1573-2681 (electronic)",
  ISSN-L =       "0374-3535",
  MRclass =      "74K10 (35Q74 74B05 74H45)",
  MRnumber =     "2746911 (2011k:74064)",
  bibdate =      "Wed Dec 22 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s10659-010-9260-y",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of Elasticity",
  fjournal =     "Journal of Elasticity. The Physical and Mathematical
                 Science of Solids",
  journal-URL =  "http://link.springer.com/journal/10659",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{GuevaraVasquez:2011:ECA,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Exterior cloaking with active sources in two
                 dimensional acoustics",
  journal =      j-WAVE-MOTION,
  volume =       "48",
  number =       "6",
  pages =        "515--524",
  year =         "2011",
  CODEN =        "WAMOD9",
  DOI =          "https://doi.org/10.1016/j.wavemoti.2011.03.005",
  ISSN =         "0165-2125 (print), 1878-433X (electronic)",
  ISSN-L =       "0165-2125",
  MRclass =      "76Q05",
  MRnumber =     "2811880 (2012g:76141)",
  bibdate =      "Fri May 29 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165212511000382",
  acknowledgement = ack-gwm,
  fjournal =     "Wave Motion. An International Journal Reporting
                 Research on Wave Phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01652125",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{GuevaraVasquez:2011:MAT,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Mathematical analysis of the two dimensional active
                 exterior cloaking in the quasistatic regime",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "16",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13324-012-0031-8",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Analysis and Mathematical Physics, 2
                 (2012), no. 3, pp 231-246",
  URL =          "https://arxiv.org/abs/1109.3526",
  abstract =     "We design a device that generates fields canceling out
                 a known probing field inside a region to be cloaked
                 while generating very small fields far away from the
                 device. The fields we consider satisfy the Laplace
                 equation, but the approach remains valid in the
                 quasistatic regime in a homogeneous medium. We start by
                 relating the problem of designing an exterior cloak in
                 the quasistatic regime to the classic problem of
                 approximating a harmonic function with harmonic
                 polynomials. An explicit polynomial solution to the
                 problem was given earlier in [Phys. Rev. Lett. 103
                 (2009), 073901]. Here we show convergence of the device
                 field to the field needed to perfectly cloak an object.
                 The convergence region limits the size of the cloaked
                 region, and the size and position of the device.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{GuevaraVasquez:2011:TEA,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei and Pierre Seppecher",
  title =        "Transformation elastodynamics and active exterior
                 acoustic cloaking",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "6",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/978-94-007-4813-2_12",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Submitted as a chapter for the volume
                 \booktitle{Acoustic metamaterials: Negative refraction,
                 imaging, lensing and cloaking}, Craster and Guenneau
                 ed., Springer.",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1105.1221G;
                 https://arxiv.org/abs/1105.1221",
  abstract =     "This chapter consists of three parts. In the first
                 part we recall the elastodynamic equations under
                 coordinate transformations. The idea is to use
                 coordinate transformations to manipulate waves
                 propagating in an elastic material. Then we study the
                 effect of transformations on a mass-spring network
                 model. The transformed networks can be realized with
                 ``torque springs'', which are introduced here and are
                 springs with a force proportional to the displacement
                 in a direction other than the direction of the spring
                 terminals. Possible homogenizations of the transformed
                 networks are presented, with potential applications to
                 cloaking. In the second and third parts we present
                 cloaking methods that are based on cancelling an
                 incident field using active devices which are exterior
                 to the cloaked region and that do not generate
                 significant fields far away from the devices. In the
                 second part, the exterior cloaking problem for the
                 Laplace equation is reformulated as the problem of
                 polynomial approximation of analytic functions. An
                 explicit solution is given that allows to cloak larger
                 objects at a fixed distance from the cloaking device,
                 compared to previous explicit solutions. In the third
                 part we consider the active exterior cloaking problem
                 for the Helmholtz equation in 3D. Our method uses the
                 Green's formula and an addition theorem for spherical
                 outgoing waves to design devices that mimic the effect
                 of the single and double layer potentials in Green's
                 formula.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Helsing:2011:SSRa,
  author =       "Johan Helsing and Ross C. McPhedran and Graeme W.
                 Milton",
  title =        "Spectral super-resolution in metamaterial composites",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/13/11/115005",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1105.5012",
  abstract =     "We investigate the optical properties of periodic
                 composites containing metamaterial inclusions in a
                 normal material matrix. We consider the case where
                 these inclusions have sharp corners, and following
                 Hetherington and Thorpe, use analytic results to argue
                 that it is then possible to deduce the shape of the
                 corner (its included angle) by measurements of the
                 absorptance of such composites when the scale size of
                 the inclusions and period cell is much finer than the
                 wavelength. These analytic arguments are supported by
                 highly accurate numerical results for the effective
                 permittivity function of such composites as a function
                 of the permittivity ratio of inclusions to matrix. The
                 results show that this function has a continuous
                 spectral component with limits independent of the area
                 fraction of inclusions, and with the same limits for
                 both square and staggered square arrays.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "17",
  subject =      "Optics (physics.optics); Materials Science
                 (cond-mat.mtrl-sci); Analysis of PDEs (math.AP)",
}

@Article{Helsing:2011:SSRb,
  author =       "Johan Helsing and Ross C. McPhedran and Graeme W.
                 Milton",
  title =        "Spectral super-resolution in metamaterial composites",
  journal =      j-NEW-J-PHYS,
  volume =       "13",
  number =       "11",
  pages =        "115005",
  year =         "2011",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/13/11/115005",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Wed Oct 21 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://iopscience.iop.org/1367-2630/13/11/115005",
  acknowledgement = ack-gwm,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://stacks.iop.org/1367-2630/13/i=11/a=115005",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/13/11/115005/",
}

@Article{Kang:2011:SBV,
  author =       "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton",
  title =        "Sharp bounds on the volume fractions of two materials
                 in a two-dimensional body from electrical boundary
                 measurements: the translation method",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "4",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s00526-011-0462-3",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1105.0949",
  abstract =     "We deal with the problem of estimating the volume of
                 inclusions using a finite number of boundary
                 measurements in electrical impedance tomography. We
                 derive upper and lower bounds on the volume fractions
                 of inclusions, or more generally two phase mixtures,
                 using two boundary measurements in two dimensions.
                 These bounds are optimal in the sense that they are
                 attained by certain configurations with some boundary
                 data. We derive the bounds using the translation method
                 which uses classical variational principles with a null
                 Lagrangian. We then obtain necessary conditions for the
                 bounds to be attained and prove that these bounds are
                 attained by inclusions inside which the field is
                 uniform. When special boundary conditions are imposed
                 the bounds reduce to those obtained by Milton and these
                 in turn are shown here to reduce to those of
                 Capdeboscq-Vogelius in the limit when the volume
                 fraction tends to zero. The bounds of this paper, and
                 those of Milton, work for inclusions of arbitrary
                 volume fractions. We then perform some numerical
                 experiments to demonstrate how good these bounds are.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "34",
  subject =      "Materials Science (cond-mat.mtrl-sci); Mathematical
                 Physics (math-ph); Analysis of PDEs (math.AP); Medical
                 Physics (physics.med-ph)",
}

@Article{Milton:2011:BVF,
  author =       "Graeme Walter Milton and Loc Hoang Nguyen",
  title =        "Bounds on the volume fraction of $2$-phase,
                 $2$-dimensional elastic bodies and on (stress, strain)
                 pairs in composites",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "29",
  month =        aug,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.crme.2012.02.002",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1108.5764",
  abstract =     "Bounds are obtained on the volume fraction in a
                 two-dimensional body containing two elastically
                 isotropic materials with known bulk and shear moduli.
                 These bounds use information about the average stress
                 and strain fields, energy, determinant of the stress,
                 and determinant of the displacement gradient, which can
                 be determined from measurements of the traction and
                 displacement at the boundary. The bounds are sharp if
                 in each phase certain displacement field components are
                 constant. The inequalities we obtain also directly give
                 bounds on the possible (average stress, average strain)
                 pairs in a two-phase, two-dimensional, periodic or
                 statistically homogeneous composite",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "16",
  subject =      "Analysis of PDEs (math.AP); Materials Science
                 (cond-mat.mtrl-sci); Classical Physics
                 (physics.class-ph)",
}

@Article{Milton:2011:MHF,
  author =       "Graeme Milton and Pierre Seppecher",
  title =        "A metamaterial having a frequency dependent elasticity
                 tensor and a zero effective mass density",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "4",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1002/pssb.201084214",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1105.0941",
  abstract =     "Within the context of linear elasticity we show that a
                 two-terminal network of springs and masses, can respond
                 exactly the same as a normal spring, but with a
                 frequency dependent spring constant. As a consequence a
                 network of such springs can have a frequency dependent
                 effective elasticity tensor but zero effective mass
                 density. The internal masses influence the elasticity
                 tensor, but do not contribute to the effective mass
                 density at any frequency.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "5",
  subject =      "Classical Physics (physics.class-ph); Materials
                 Science (cond-mat.mtrl-sci); Mathematical Physics
                 (math-ph); Analysis of PDEs (math.AP)",
}

@Article{Milton:2011:UBE,
  author =       "Graeme W. Milton",
  title =        "Universal bounds on the electrical and elastic
                 response of two-phase bodies and their application to
                 bounding the volume fraction from boundary
                 measurements",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "4",
  month =        may,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jmps.2011.09.007",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1105.0954",
  abstract =     "Universal bounds on the electrical and elastic
                 response of two-phase (and multiphase) ellipsoidal or
                 parallelopipedic bodies have been obtained by
                 Nemat-Nasser and Hori. Here we show how their bounds
                 can be improved and extended to bodies of arbitrary
                 shape. Although our analysis is for two-phase bodies
                 with isotropic phases it can easily be extended to
                 multiphase bodies with anisotropic constituents. Our
                 two-phase bounds can be used in an inverse fashion to
                 bound the volume fractions occupied by the phases, and
                 for electrical conductivity reduce to those of
                 Capdeboscq and Vogelius when the volume fraction is
                 asymptotically small. Other volume fraction bounds
                 derived here utilize information obtained from thermal,
                 magnetic, dielectric or elastic responses. One bound on
                 the volume fraction can be obtained by simply immersing
                 the body in a water filled cylinder with a piston at
                 one end and measuring the change in water pressure when
                 the piston is displaced by a known small amount. This
                 bound may be particularly effective for estimating the
                 volume of cavities in a body. We also obtain new bounds
                 utilizing just one pair of (voltage, flux) electrical
                 measurements at the boundary of the body.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "5",
  subject =      "Materials Science (cond-mat.mtrl-sci); Mathematical
                 Physics (math-ph); Analysis of PDEs (math.AP);
                 Classical Physics (physics.class-ph)",
}

@Article{Ammari:2012:STN,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Spectral theory of a {Neumann--Poincar{\'e}}-type
                 operator and analysis of anomalous localized resonance
                 {II}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "20",
  month =        dec,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s00205-012-0605-5",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1212.5066",
  abstract =     "If a body of dielectric material is coated by a
                 plasmonic structure of negative dielectric constant
                 with nonzero loss parameter, then cloaking by anomalous
                 localized resonance (CALR) may occur as the loss
                 parameter tends to zero. The aim of this paper is to
                 investigate this phenomenon in two and three dimensions
                 when the coated structure is radial, and the core,
                 shell and matrix are isotropic materials. In two
                 dimensions, we show that if the real part of the
                 permittivity of the shell is -1 (under the assumption
                 that the permittivity of the background is 1), then
                 CALR takes place. If it is different from -1, then CALR
                 does not occur. In three dimensions, we show that CALR
                 does not occur. The analysis of this paper reveals that
                 occurrence of CALR is determined by the eigenvalue
                 distribution of the Neumann--Poincar{\'e}-type operator
                 associated with the structure.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Buckmann:2012:RTD,
  author =       "Tiemo B{\"u}ckmann and Muamer Kadic and Graeme W.
                 Milton and Michael Thiel and Martin Wegener",
  title =        "Realizability of three-dimensional dilational
                 materials",
  journal =      "????",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Fri May 25 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "In preparation.",
  acknowledgement = ack-gwm,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Not found in Web search on 26 November 2015.",
}

@Article{GuevaraVasquez:2012:MAT,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei",
  title =        "Mathematical analysis of the two dimensional active
                 exterior cloaking in the quasistatic regime",
  journal =      j-ANAL-MATH-PHYS,
  volume =       "2",
  number =       "3",
  pages =        "231--246",
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13324-012-0031-8",
  ISSN =         "1664-235X (print), 1664-2368 (electronic)",
  ISSN-L =       "1664-2368",
  MRclass =      "35J05 (30E10 31A05 35J25)",
  MRnumber =     "2958358",
  bibdate =      "Sat Apr 27 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s13324-012-0031-8",
  acknowledgement = ack-gwm,
  ajournal =     "Anal. Math. Phys.",
  fjournal =     "Analysis and Mathematical Physics",
  journal-URL =  "http://link.springer.com/journal/13324",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Kang:2012:BVFa,
  author =       "Hyeonbae Kang and Graeme W. Milton and Jenn-Nan Wang",
  title =        "Bounds on the volume fraction of the two-phase shallow
                 shell using one measurement",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "23",
  month =        apr,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1204.4962",
  abstract =     "We study the size estimate problem for the two-phase
                 shallow shell equations in this paper. Our aim is to
                 derive bounds on the volume fraction of each phase
                 assuming that the material properties of the two phases
                 are given. The approach in this paper is based on the
                 translation method. One of the key steps is to connect
                 the shallow shell equations to the thin plate
                 equation.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Kang:2012:BVFb,
  author =       "Hyeonbae Kang and Graeme W. Milton",
  title =        "Bounds on the volume fractions of two materials in a
                 three dimensional body from boundary measurements by
                 the translation method",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "4",
  month =        jun,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1206.0631",
  abstract =     "Using the translation method of Tartar, Murat, Lurie,
                 and Cherkaev bounds are derived on the volume occupied
                 by an inclusion in a three-dimensional conducting body.
                 They assume electrical impedance tomography
                 measurements have been made for three sets of pairs of
                 current flux and voltage measurements around the
                 boundary. Additionally the conductivity of the
                 inclusion and surrounding medium are assumed to be
                 known. If the boundary data (Dirichlet or Neumann) is
                 special, i.e. such that the fields inside the body
                 would be uniform were the body homogeneous, then the
                 bounds reduce to those of Milton and thus when the
                 volume fraction is small to those of Capdeboscq and
                 Vogelius.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "13",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Kang:2012:EIP,
  author =       "Hyeonbae Kang and Graeme Milton and Jenn-Nan Wang",
  title =        "Equivalence of inverse problems for {$2$D} elasticity
                 and for the thin plate with finite measurements and its
                 applications",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "17",
  month =        mar,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1203.3833",
  abstract =     "In this paper, we prove that the inverse problems for
                 2D elasticity and for the thin plate with boundary data
                 (finite or full measurements) are equivalent. Having
                 proved this equivalence, we can solve inverse problems
                 for the plate equation with boundary data by solving
                 the corresponding inverse problems for 2D elasticity,
                 and vice versa. For example, we can derive bounds on
                 the volume fraction of the two-phase thin plate from
                 the knowledge of one pair of boundary measurements
                 using the known result for 2D elasticity \cite{ml}.
                 Similarly, we give another approach to the size
                 estimate problem for the thin plate studied by Morassi,
                 Rosset, and Vessella \cite{mrv07, mrv09}.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "9",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Kang:2012:SBV,
  author =       "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton",
  title =        "Sharp bounds on the volume fractions of two materials
                 in a two-dimensional body from electrical boundary
                 measurements: the translation method",
  journal =      j-CALC-VAR-PARTIAL-DIFFER-EQU,
  volume =       "45",
  number =       "3--4",
  pages =        "367--401",
  month =        nov,
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s00526-011-0462-3",
  ISSN =         "0944-2669 (print), 1432-0835 (electronic)",
  ISSN-L =       "0944-2669",
  MRclass =      "35R30",
  MRnumber =     "2984137",
  bibdate =      "Thu Apr 28 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s00526-011-0462-3",
  acknowledgement = ack-gwm,
  fjournal =     "Calculus of Variations and Partial Differential
                 Equations",
  journal-URL =  "http://link.springer.com/journal/526;
                 http://www.springer.com/mathematics/analysis/journal/526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxyear =       "2011",
}

@Article{Milton:2012:ANB,
  author =       "Graeme Walter Milton",
  title =        "Adaptable nonlinear bimode metamaterials with rigid
                 bars, pivots, and actuators",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "1",
  month =        jun,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1206.0325",
  abstract =     "A large family of periodic planar non-linear bimode
                 metamaterials are constructed from rigid bars and
                 pivots. They are affine materials in the sense that
                 their macroscopic deformations are only affine
                 deformations: at large distances any deformation must
                 be close to an affine deformation. Bimode means that
                 the paths of all possible deformations of Bravais
                 lattices that preserve the periodicity of the lattice
                 lie on a two dimensional surface in the three
                 dimensional space of invariants describing the
                 deformation (excluding translations and rotations). By
                 adding two actuators inside a single microscopic cell
                 one can control the macroscopic deformation, which may
                 be useful for the design of adaptive structures. The
                 design of adaptable nonlinear affine trimode
                 metamaterials (for which the macroscopic deformations
                 lie within a three-dimensional region in the space of
                 invariants) is discussed, although their realization
                 remains an open problem. Examples are given of
                 non-affine unimode and non-affine bimode materials. In
                 these materials the deformation can vary from cell to
                 cell in such a way that the macroscopic deformation is
                 non-affine.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "13",
  subject =      "Materials Science (cond-mat.mtrl-sci); Mathematical
                 Physics (math-ph); Algebraic Geometry (math.AG)",
}

@Article{Milton:2012:BVF,
  author =       "Graeme W. Milton and Loc Hoang Nguyen",
  title =        "Bounds on the volume fraction of $2$-phase,
                 $2$-dimensional elastic bodies and on (stress, strain)
                 pairs in composites",
  journal =      j-C-R-MEC,
  volume =       "340",
  number =       "4--5",
  pages =        "193--204",
  year =         "2012",
  CODEN =        "CRMOC9",
  DOI =          "https://doi.org/10.1016/j.crme.2012.02.002",
  ISSN =         "1631-0721 (print), 1873-7234 (electronic)",
  ISSN-L =       "1631-0721",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1631072112000393",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Comptes Rendus M{'e}canique",
  journal-URL =  "http://www.sciencedirect.com/science/journal/16310721",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Recent Advances in Micromechanics of Materials, Edited
                 by M. Bornert, R. Brenner, O. Castelnau, P. Ponte
                 Casta{\~n}eda and P. Suquet.",
}

@Article{Milton:2012:CCM,
  author =       "Graeme Walter Milton",
  title =        "Complete characterization of the macroscopic
                 deformations of periodic unimode metamaterials of rigid
                 bars and pivots",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "28",
  month =        may,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1205.6213",
  abstract =     "A complete characterization is given of the possible
                 macroscopic deformations of periodic nonlinear affine
                 unimode metamaterials constructed from rigid bars and
                 pivots. The materials are affine in the sense that
                 their macroscopic deformations can only be affine
                 deformations: on a local level the deformation may vary
                 from cell to cell. Unimode means that macroscopically
                 the material can only deform along a one dimensional
                 trajectory in the six dimensional space of invariants
                 describing the deformation (excluding translations and
                 rotations). We show by explicit construction that any
                 continuous trajectory is realizable to an arbitrarily
                 high degree of approximation provided at all points
                 along the trajectory the geometry does not collapse to
                 a lower dimensional one. In particular, we present two
                 and three dimensional dilational materials having an
                 arbitrarily large flexibility window. These are perfect
                 auxetic materials for which a dilation is the only easy
                 mode of deformation. They are free to dilate to
                 arbitrarily large strain with zero bulk modulus.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "34",
  subject =      "Materials Science (cond-mat.mtrl-sci); Mathematical
                 Physics (math-ph); Algebraic Geometry (math.AG)",
}

@Article{Milton:2012:UBE,
  author =       "Graeme W. Milton",
  title =        "Universal bounds on the electrical and elastic
                 response of two-phase bodies and their application to
                 bounding the volume fraction from boundary
                 measurements",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "60",
  number =       "1",
  pages =        "139--155",
  year =         "2012",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2011.09.007",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74F15 (78A30 78A45)",
  MRnumber =     "2907437 (2012j:74058)",
  bibdate =      "Wed Aug 17 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509611001748",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Alali:2013:ECTa,
  author =       "Bacim Alali and Graeme W. Milton",
  title =        "Effective Conductivities of Thin-Interphase
                 Composites",
  journal =      "arXiv.org",
  volume =       "????",
  number =       "??",
  pages =        "??--??",
  day =          "12",
  month =        feb,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jmps.2013.08.022",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1302.2943",
  abstract =     "A method is presented for approximating the effective
                 conductivity of composite media with thin interphase
                 regions, which is exact to first order in the
                 interphase thickness. The approximations are
                 computationally efficient in the sense the fields need
                 to be computed only in a reference composite in which
                 the interphases have been replaced by perfect
                 interfaces. The results apply whether any two phases of
                 the composite are separated by a single interphase or
                 multiple interphases, whether the conductivities of the
                 composite phases are isotropic or anisotropic, and
                 whether the thickness of an interphase is uniform or
                 varies as a function of position. It is assumed that
                 the conductivities of the interphase materials have
                 intermediate values as opposed to very high or very low
                 conductivities.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "",
  subject =      "Analysis of PDEs (math.AP); Materials Science
                 (cond-mat.mtrl-sci)",
}

@Article{Alali:2013:ECTb,
  author =       "Bacim Alali and Graeme W. Milton",
  title =        "Effective conductivities of thin-interphase
                 composites",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "61",
  number =       "12",
  pages =        "2680--2691",
  year =         "2013",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2013.08.022",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74A50 (74F15)",
  MRnumber =     "3111584",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509613001750",
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Ammari:2013:ALRa,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Anomalous localized resonance using a folded geometry
                 in three dimensions",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        jan,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2013.0048",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1301.5712",
  abstract =     "If a body of dielectric material is coated by a
                 plasmonic structure of negative dielectric material
                 with nonzero loss parameter, then cloaking by anomalous
                 localized resonance (CALR) may occur as the loss
                 parameter tends to zero. It was proved in other papers
                 by authors that if the coated structure is circular
                 (2D) and dielectric constant of the shell is a negative
                 constant (with loss parameter), then CALR occurs, and
                 if the coated structure is spherical (3D), then CALR
                 does not occur. The aim of this paper is to show that
                 the CALR takes place if the spherical coated structure
                 has a specially designed anisotropic dielectric tensor.
                 The anisotropic dielectric tensor is designed by
                 unfolding a folded geometry.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Mathematical Physics (math-ph); Analysis of PDEs
                 (math.AP)",
}

@Article{Ammari:2013:ALRb,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Anomalous localized resonance using a folded geometry
                 in three dimensions",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "469",
  number =       "2154",
  pages =        "20130048",
  day =          "8",
  month =        jun,
  year =         "2013",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2013.0048",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Also available as arXiv:1301.5712 [math-ph].",
  URL =          "http://rspa.royalsocietypublishing.org/content/469/2154/20130048",
  abstract =     "If a body of dielectric material is coated by a
                 plasmonic structure of negative dielectric material
                 with non-zero loss parameter, then cloaking by
                 anomalous localized resonance (CALR) may occur as the
                 loss parameter tends to zero. If the coated structure
                 is circular (two dimensions) and the dielectric
                 constant of the shell is a negative constant (with loss
                 parameter), then CALR occurs, and if the coated
                 structure is spherical (three dimensions), then CALR
                 does not occur. The aim of this paper is to show that
                 CALR takes place if the spherical coated structure has
                 a specially designed anisotropic dielectric tensor. The
                 anisotropic dielectric tensor is designed by unfolding
                 a folded geometry.",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Ammari:2013:STN,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Spectral theory of a {Neumann--Poincar{\'e}}-type
                 operator and analysis of cloaking due to anomalous
                 localized resonance",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "208",
  number =       "2",
  pages =        "667--692",
  month =        may,
  year =         "2013",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s00205-012-0605-5",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "78A46 (35A08 35J25 78M22)",
  MRnumber =     "3035988",
  MRreviewer =   "Yoichi Miyazaki",
  bibdate =      "Fri Jan 25 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "See also arXiv:1109.0479 [math.AP].",
  URL =          "http://link.springer.com/article/10.1007/s00205-012-0605-5",
  acknowledgement = ack-gwm,
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Ammari:2013:STNII,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  title =        "Spectral theory of a {Neumann--Poincar{\'e}}-type
                 operator and analysis of cloaking due to anomalous
                 localized resonance {II}",
  journal =      "arXiv.org",
  volume =       "",
  number =       "",
  pages =        "",
  year =         "2013",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Fri Jan 25 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Submitted. Available as arXiv:1212.5066 [math.AP].",
  acknowledgement = ack-gwm,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2013:WEF,
  author =       "Marc Briane and (IRMAR, INSA Rennes), Graeme W. Milton
                 and Andrejs Treibergs",
  title =        "Which electric fields are realizable in conducting
                 materials?",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        jan,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1301.1613",
  abstract =     "In this paper we study the realizability of a given
                 smooth periodic gradient field $ \nabla u $ defined in
                 $ \RR^d $, in the sense of finding when one can obtain
                 a matrix conductivity $ \si $ such that $ \si \nabla u
                 $ is a divergence free current field. The construction
                 is shown to be always possible locally in $ \RR^d $
                 provided that $ \nabla u $ is non-vanishing. This
                 condition is also necessary in dimension two but not in
                 dimension three. In fact the realizability may fail for
                 non-regular gradient fields, and in general the
                 conductivity cannot be both periodic and isotropic.
                 However, using a dynamical systems approach the
                 isotropic realizability is proved to hold in the whole
                 space (without periodicity) under the assumption that
                 the gradient does not vanish anywhere. Moreover, a
                 sharp condition is obtained to ensure the isotropic
                 realizability in the torus. The realizability of a
                 matrix field is also investigated both in the periodic
                 case and in the laminate case. In this context the sign
                 of the matrix field determinant plays an essential role
                 according to the space dimension.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "19",
  subject =      "Analysis of PDEs (math.AP); Classical Physics
                 (physics.class-ph)",
}

@Article{Kang:2013:BSI,
  author =       "Hyeonbae Kang and Kyoungsun Kim and Hyundae Lee and
                 Xiaofei Li and Graeme W. Milton",
  title =        "Bounds on the size of an inclusion using the
                 translation method for two-dimensional complex
                 conductivity",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "9",
  month =        oct,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1310.2439",
  abstract =     "The size estimation problem in electrical impedance
                 tomography is considered when the conductivity is a
                 complex number and the body is two-dimensional. Upper
                 and lower bounds on the volume fraction of the unknown
                 inclusion embedded in the body are derived in terms of
                 two pairs of voltage and current data measured on the
                 boundary of the body. These bounds are derived using
                 the translation method. We also provide numerical
                 examples to show that these bounds are quite tight and
                 stable under measurement noise.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "15",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Kang:2013:BVF,
  author =       "Hyeonbae Kang and Graeme W. Milton",
  title =        "Bounds on the Volume Fractions of Two Materials in a
                 Three-Dimensional Body from Boundary Measurements by
                 the Translation Method",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "73",
  number =       "1",
  pages =        "475--492",
  month =        "????",
  year =         "2013",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/120879713",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "65N21 (35J25 35R30 45Q05)",
  MRnumber =     "3033159",
  MRreviewer =   "Mansur I. Ismailov",
  bibdate =      "Thu Mar 7 10:00:39 MST 2013",
  bibsource =    "http://epubs.siam.org/toc/smjmap/73/1;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/120879713",
  acknowledgement = ack-nhfb,
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  onlinedate =   "January 2013",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2013:ANB,
  author =       "Graeme Walter Milton",
  title =        "Adaptable nonlinear bimode metamaterials using rigid
                 bars, pivots, and actuators",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "61",
  number =       "7",
  pages =        "1561--1568",
  year =         "2013",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2012.08.012",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74N15 (74B20)",
  MRnumber =     "3063487",
  bibdate =      "Mon Oct 13 2014",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxtitle =      "Complete characterization of the macroscopic
                 deformations of periodic unimode metamaterials of rigid
                 bars and pivots",
}

@Article{Milton:2013:BVI,
  author =       "Graeme W. Milton and A. E. Thaler",
  title =        "Bounds on the volume of an inclusion in a body from a
                 complex conductivity measurement",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2013",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1306.6608",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2013:CCM,
  author =       "Graeme Walter Milton",
  title =        "Complete characterization of the macroscopic
                 deformations of periodic unimode metamaterials of rigid
                 bars and pivots",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "61",
  number =       "7",
  pages =        "1543--1560",
  year =         "2013",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2012.08.011",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74N15 (74B20 74K10)",
  MRnumber =     "3063486",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2013:SEHa,
  author =       "Graeme W. Milton and Ross C. McPhedran and Ari
                 Sihvola",
  title =        "The searchlight effect in hyperbolic materials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        feb,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1364/OE.21.014926",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1302.5980",
  abstract =     "The quasistatic field around a circular hole in a
                 two-dimensional hyperbolic medium is studied. As the
                 loss parameter goes to zero, it is found that the
                 electric field diverges along four lines each tangent
                 to the hole. In this limit, the power dissipated by the
                 field in the vicinity of these lines, per unit length
                 of the line, goes to zero but extends further and
                 further out so that the net power dissipated remains
                 finite. Additionally the interaction between
                 polarizable dipoles in a hyperbolic medium is studied.
                 It is shown that a dipole with small polarizability can
                 dramatically influence the dipole moment of a distant
                 polarizable dipole, if it is appropriately placed. We
                 call this the searchlight effect, as the enhancement
                 depends on the orientation of the line joining the
                 polarizable dipoles and can be varied by changing the
                 frequency. For some particular polarizabilities the
                 enhancement can actually increase the further the
                 polarizable dipoles are apart.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "21",
  subject =      "Optics (physics.optics); Mathematical Physics
                 (math-ph); Analysis of PDEs (math.AP)",
}

@Article{Milton:2013:SEHb,
  author =       "Graeme W. Milton and Ross C. McPhedran and Ari
                 Sihvola",
  title =        "The searchlight effect in hyperbolic materials",
  journal =      j-OPT-EXPRESS,
  volume =       "21",
  number =       "12",
  pages =        "14926--14942",
  day =          "17",
  month =        jun,
  year =         "2013",
  CODEN =        "OPEXFF",
  DOI =          "https://doi.org/10.1364/OE.21.014926",
  ISSN =         "1094-4087",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.osapublishing.org/abstract.cfm?uri=oe-21-12-14926",
  acknowledgement = ack-nhfb,
  fjournal =     "Optics Express",
  journal-URL =  "http://opticsexpress.org/Issue.cfm",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2013:SIG,
  author =       "Graeme W. Milton",
  title =        "Sharp inequalities that generalize the divergence
                 theorem: an extension of the notion of
                 quasi-convexity",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "469",
  number =       "2157",
  pages =        "20130075, 18",
  year =         "2013",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2013.0075",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "49J45 (49N15)",
  MRnumber =     "3078206",
  MRreviewer =   "Jos{\'e} Carlos Pedro Cardoso Matias",
  bibdate =      "Tue Nov 4 2014",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "See addendum \cite{Milton:2015:ASI}.",
  URL =          "http://rspa.royalsocietypublishing.org/content/469/2157/20130075",
  acknowledgement = ack-gwm,
  fjournal =     "Proceedings of The Royal Society of London. Series A.
                 Mathematical, Physical and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "18",
}

@Article{Milton:2013:SIW,
  author =       "Graeme W. Milton",
  title =        "Sharp inequalities which generalize the divergence
                 theorem --- an extension of the notion of
                 quasiconvexity, with an addendum",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "5",
  month =        feb,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1302.0942",
  abstract =     "Subject to suitable boundary conditions being imposed,
                 sharp inequalities are obtained on integrals over a
                 region $ \Omega $ of certain special quadratic
                 functions $ f(E) $ where $ E(x) $ derives from a
                 potential $ U(x) $. With $ E = \nabla U $ it is known
                 that such sharp inequalities can be obtained when $
                 f(E) $ is a quasiconvex function and when $U$ satisfies
                 affine boundary conditions (i.e., for some matrix $D$,
                 $ U = D x$ on $ \partial \Omega $). Here we allow for
                 other boundary conditions and for fields $E$ that
                 involve derivatives of a variety orders of $U$. We
                 define a notion of convexity that generalizes
                 quasiconvexity. $ Q_*$-convex quadratic functions are
                 introduced, characterized and an algorithm is given for
                 generating sharply $ Q_*$-convex functions. We
                 emphasize that this also solves the outstanding problem
                 of finding an algorithm for generating extremal
                 quasiconvex quadratic functions. We also treat
                 integrals over $ \Omega $ of special quadratic
                 functions $ g(J)$ where $ J(x)$ satisfies a
                 differential constraint involving derivatives with,
                 possibly, a variety of orders. The results generalize
                 an example of Kang and the author in three spatial
                 dimensions where $ J(x)$ is a $ 3 \times 3$ matrix
                 valued field satisfying $ \nabla \cdot J = 0$. In the
                 addendum the paper is clarified. Notably, much more
                 general boundary conditions are given under which sharp
                 lower bounds on the integrals of certain quadratic
                 functions of the fields can be obtained. As a
                 consequence, strict $ Q_*$-convexity is found to be an
                 appropriate condition to ensure uniqueness of the
                 solutions of a wide class of partial differential
                 equations with constant coefficients, in a given domain
                 $ \Omega $ with appropriate boundary conditions.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "23 + 7",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Thaler:2013:BVI,
  author =       "Andrew E. Thaler and Graeme W. Milton",
  title =        "Bounds on the volume of an inclusion in a body from a
                 complex conductivity measurement",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "27",
  month =        jun,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4310/CMS.2015.v13.n4.a2",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Communications in Mathematical Sciences
                 13(4): 863--892, 2015",
  URL =          "https://arxiv.org/abs/1306.6608",
  abstract =     "We derive bounds on the volume of an inclusion in a
                 body in two or three dimensions when the conductivities
                 of the inclusion and the surrounding body are complex
                 and assumed to be known. The bounds are derived in
                 terms of average values of the electric field, current,
                 and certain products of the electric field and current.
                 All of these average values are computed from a single
                 electrical impedance tomography measurement of the
                 voltage and current on the boundary of the body.
                 Additionally, the bounds are tight in the sense that at
                 least one of the bounds gives the exact volume of the
                 inclusion for certain geometries and boundary
                 conditions.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Analysis of PDEs (math.AP)",
}

@InProceedings{Vasquez:2013:SRP,
  author =       "Fernando {Guevara Vasquez} and Graeme W. Milton and
                 Daniel Onofrei and Pierre Seppecher",
  editor =       "Richard V. Craster and S{\'e}bastien Guenneau",
  booktitle =    "Acoustic Metamaterials: Negative Refraction, Imaging,
                 Lensing and Cloaking",
  title =        "Transformation elastodynamics and active exterior
                 acoustic cloaking",
  volume =       "166",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "289--318",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-94-007-4813-2_12",
  ISBN =         "94-007-4813-2",
  ISBN-13 =      "978-94-007-4813-2",
  LCCN =         "????",
  bibdate =      "Sat Apr 27 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Springer Series in Materials Science",
  URL =          "http://link.springer.com/chapter/10.1007/978-94-007-4813-2_12",
  acknowledgement = ack-gwm,
  book-DOI =     "https://doi.org/10.1007/978-94-007-4813-2",
  book-URL =     "http://www.springerlink.com/content/978-94-007-4813-2",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InProceedings{Ammari:2014:STN,
  author =       "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and
                 Hyundae Lee and Graeme W. Milton",
  editor =       "Plamen Stefanov and Andr{\'a}s Vasy and Maciej
                 Zworski",
  booktitle =    "{Inverse problems and applications: Conference in
                 honor of Gunther Uhlmann on Inverse Problems, June
                 18--22, 2012, University of California, Irvine, CA:
                 International Conference in honor of Gunther Uhlmann's
                 60th birthday on Inverse Problems and applications,
                 September 17--21, 2012, Yuquan Campus, Zhejiang
                 University, Hangzhou, China}",
  title =        "Spectral theory of a {Neumann--Poincar{\'e}}-type
                 operator and analysis of cloaking by anomalous
                 localized resonance {II}",
  volume =       "615",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  bookpages =    "vii + 309",
  pages =        "1--14",
  year =         "2014",
  DOI =          "https://doi.org/10.1090/conm/615/12244",
  ISBN =         "978-147-041-0-7-9-7 (print), 978-147-041-6-5-9-1
                 (online)",
  ISBN-13 =      "978-1-4704-1079-7 (print), 978-1-4704-1659-1
                 (online)",
  LCCN =         "QA378.5 .C665 2014",
  MRclass =      "35J25 (35A08 35B30 35Q60 35R30 78A48)",
  MRnumber =     "3221596",
  MRreviewer =   "Yoichi Miyazaki",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  series =       "Contemporary Mathematics",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1090/conm/615",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Briane:2014:IRC,
  author =       "Marc Briane and Graeme W. Milton",
  title =        "Isotropic realizability of current fields in {$ R^3
                 $}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "26",
  month =        sep,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1409.7658",
  abstract =     "This paper deals with the isotropic realizability of a
                 given regular divergence free field $j$ in $ R^3$ as a
                 current field, namely to know when $j$ can be written
                 as $ \sigma D_u$ for some isotropic conductivity $
                 \sigma $, and some gradient field $ D_u$. The local
                 isotropic realizability in $ R^3$ is obtained by
                 Frobenius' theorem provided that $j$ and $ \curl j$ are
                 orthogonal in $ R^3$. A counter-example shows that
                 Frobenius' condition is not sufficient to derive the
                 global isotropic realizability in $ R^3$. However,
                 assuming that ($j$, $ \curl j$, $ \j \times c u r l j$)
                 is an orthogonal basis of $ R^3$, an admissible
                 conductivity sigma is constructed from a combination of
                 the three dynamical flows along the directions $ j /
                 |j|$, $ \curl j / | \curl j|$ and $ (j / |j|^2) \times
                 \curl j$. When the field $j$ is periodic, the isotropic
                 realizability in the torus needs in addition a
                 boundedness assumption satisfied by the flow along the
                 third direction $ (j / |j|^2) \times \curl j$. Several
                 examples illustrate the sharpness of the realizability
                 conditions.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "22",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Briane:2014:WEF,
  author =       "Marc Briane and Graeme W. Milton and Andrejs
                 Treibergs",
  title =        "Which electric fields are realizable in conducting
                 materials?",
  journal =      j-MATH-MODEL-NUM-ANA,
  volume =       "48",
  number =       "2",
  pages =        "307--323",
  month =        mar # "\slash " # apr,
  year =         "2014",
  CODEN =        "RMMAEV",
  DOI =          "https://doi.org/10.1051/m2an/2013109",
  ISSN =         "0764-583X (print), 1290-3841 (electronic)",
  ISSN-L =       "0764-583X",
  MRclass =      "65N21 (78A30)",
  MRnumber =     "3177847",
  MRreviewer =   "Mansur I. Ismailov",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://journals.cambridge.org/abstract_S0764583X1300109X",
  acknowledgement = ack-nhfb,
  fjournal =     "ESAIM. Mathematical Modelling and Numerical Analysis",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=MZA;
                 http://www.esaim-m2an.org/component/issues",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Buckmann:2014:TDD,
  author =       "Tiemo B{\"u}ckmann and Robert Schittny and Michael
                 Thiel and Muamer Kadic and Graeme W. Milton and Martin
                 Wegener",
  title =        "On three-dimensional dilational elastic
                 metamaterials",
  journal =      j-NEW-J-PHYS,
  volume =       "16",
  number =       "3",
  pages =        "033032",
  month =        mar,
  year =         "2014",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/16/3/033032",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Sun Oct 12 2014",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://stacks.iop.org/1367-2630/16/i=3/a=033032",
  abstract =     "Dilational materials are stable, three-dimensional
                 isotropic auxetics with an ultimate Poisson's ratio of
                 1. Inspired by previous theoretical work, we design a
                 feasible blueprint for an artificial material, a
                 metamaterial, which approaches the ideal of a
                 dilational material. The main novelty of our work is
                 that we also fabricate and characterize corresponding
                 metamaterial samples. To reveal all modes in the
                 design, we calculate the phonon band structures. On
                 this basis, using cubic symmetry we can unambiguously
                 retrieve all different non-zero elements of the
                 rank-four effective metamaterial elasticity tensor from
                 which all effective elastic metamaterial properties
                 follow. While the elastic properties and the phase
                 velocity remain anisotropic, the effective Poisson's
                 ratio indeed becomes isotropic and approaches 1 in the
                 limit of small internal connections. This finding is
                 also supported by independent, static
                 continuum-mechanics calculations. In static experiments
                 on macroscopic polymer structures fabricated by
                 three-dimensional printing, we measure Poisson's ratios
                 as low as 0.8 in good agreement with the theory.
                 Microscopic samples are also presented.",
  acknowledgement = ack-gwm,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxURL =        "http://iopscience.iop.org/article/10.1088/1367-2630/16/3/033032/",
}

@Article{Harutyunyan:2014:EEE,
  author =       "Davit Harutyunyan and Graeme Walter Milton",
  title =        "Explicit examples of extremal quasiconvex quadratic
                 forms that are not polyconvex",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14",
  month =        mar,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1403.3718",
  abstract =     "We prove that if the associated fourth order tensor of
                 a quadratic form has a linear elastic cubic symmetry
                 then it is quasiconvex if and only if it is polyconvex,
                 i.e., a sum of convex and null-Lagrangian quadratic
                 forms. We prove that allowing for slightly less
                 symmetry, namely only cyclic and axis-reflection
                 symmetry, gives rise to a class of extremal quasiconvex
                 quadratic forms, that are not polyconvex. Non-affine
                 boundary conditions on the potential are identified
                 which allow one to obtain sharp bounds on the integrals
                 of these extremal quasiconvex quadratic forms of $
                 \nabla u $ over an arbitrary region.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "17",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Harutyunyan:2014:RBE,
  author =       "Davit Harutyunyan and Graeme Walter Milton",
  title =        "On the relation between extremal elasticity tensors
                 with orthotropic symmetry and extremal polynomials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "16",
  month =        nov,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1411.4216",
  abstract =     "We prove that an elasticity tensor with orthotropic
                 symmetry is extremal if the determinant of its acoustic
                 tensor is an extremal polynomial that is not a perfect
                 square.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "17",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Kang:2014:BSI,
  author =       "Hyeonbae Kang and Kyoungsun Kim and Hyundae Lee and
                 Xiaofei Li and Graeme W. Milton",
  title =        "Bounds on the Size of an Inclusion Using the
                 Translation Method for Two-Dimensional Complex
                 Conductivity",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "74",
  number =       "4",
  pages =        "939--958",
  month =        "????",
  year =         "2014",
  CODEN =        "SMJMAP",
  DOI =          "https://doi.org/10.1137/130940426",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "65N21 (45Q05)",
  MRnumber =     "3229662",
  MRreviewer =   "Barbara Zubik-Kowal",
  bibdate =      "Sat Sep 13 08:30:15 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/smjmap/74/4;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/130940426",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  onlinedate =   "January 2014",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Kang:2014:BVF,
  author =       "Hyeonbae Kang and Graeme W. Milton and Jenn-Nan Wang",
  title =        "Bounds on the volume fraction of the two-phase shallow
                 shell using one measurement",
  journal =      j-J-ELAST,
  volume =       "114",
  number =       "1",
  pages =        "41--53",
  month =        jan,
  year =         "2014",
  CODEN =        "JELSAY",
  DOI =          "https://doi.org/10.1007/s10659-012-9425-y",
  ISSN =         "0374-3535 (print), 1573-2681 (electronic)",
  ISSN-L =       "0374-3535",
  MRclass =      "74K25 (74E30 74G45 74G75 74K20)",
  MRnumber =     "3144824",
  MRreviewer =   "Victor A. Eremeyev",
  bibdate =      "Sat Apr 11 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://link.springer.com/article/10.1007/s10659-012-9425-y",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of Elasticity. The Physical and Mathematical
                 Science of Solids",
  journal-URL =  "http://link.springer.com/journal/10659",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxyear =       "2011",
}

@Article{Kochmann:2014:RBEa,
  author =       "Dennis M. Kochmann and Graeme W. Milton",
  title =        "Rigorous bounds on the effective moduli of composites
                 and inhomogeneous bodies with negative-stiffness
                 phases",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "16",
  month =        jun,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jmps.2014.06.010",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1401.4142",
  abstract =     "We review the theoretical bounds on the effective
                 properties of linear elastic inhomogeneous solids
                 (including composite materials) in the presence of
                 constituents having non-positive-definite elastic
                 moduli (so-called negative-stiffness phases). We show
                 that for statically stable bodies the classical
                 displacement-based variational principles for Dirichlet
                 and Neumann boundary problems hold but that the dual
                 variational principle for traction boundary problems
                 does not apply. We illustrate our findings by the
                 example of a coated spherical inclusion whose stability
                 conditions are obtained from the variational
                 principles. We further show that the classical Voigt
                 upper bound on the linear elastic moduli in multi-phase
                 inhomogeneous bodies and composites applies and that it
                 imposes a stability condition: overall stability
                 requires that the effective moduli do not surpass the
                 Voigt upper bound. This particularly implies that,
                 while the geometric constraints among constituents in a
                 composite can stabilize negative-stiffness phases, the
                 stabilization is insufficient to allow for extreme
                 overall static elastic moduli (exceeding those of the
                 constituents). Stronger bounds on the effective elastic
                 moduli of isotropic composites can be obtained from the
                 Hashin--Shtrikman variational inequalities, which are
                 also shown to hold in the presence of negative
                 stiffness.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Materials Science (cond-mat.mtrl-sci)",
}

@Article{Kochmann:2014:RBEb,
  author =       "Dennis M. Kochmann and Graeme W. Milton",
  title =        "Rigorous bounds on the effective moduli of composites
                 and inhomogeneous bodies with negative-stiffness
                 phases",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "71",
  pages =        "46--63",
  month =        nov,
  year =         "2014",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2014.06.010",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRclass =      "74Q15 (74A40 74B05)",
  MRnumber =     "3255662",
  MRreviewer =   "Alain Brillard",
  bibdate =      "Sat Jul 4 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022509614001367",
  acknowledgement = ack-gwm,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  xxyear =       "2015",
}

@Article{Meklachi:2014:SAL,
  author =       "Taoufik Meklachi and Graeme W. Milton and Daniel
                 Onofrei and Andrew E. Thaler and Gregory Funchess",
  title =        "Sensitivity of anomalous localized resonance phenomena
                 with respect to dissipation",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "26",
  month =        jun,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1406.7044",
  abstract =     "We analyze cloaking due to anomalous localized
                 resonance in the quasistatic regime in the case when a
                 general charge density distribution is brought near a
                 slab superlens. If the charge density distribution is
                 within a critical distance of the slab, then the power
                 dissipation within the slab blows up as certain
                 electrical dissipation parameters go to zero. The
                 potential remains bounded far away from the slab in
                 this limit, which leads to cloaking due to anomalous
                 localized resonance. On the other hand, if the charge
                 density distribution is further than this critical
                 distance from the slab, then the power dissipation
                 within the slab remains bounded and cloaking due to
                 anomalous localized resonance does not occur. The
                 critical distance is shown to strongly depend on the
                 the rate at which the dissipation outside of the slab
                 goes to zero.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "34",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Milton:2014:IRC,
  author =       "Graeme W. Milton and M. Briane",
  title =        "Isotropic realizability of current fields in {$
                 \mathbb {R}^3 $}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2014",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1409.7658",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2014:NET,
  author =       "Graeme Walter Milton",
  title =        "New examples of three-dimensional dilational
                 materials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        oct,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1410.4143",
  abstract =     "Two-dimensional dilational materials, for which the
                 only easy mode of deformation is a dilation are
                 reviewed and connections are drawn between models
                 previously proposed in the literature. Some models
                 which appear to be dilational materials, but which in
                 fact are not, are also discussed. Finally, four new
                 examples of three-dimensional dilational materials are
                 given.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "11",
  subject =      "Materials Science (cond-mat.mtrl-sci); Mathematical
                 Physics (math-ph)",
}

@Article{Milton:2014:SAL,
  author =       "Graeme W. Milton and T. Meklachi and D. Onofrei and A.
                 E. Thaler",
  title =        "Sensitivity of anomalous localized resonance phenomena
                 with respect to dissipation",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2014",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1406.7044",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Thaler:2014:EDVa,
  author =       "Andrew E. Thaler and Graeme W. Milton",
  title =        "Exact determination of the volume of an inclusion in a
                 body having constant shear modulus",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        jun,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/0266-5611/30/12/125008",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Inverse Problems 30 (2014) 1250008",
  URL =          "https://arxiv.org/abs/1406.6656",
  abstract =     "We derive an exact formula for the volume fraction of
                 an inclusion in a body when the inclusion and the body
                 are linearly elastic materials with the same shear
                 modulus. Our formula depends on an appropriate
                 measurement of the displacement and traction around the
                 boundary of the body. In particular, the boundary
                 conditions around the boundary of the body must be such
                 that they mimic the body being placed in an infinite
                 medium with an appropriate displacement applied at
                 infinity.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "16",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Thaler:2014:EDVb,
  author =       "Andrew E. Thaler and Graeme W. Milton",
  title =        "Exact determination of the volume of an inclusion in a
                 body having constant shear modulus",
  journal =      j-INVERSE-PROBLEMS,
  volume =       "30",
  number =       "12",
  pages =        "125008, 16",
  month =        dec,
  year =         "2014",
  CODEN =        "INPEEY",
  DOI =          "https://doi.org/10.1088/0266-5611/30/12/125008",
  ISSN =         "0266-5611 (print), 1361-6420 (electronic)",
  ISSN-L =       "0266-5611",
  MRclass =      "74B05 (35Q74 74G05)",
  MRnumber =     "3291122",
  MRreviewer =   "Rui Li",
  bibdate =      "Sat Apr 11 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://iopscience.iop.org/0266-5611/30/12/125008",
  abstract =     "We derive an exact formula for the volume fraction of
                 an inclusion in a body when the inclusion and the body
                 are linearly elastic materials with the same shear
                 modulus. Our formula depends on an appropriate
                 measurement of the displacement and traction around the
                 boundary of the body. In particular, the boundary
                 conditions around the boundary of the body must be such
                 that they mimic the body being placed in an infinite
                 medium with an appropriate displacement applied at
                 infinity.",
  acknowledgement = ack-gwm,
  fjournal =     "Inverse Problems. An International Journal on the
                 Theory and Practice of Inverse Problems, Inverse
                 Methods and Computerized Inversion of Data",
  journal-URL =  "http://iopscience.iop.org/0266-5611/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "16",
  xxURL =        "http://stacks.iop.org/0266-5611/30/i=12/a=125008",
  xxURL =        "http://iopscience.iop.org/article/10.1088/0266-5611/30/12/125008/",
}

@Article{Briane:2015:IRC,
  author =       "M. Briane and Graeme W. Milton",
  title =        "Isotropic Realizability of Current Fields in {$
                 \mathbb {R}^3 $}",
  journal =      j-SIAM-J-APPL-DYN-SYST,
  volume =       "14",
  number =       "2",
  pages =        "1165--1188",
  month =        "????",
  year =         "2015",
  CODEN =        "SJADAY",
  DOI =          "https://doi.org/10.1137/140989121",
  ISSN =         "1536-0040",
  MRclass =      "35B27 (35F40 37C10 78A30)",
  MRnumber =     "3359673",
  MRreviewer =   "Simon Labrunie",
  bibdate =      "Sat Aug 8 07:10:05 MDT 2015",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIADS/14/2;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjappldynsyst.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Dynamical Systems",
  journal-URL =  "http://epubs.siam.org/siads",
  onlinedate =   "January 2015",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Buckmann:2015:TDD,
  author =       "Tiemo B{\"u}ckmann and Robert Schittny and Michael
                 Thiel and Muamer Kadic and Graeme W. Milton and Martin
                 Wegener",
  title =        "On three-dimensional dilational elastic
                 metamaterials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "11",
  month =        oct,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/16/3/033032",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1310.3719",
  abstract =     "Dilational materials are stable three-dimensional
                 isotropic auxetics with an ultimate Poisson's ratio of
                 -1. We design, evaluate, fabricate, and characterize
                 crystalline metamaterials approaching this ideal. To
                 reveal all modes, we calculate the phonon band
                 structures. On this basis, using cubic symmetry, we can
                 unambiguously retrieve all different non-zero elements
                 of the rank-4 effective metamaterial elasticity tensor,
                 from which all effective elastic metamaterial
                 properties follow. While the elastic properties and the
                 phase velocity remain anisotropic, the effective
                 Poisson's ratio indeed becomes isotropic and approaches
                 -1 in the limit of small internal connections. This
                 finding is also supported by independent static
                 continuum-mechanics calculations. In static experiments
                 on macroscopic polymer structures fabricated by
                 three-dimensional printing, we measure Poisson's ratios
                 as low as -0.8 in good agreement with theory.
                 Microscopic samples are also presented.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "??",
  subject =      "Materials Science (cond-mat.mtrl-sci)",
}

@Article{Cassier:2015:ADN,
  author =       "Maxence Cassier and Aaron Welters and Graeme W.
                 Milton",
  title =        "Analyticity of the {Dirichlet}-to-{Neumann} map for
                 the time-harmonic {Maxwell}'s equations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        dec,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "This is a copy of chapter 4 in the book
                 \booktitle{Extending the Theory of Composites to Other
                 Areas of Science} edited by Graeme W. Milton, 2016,
                 Milton-Patton Publishers, ISBN-13 978-1-4835-6919-2.",
  URL =          "https://arxiv.org/abs/1512.05838",
  abstract =     "In this chapter of the book entitled,
                 \booktitle{0Extending the Theory of Composites to Other
                 Areas of Science} [edited by Graeme W. Milton, 2016] we
                 derive the analyticity properties of the
                 electromagnetic Dirichlet-to-Neumann map for the
                 time-harmonic Maxwell's equations for passive linear
                 multicomponent media. Moreover, we discuss the
                 connection of this map to Herglotz functions for
                 isotropic and anisotropic multicomponent composites.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "33",
  subject =      "Analysis of PDEs (math.AP); Mathematical Physics
                 (math-ph)",
}

@Article{Harutyunyan:2015:EEE,
  author =       "Davit Harutyunyan and Graeme Walter Milton",
  title =        "Explicit examples of extremal quasiconvex quadratic
                 forms that are not polyconvex",
  journal =      j-CALC-VAR-PARTIAL-DIFFER-EQU,
  volume =       "54",
  number =       "2",
  pages =        "1575--1589",
  month =        oct,
  year =         "2015",
  DOI =          "https://doi.org/10.1007/s00526-015-0836-z",
  ISSN =         "0944-2669 (print), 1432-0835 (electronic)",
  ISSN-L =       "0944-2669",
  MRclass =      "26B25 (35A23 49J40 74B05)",
  MRnumber =     "3396424",
  MRreviewer =   "Hans Arwed Keller",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "See also arXiv:1403.3718 [math.AP].",
  acknowledgement = ack-gwm,
  fjournal =     "Calculus of variations and partial differential
                 equations",
  journal-URL =  "http://www.springer.com/mathematics/analysis/journal/526",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Harutyunyan:2015:RBE,
  author =       "Davit Harutyunyan and Graeme W. Milton",
  title =        "On the relation between extremal elasticity tensors
                 with orthotropic symmetry and extremal polynomials",
  journal =      "arXiv.org",
  year =         "2015",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Nov 26 16:58:19 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1411.4216",
  abstract =     "We prove that an elasticity tensor with orthotropic
                 symmetry is extremal if the determinant of its acoustic
                 tensor is an extremal polynomial that is not a perfect
                 square.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "17",
  received =     "16 November 2014",
}

@Article{Harutyunyan:2015:TCA,
  author =       "Davit Harutyunyan and Graeme W. Milton",
  title =        "Towards characterization of all $ 3 \times 3 $
                 extremal quasiconvex quadratic forms",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14,",
  month =        dec,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1512.04174",
  abstract =     "Given a $ d \times d $ quasiconvex quadratic form, $ d
                 \geq 3 $, we prove that if the determinant of its
                 acoustic tensor is an irreducible extremal polynomial
                 that is not identically zero, then the form itself is
                 an extremal quasiconvex quadratic form, i.e. it loses
                 its quasiconvexity whenever a convex quadratic form is
                 subtracted from it. In the special case d=3, we
                 slightly weaken the condition, namely we prove, that if
                 the determinant of the acoustic tensor of the quadratic
                 form is an extremal polynomial that is not a perfect
                 square, then the form itself is an extremal quadratic
                 form. In the case d=3 we also prove, that if the
                 determinant of the acoustic tensor of the form is
                 identically zero, then the form is either an extremal
                 or polyconvex. Also, if the determinant of the acoustic
                 tensor of the form is a perfect square, then the form
                 is either extremal, polycovex, or is a sum of a
                 rank-one form and an extremal, whose acoustic tensor
                 determinant is identically zero. Here we use the notion
                 of extremality introduced by Milton in [???]",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "26",
  subject =      "Algebraic Geometry (math.AG); Analysis of PDEs
                 (math.AP)",
}

@Article{Mattei:2015:BRV,
  author =       "Ornella Mattei and Graeme W. Milton",
  title =        "Bounds for the response of viscoelastic composites
                 under antiplane loadings in the time domain",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        dec,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "To be published as a chapter of the book
                 \booktitle{Extending the Theory of Composites to Other
                 Areas of Science}, edited by G. W. Milton, and as a
                 part of the PhD thesis \booktitle{On bounding the
                 response of linear viscoelastic composites in the time
                 domain: The variational approach and the analytic
                 method} by O. Mattei, Universit{\`a} degli Studi di
                 Brescia.",
  URL =          "https://arxiv.org/abs/1602.03383",
  abstract =     "To derive bounds on the strain and stress response of
                 a two-component composite material with viscoelastic
                 phases, we revisit the so-called analytic method
                 (Bergman 1978), which allows one to approximate the
                 complex effective tensor, function of the ratio of the
                 component shear moduli, as the sum of poles weighted by
                 positive semidefinite residue matrices. The novelty of
                 this investigation lies in the application of such a
                 method, previously applied (Milton 1980; Bergman 1980)
                 to problems involving cyclic loadings in the frequency
                 domain, to derive bounds in the time domain for the
                 antiplane viscoelasticity case. The position of the
                 poles and the residues matrices are the variational
                 parameters of the problem: the aim is to determine such
                 parameters in order to have the minimum (or maximum)
                 response at any given moment in time. All the
                 information about the composite is translated for each
                 fixed pole configuration into constraints on the
                 residues, the so-called sum rules. The linearity of the
                 constraints, along with the observation that the
                 response at a fixed time is linear in the residues,
                 enables one to use the theory of linear programming to
                 reduce the problem to one involving relatively few
                 non-zero residues. Finally, bounds on the response are
                 obtained by numerically optimizing over the pole
                 positions. In the examples studied, the results turn
                 out to be very accurate estimates: if sufficient
                 information about the composite is available, the
                 bounds can be quite tight over the entire range of
                 time, allowing one to predict the transient behavior of
                 the composite. Furthermore, the bounds incorporating
                 the volume fractions (and possibly transverse isotropy)
                 can be extremely tight at certain specific times.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "33",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2015:ASC,
  author =       "Graeme W. Milton",
  title =        "The algebra of subspace collections and their
                 association with rational functions of several
                 variables",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2015",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Sun Nov 29 15:57:31 MST 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1504.08061",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://arxiv.org",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2015:ASI,
  author =       "Graeme W. Milton",
  title =        "Addendum to `{Sharp inequalities that generalize the
                 divergence theorem: an extension of the notion of
                 quasi-convexity' [MR3078206]}",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "471",
  number =       "2176",
  pages =        "20140886",
  day =          "4",
  month =        mar,
  year =         "2015",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2014.0886",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "49J45 (49N15)",
  MRnumber =     "3325210",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "See \cite{Milton:2013:SIG}.",
  URL =          "http://rspa.royalsocietypublishing.org/content/471/2176/20140886.abstract",
  abstract =     "The paper ``Sharp inequalities that generalize the
                 divergence theorem: an extension of the notion of
                 quasi-convexity'' published in Proc. R. Soc. A 2013,
                 469, 20130075 (doi:10.1098/rspa.2013.0075) is
                 clarified. Notably, much more general boundary
                 conditions are given under which sharp lower bounds on
                 the integrals of certain quadratic functions of the
                 fields can be obtained. More precisely, if the
                 quadratic form is Q*-convex then any solution of the
                 Euler--Lagrange equations will necessarily minimize the
                 integral. As a consequence, strict Q*-convexity is
                 found to be an appropriate condition to ensure
                 uniqueness of the solutions of a wide class of linear
                 Euler--Lagrange equations in a given domain $ \Omega $
                 with appropriate boundary conditions.",
  fjournal =     "Proceedings A",
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "8",
  remark =       "Bizarrely, this addendum has no assigned page
                 numbers!",
}

@Article{Milton:2015:NET,
  author =       "Graeme W. Milton",
  title =        "New examples of three-dimensional dilational
                 materials",
  journal =      j-PHYS-STATUS-SOLIDI-B-BASIC-RES,
  volume =       "252",
  number =       "7",
  pages =        "1426--1430",
  month =        jul,
  year =         "2015",
  CODEN =        "PSSBBD",
  DOI =          "https://doi.org/10.1002/pssb.201552297",
  ISSN =         "0370-1972 (print), 1521-3951 (electronic)",
  ISSN-L =       "0370-1972",
  bibdate =      "Sun Nov 15 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/pssb.201552297/abstract",
  acknowledgement = ack-gwm,
  fjournal =     "Physica Status Solidi. B, Basic Research",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3951/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2015:SAS,
  author =       "Graeme W. Milton",
  title =        "Superfunctions and the algebra of subspace collections
                 and their association with rational functions of
                 several complex variables",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        apr,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1504.08061",
  abstract =     "A natural connection between rational functions of
                 several real or complex variables, and subspace
                 collections is explored. A new class of function,
                 superfunctions, are introduced which are the
                 counterpart to functions at the level of subspace
                 collections. Operations on subspace collections are
                 found to correspond to various operations on rational
                 functions, such as addition, multiplication and
                 substitution. It is established that every rational
                 matrix valued function which is homogeneous of degree 1
                 can be generated from an appropriate, but not
                 necessarily unique, subspace collection: the mapping
                 from subspace collections to rational functions is
                 onto, but not one to one. For some applications
                 superfunctions may be more important than functions, as
                 they incorporate more information about the physical
                 problem, yet can be manipulated in much the same way as
                 functions. Previously subspace collections had been
                 introduced when there was an inner product on the
                 vector (or Hilbert) space, and appropriate subspaces
                 were mutually orthogonal. In that setting certain
                 normalization and reduction operations on subspace
                 collections led to a continued fraction expansion of
                 the associated function, which allowed one to bound the
                 function in terms of a set of weight matrices and
                 normalization matrices that are derived from series
                 expansions. Here we also initiate the theory of
                 normalization and reduction operations, appropriate
                 when there is no inner product on the space.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "60",
  subject =      "Algebraic Geometry (math.AG)",
}

@Article{Thaler:2015:BVI,
  author =       "Andrew E. Thaler and Graeme W. Milton",
  title =        "Bounds on the volume of an inclusion in a body from a
                 complex conductivity measurement",
  journal =      j-COMMUN-MATH-SCI,
  volume =       "13",
  number =       "4",
  pages =        "863--892",
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4310/CMS.2015.v13.n4.a2",
  ISSN =         "1539-6746 (print), 1945-0796 (electronic)",
  ISSN-L =       "1539-6746",
  MRclass =      "35Q60 (31A25 31B20 35J25)",
  MRnumber =     "3325081",
  MRreviewer =   "Shintaro Kondo",
  bibdate =      "Sat Apr 11 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-gwm,
  fjournal =     "Communications in Mathematical Sciences",
  journal-URL =  "http://ProjectEuclid.org/cms",
  journal-URL =  "http://www.intlpress.com/site/pub/pages/journals/items/cms/content/_home/index.html",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Bardsley:2016:CGB,
  author =       "Patrick Bardsley and Michael S. Primrose and Michael
                 Zhao and Jonathan Boyle and Nathan Briggs and Zoe Koch
                 and Graeme W. Milton",
  title =        "Criteria for guaranteed breakdown in two-phase
                 inhomogeneous bodies",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        apr,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1361-6420/aa76c5",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1604.04881",
  abstract =     "Lower bounds are obtained on the maximum field
                 strength in one or both phases in a body containing
                 two-phases. These bounds only incorporate boundary data
                 that can be obtained from measurements at the surface
                 of the body, and thus may be useful for determining if
                 breakdown has necessarily occurred in one of the
                 phases, or that some other nonlinearities have
                 occurred. It is assumed the response of the phases is
                 linear up to the point of electric, dielectric, or
                 elastic breakdown, or up to the point of the onset of
                 nonlinearities. These bounds are calculated for
                 conductivity, with one or two sets of boundary
                 conditions, for complex conductivity (as appropriate at
                 fixed frequency when the wavelength is much larger than
                 the body, i.e., for quasistatics), and for
                 two-dimensional elasticity. Sometimes the bounds are
                 optimal when the field is constant in one of the
                 phases, and using the algorithm of Kang, Kim, and
                 Milton (2012) a wide variety of inclusion shapes having
                 this property, for appropriately chosen bodies and
                 appropriate boundary conditions, are numerically
                 constructed. Such inclusions are known as $ E_\Omega
                 $-inclusions.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "30",
  pagecount =    "17",
  subject =      "Analysis of PDEs (math.AP)",
}

@InCollection{Cassier:2016:ADN,
  author =       "Aaron Welters Maxence Cassier and Graeme W. Milton",
  title =        "Analyticity of the {Dirichlet-to-Neumann} map for the
                 time-harmonic {Maxwell}'s equations",
  crossref =     "Milton:2016:ETC",
  chapter =      "4",
  pages =        "95--122",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Cassier:2016:BHF,
  author =       "Maxence Cassier and Graeme W. Milton",
  title =        "Bounds on {Herglotz} functions and fundamental limits
                 of broadband passive quasi-static cloaking",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "27",
  month =        oct,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1063/1.4989990",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1610.08592",
  abstract =     "Using a sum rule, we derive new bounds on Herglotz
                 functions that generalize those given in (Gustafson and
                 Sj{\"o}berg 2010) and (Bernland, Luger and Gustafson
                 2011). These bounds apply to a wide class of linear
                 passive systems such as electromagnetic passive
                 materials. Among these bounds, we describe the optimal
                 ones and also discuss their meaning in various physical
                 situations like in the case of a transparency window,
                 where we exhibit sharp bounds. Then, we apply these
                 bounds in the context of broadband passive cloaking in
                 the quasi-static regime to negatively answer the
                 following challenging question: is it possible to
                 construct a passive cloaking device that cloaks an
                 object over a whole frequency band? Our rigorous
                 approach, although limited to quasi-statics, gives
                 quantitative limitations on the cloaking effect over a
                 finite frequency range by providing inequalities on the
                 polarizabilty tensor associated with the cloaking
                 device. We emphasize that our results hold for a cloak
                 or object of any geometrical shape.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "36",
  subject =      "Mathematical Physics (math-ph); Analysis of PDEs
                 (math.AP); Complex Variables (math.CV)",
}

@Article{Cassier:2016:RAFa,
  author =       "Maxence Cassier and Aaron Welters and Graeme W.
                 Milton",
  title =        "A rigorous approach to the field recursion method for
                 two-component composites with isotropic phases",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "7",
  month =        jan,
  year =         "2016",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "This is a copy of chapter 10 in the book
                 \booktitle{Extending the Theory of Composites to Other
                 Areas of Science} edited by Graeme W. Milton, 2016,
                 Milton-Patton Publishers, ISBN-13 978-1-4835-6919-2.",
  URL =          "https://arxiv.org/abs/1601.01378",
  abstract =     "In this chapter of the book entitled,
                 \booktitle{Extending the Theory of Composites to Other
                 Areas of Science} [edited by Graeme W. Milton, 2016] we
                 give a rigorous derivation of the field equation
                 recursion method in the abstract theory of composites
                 to two-component composites with isotropic phases. This
                 method is of great interest since it has proven to be a
                 powerful tool in developing sharp bounds for the
                 effective tensor of a composite material. The reason is
                 that the effective tensor $ L_* $ can be interpreted in
                 the general framework of the abstract theory of
                 composites as the Z-operator on a certain orthogonal
                 Z(2) subspace collection. The base case of the
                 recursion starts with an orthogonal Z(2) subspace
                 collection on a Hilbert space H, the Z-problem, and the
                 associated Y-problem. We provide some new conditions
                 for the solvability of both the Z-problem and the
                 associated Y-problem. We also give explicit
                 representations of the associated Z-operator and
                 Y-operator and study their analytical properties. An
                 iteration method is then developed from a hierarchy of
                 subspace collections and their associated operators
                 which leads to a continued fraction representation of
                 the initial effective tensor $ L_* $.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "27",
  subject =      "Mathematical Physics (math-ph)",
}

@InCollection{Cassier:2016:RAFb,
  author =       "Aaron Welters Maxence Cassier and Graeme W. Milton",
  title =        "A rigorous approach to the field recursion method",
  crossref =     "Milton:2016:ETC",
  chapter =      "10",
  pages =        "287--308",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Harutyunyan:2016:HFHa,
  author =       "Davit Harutyunyan and Richard V. Craster and Graeme W.
                 Milton",
  title =        "High frequency homogenization for travelling waves in
                 periodic media",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "11",
  month =        feb,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2016.0066",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1602.03603",
  abstract =     "We consider high frequency homogenization in periodic
                 media for travelling waves of several different
                 equations: the wave equation for scalar-valued waves
                 such as acoustics; the wave equation for vector-valued
                 waves such as electromagnetism and elasticity; and a
                 system that encompasses the Schr{\"o}dinger equation.
                 This homogenization applies when the wavelength is of
                 the order of the size of the medium periodicity cell.
                 The travelling wave is assumed to be the sum of two
                 waves: a modulated Bloch carrier wave having crystal
                 wave vector $ B_k $ and frequency $ \omega_1 $ plus a
                 modulated Bloch carrier wave having crystal wave vector
                 $ B_m $ and frequency $ \omega_2 $. We derive effective
                 equations for the modulating functions, and then prove
                 that there is no coupling in the effective equations
                 between the two different waves both in the scalar and
                 the system cases. To be precise, we prove that there is
                 no coupling unless $ \omega_1 = \omega_2 $ and $ (B_-
                 B_m) \odot \Lambda \in 2 \pi \mathbb Z^d $, where $
                 \Lambda = (\lambda_1 \lambda_2 \ldots {} \lambda_d) $
                 is the periodicity cell of the medium and for any two
                 vectors $ a = (a_1, a_2, \ldots {}, a_d) $,$ b = (b_1,
                 b_2, \ldots {}, b_d) \in R^d $, the product $ a \cdot b
                 $ is defined to be the vector $ (a_1 b_1, a_2 b_2,
                 \ldots {}, a_d b_d) $. This last condition forces the
                 carrier waves to be equivalent Bloch waves meaning that
                 the coupling constants in the system of effective
                 equations vanish. We use two-scale analysis and some
                 new weak-convergence type lemmas. The analysis is not
                 at the same level of rigor as that of Allaire and
                 coworkers who use two-scale convergence theory to treat
                 the problem, but has the advantage of simplicity which
                 will allow it to be easily extended to the case where
                 there is degeneracy of the Bloch eigenvalue.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "30",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Harutyunyan:2016:HFHb,
  author =       "Davit Harutyunyan and Graeme W. Milton and Richard V.
                 Craster",
  title =        "High-frequency homogenization for travelling waves in
                 periodic media",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "472",
  number =       "2191",
  pages =        "20160066",
  month =        jul,
  year =         "2016",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2016.0066",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "35B27 (35C07 35L10)",
  MRnumber =     "3540732",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings A",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "18",
}

@Article{Harutyunyan:2016:IDCa,
  author =       "Davit Harutyunyan and Graeme W. Milton and Trevor J.
                 Dick and Justin Boyer",
  title =        "On ideal dynamic climbing ropes",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14",
  month =        nov,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1177/1754337116653539",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1611.04327",
  abstract =     "We consider the rope climber fall problem in two
                 different settings. The simplest formulation of the
                 problem is when the climber falls from a given altitude
                 and is attached to one end of the rope while the other
                 end of the rope is attached to the rock at a given
                 height. The problem is then finding the properties of
                 the rope for which the peak force felt by the climber
                 during the fall is minimal. The second problem of our
                 consideration is again minimizing the same quantity in
                 the presence of a carabiner. We will call such ropes
                 {\it mathematically ideal}. Given the height of the
                 carabiner, the initial height and the mass of the
                 climber, the length of the unstretched rope, and the
                 distance between the belayer and the carabineer, we
                 find the optimal (in the sense of minimized the peak
                 force to a given elongation) dynamic rope in the
                 framework of nonlinear elasticity. Wires of shape
                 memory materials have some of the desired features of
                 the tension-strain relation of a mathematically ideal
                 dynamic rope, namely a plateau in the tension over a
                 range of strains. With a suitable hysteresis loop, they
                 also absorb essentially all the energy from the fall,
                 thus making them an ideal rope in this sense too.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "21",
  subject =      "Optimization and Control (math.OC)",
}

@Article{Harutyunyan:2016:IDCb,
  author =       "David Harutyunyan and Graeme W. Milton and Trevor J.
                 Dick and Justin Boyer",
  title =        "On ideal dynamic climbing ropes",
  journal =      "Proceedings of the Institution of Mechanical
                 Engineers, Part P: Journal of Sports Engineering and
                 Technology",
  volume =       "230",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1177/1754337116653539",
  ISSN =         "1754-3371 (print), 1754-338X (electronic)",
  ISSN-L =       "1754-3371",
  bibdate =      "Wed Jul 6 09:28:16 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://pip.sagepub.com/content/early/2016/06/16/1754337116653539.abstract",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Check issue number and pages; not yet available on
                 journal Web site.",
}

@InCollection{Mattei:2016:BTR,
  author =       "Ornella Mattei and Graeme W. Milton",
  title =        "Bounds for the transient response of viscoelastic
                 composites",
  crossref =     "Milton:2016:ETC",
  chapter =      "6",
  pages =        "149--178",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Meklachi:2016:SAL,
  author =       "Taoufik Meklachi and Graeme W. Milton and Daniel
                 Onofrei and Andrew E. Thaler and Gregory Funchess",
  title =        "Sensitivity of anomalous localized resonance phenomena
                 with respect to dissipation",
  journal =      j-QUART-APPL-MATH,
  volume =       "74",
  number =       "2",
  pages =        "201--234",
  year =         "2016",
  CODEN =        "QAMAAY",
  DOI =          "https://doi.org/10.1090/qam/1408",
  ISSN =         "0033-569x (print), 1552-4485 (electronic)",
  ISSN-L =       "0033-569X",
  MRclass =      "35Q60 (35J15 78A48)",
  MRnumber =     "3505601",
  MRreviewer =   "Bruno Scheurer",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Quarterly of Applied Mathematics",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J641;
                 http://www.ams.org/journals/qam",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milgrom:2016:RLI,
  author =       "Mordehai Milgrom and Graeme W. Milton",
  title =        "The response of linear inhomogeneous systems to
                 coupled fields: Bounds and perturbation expansions",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "21",
  month =        feb,
  year =         "2016",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "To appear as Chapter 9 in the book
                 \booktitle{Extending the Theory of Composites to other
                 Areas of Science}, edited by Graeme W. Milton.",
  URL =          "https://arxiv.org/abs/1602.06487",
  abstract =     "We consider the response of a multicomponent body to n
                 fields, such as electric fields, magnetic fields,
                 temperature gradients, concentration gradients, etc.,
                 where each component, which is possibly anisotropic,
                 may cross couple the various fields with different
                 fluxes, such as electrical currents, electrical
                 displacement currents, magnetic induction fields,
                 energy fluxes, particle fluxes, etc. We obtain the form
                 of the perturbation expansions of the fields and
                 response tensor in powers of matrices which measure the
                 difference between each component tensor and a
                 homogeneous reference tensor L0. For the case of a
                 statistically homogeneous or periodic composite the
                 expansion coefficients can be expressed in terms of
                 positive semidefinite normalization matrices
                 alternating with positive semidefinite weight matrices,
                 which at each given level sum to the identity matrix.
                 In an appropriate basis the projection operators onto
                 the relevant subspaces can be expressed in block
                 tridiagonal form, where the blocks are functions of
                 these weight and normalization matrices. This leads to
                 continued fraction expansions for the effective tensor,
                 and by truncating the continued fraction at successive
                 levels one obtains a nested sequence of bounds on the
                 effective tensor incorporating successively more weight
                 and normalization matrices. The weight matrices and
                 normalization matrices can be calculated from the
                 series expansions of the fields which solve the
                 conductivity problem alone, without any couplings to
                 other fields, and then they can be used to obtain the
                 solution for the fields and effective tensor in coupled
                 field problems in composites.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "33",
  subject =      "Materials Science (cond-mat.mtrl-sci)",
}

@InCollection{Milgrom:2016:RSC,
  author =       "Mordehai Milgrom and Graeme W. Milton",
  title =        "The response of systems with coupled fields",
  crossref =     "Milton:2016:ETC",
  chapter =      "9",
  pages =        "255--286",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:AFM,
  author =       "Graeme W. Milton",
  title =        "Accelerating {FFT} methods for conducting composites",
  crossref =     "Milton:2016:ETC",
  chapter =      "8",
  pages =        "235--254",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2016:AMa,
  author =       "Graeme W. Milton",
  title =        "Analytic Materials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "18",
  month =        oct,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1098/rspa.2016.0613",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1610.06059",
  abstract =     "The theory of inhomogeneous analytic materials is
                 developed. These are materials where the coefficients
                 entering the equations involve analytic functions.
                 Three types of analytic materials are identified. The
                 first two types involve an integer $p$. If $p$ takes
                 its maximum value then we have a complete analytic
                 material. Otherwise it is incomplete analytic material
                 of rank $p$. For two-dimensional materials further
                 progress can be made in the identification of analytic
                 materials by using the well-known fact that a $
                 90^\circ $ rotation applied to a divergence free field
                 in a simply connected domain yields a curl-free field,
                 and this can then be expressed as the gradient of a
                 potential. Other exact results for the fields in
                 inhomogeneous media are reviewed. Also reviewed is the
                 subject of metamaterials, as these materials provide a
                 way of realizing desirable coefficients in the
                 equations.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "28",
  subject =      "Classical Physics (physics.class-ph)",
}

@Article{Milton:2016:AMb,
  author =       "Graeme W. Milton",
  title =        "Analytic materials",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "472",
  number =       "2195",
  pages =        "20160613:1--20160613:20",
  day =          "16",
  month =        nov,
  year =         "2016",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2016.0613",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "74G05 (35C05 35Q74 74A40 74E05 74Q05)",
  MRnumber =     "3592269",
  MRreviewer =   "Eugenia P\'erez",
  bibdate =      "Wed Nov 23 05:46:11 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/472/2195/20160613",
  abstract =     "The theory of inhomogeneous analytic materials is
                 developed. These are materials where the coefficients
                 entering the equations involve analytic functions.
                 Three types of analytic materials are identified. The
                 first two types involve an integer $p$. If $p$ takes
                 its maximum value, then we have a complete analytic
                 material. Otherwise, it is incomplete analytic material
                 of rank $p$. For two-dimensional materials, further
                 progress can be made in the identification of analytic
                 materials by using the well-known fact that a $
                 90^\circ $ rotation applied to a divergence-free field
                 in a simply connected domain yields a curl-free field,
                 and this can then be expressed as the gradient of a
                 potential. Other exact results for the fields in
                 inhomogeneous media are reviewed. Also reviewed is the
                 subject of metamaterials, as these materials provide a
                 way of realizing desirable coefficients in the
                 equations.",
  accepted =     "20 October 2016",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, and Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  received =     "1 August 2016",
}

@InCollection{Milton:2016:CAA,
  author =       "Graeme W. Milton",
  title =        "Composites and the associated abstract theory",
  crossref =     "Milton:2016:ETC",
  chapter =      "2",
  pages =        "47--76",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:CFL,
  author =       "Graeme W. Milton",
  title =        "Canonical forms for linear physics equations and key
                 identities",
  crossref =     "Milton:2016:ETC",
  chapter =      "1",
  pages =        "1--46",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:DMS,
  author =       "Graeme W. Milton",
  title =        "The desymmetrization method for solving the
                 {Schr{\"o}dinger} equation",
  crossref =     "Milton:2016:ETC",
  chapter =      "12",
  pages =        "319--336",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2016:FPN,
  author =       "Graeme W. Milton and Ornella Mattei",
  title =        "Field Patterns: A New Mathematical Object",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "18",
  month =        nov,
  year =         "2016",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Proc. R. Soc. A 20160819",
  URL =          "https://arxiv.org/abs/1611.06257;
                 https://arxiv.org/abs/1611.06257v1",
  abstract =     "Field patterns occur in space-time microstructures
                 such that a disturbance propagating along a
                 characteristic line does not evolve into a cascade of
                 disturbances, but rather concentrates on a pattern of
                 characteristic lines. This pattern is the field
                 pattern. In one spatial direction plus time, the field
                 patterns occur when the slope of the characteristics
                 is, in a sense, commensurate with the space-time
                 microstructure. Field patterns with different spatial
                 shifts do not generally interact, but rather evolve as
                 if they live in separate dimensions, as many dimensions
                 as the number of field patterns. Alternatively one can
                 view a collection as a multicomponent potential, with
                 as many components as the number of field patterns.
                 Presumably if one added a tiny nonlinear term to the
                 wave equation one would then see interactions between
                 these field patterns in the multidimensional space that
                 one can consider them to live, or between the different
                 field components of the multicomponent potential if one
                 views them that way. As a result of PT-symmetry many of
                 the complex eigenvalues of an appropriately defined
                 transfer matrix have unit norm and hence the
                 corresponding eigenvectors correspond to propagating
                 modes. There are also modes that blow up exponentially
                 with time.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "31",
  subject =      "Optics (physics.optics); Mathematical Physics
                 (math-ph)",
}

@InCollection{Milton:2016:GFS,
  author =       "Graeme W. Milton",
  title =        "{Green}'s functions for self-adjoint and
                 non-self-adjoint operators",
  crossref =     "Milton:2016:ETC",
  chapter =      "14",
  pages =        "355--368",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:IP,
  author =       "Graeme W. Milton",
  title =        "The inverse problem",
  crossref =     "Milton:2016:ETC",
  chapter =      "5",
  pages =        "123--148",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:NPB,
  author =       "Graeme W. Milton",
  title =        "A new perspective on boundary value problems",
  crossref =     "Milton:2016:ETC",
  chapter =      "3",
  pages =        "77--94",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2016:PEE,
  author =       "Graeme W. Milton and Marc Briane and Davit
                 Harutyunyan",
  title =        "On the possible effective elasticity tensors of
                 $2$-dimensional and $3$-dimensional printed materials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        jun,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2140/memocs.2017.5.41",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Math. Mech. Compl. Sys. 5 (2017) 41-94",
  URL =          "https://arxiv.org/abs/1606.03305",
  abstract =     "The set {$ {\rm GU}_f $} of possible effective elastic
                 tensors of composites built from two materials with
                 elasticity tensors $ \BC_1 > 0 $ and $ \BC_2 = 0 $
                 comprising the set $ U = \{ \BC_1, \BC_2 \} $ and mixed
                 in proportions $f$ and $ 1 - f$ is partly
                 characterized. The material with tensor $ \BC_2 = 0$
                 corresponds to a material which is void. (For technical
                 reasons $ \BC_2$ is actually taken to be nonzero and we
                 take the limit $ \BC_2 \to 0$). Specifically, recalling
                 that {$ {\rm GU}_f$} is completely characterized
                 through minimums of sums of energies, involving a set
                 of applied strains, and complementary energies,
                 involving a set of applied stresses, we provide
                 descriptions of microgeometries that in appropriate
                 limits achieve the minimums in many cases. In these
                 cases the calculation of the minimum is reduced to a
                 finite dimensional minimization problem that can be
                 done numerically. Each microgeometry consists of a
                 union of walls in appropriate directions, where the
                 material in the wall is an appropriate p-mode material,
                 that is easily compliant to $ p \leq 5$ independent
                 applied strains, yet supports any stress in the
                 orthogonal space. Thus the material can easily slip in
                 certain directions along the walls. The region outside
                 the walls contains ``complementary Avellaneda
                 material'' which is a hierarchical laminate which",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "39",
  subject =      "Materials Science (cond-mat.mtrl-sci); Analysis of
                 PDEs (math.AP)",
}

@InCollection{Milton:2016:PFT,
  author =       "Graeme W. Milton",
  title =        "{Projection Functional Theory} for finding excited
                 states",
  crossref =     "Milton:2016:ETC",
  chapter =      "11",
  pages =        "309--318",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@InCollection{Milton:2016:SAS,
  author =       "Graeme W. Milton",
  title =        "Superfunctions and the algebra of subspace
                 collections",
  crossref =     "Milton:2016:ETC",
  chapter =      "7",
  pages =        "179--234",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2016:TCC,
  author =       "Graeme W. Milton and Davit Harutyunyan and Marc
                 Briane",
  title =        "Towards a complete characterization of the effective
                 elasticity tensors of mixtures of an elastic phase and
                 an almost rigid phase",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "12",
  month =        jun,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2140/memocs.2017.5.95",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Math. Mech. Compl. Sys. 5 (2017)
                 95--113.",
  URL =          "https://arxiv.org/abs/1606.03722",
  abstract =     "The set {$ {\rm GU}_f $} of possible effective elastic
                 tensors of composites built from two materials with
                 positive definite elasticity tensors $ \BC_1 $ and $
                 \BC_2 = \Gd \BC_0 $ comprising the set $ U = \{ \BC_1,
                 \Gd \BC_0 \} $ and mixed in proportions f and 1 - f is
                 partly characterized in the limit $ \Gd \to \infty $.
                 The material with tensor $ \BC_2 $ corresponds to a
                 material which (for technical reasons) is almost rigid
                 in the limit $ \Gd \to \infty $. The paper, and the
                 underlying microgeometries, have many aspects in common
                 with the companion paper \booktitle{On the possible
                 effective elasticity tensors of 2-dimensional printed
                 materials}. The chief difference is that one has a
                 different algebraic problem to solve: determining the
                 subspaces of stress fields for which the thin walled
                 structures can be rigid, rather than determining, as in
                 the companion paper, the subspaces of strain fields for
                 which the thin walled structure is compliant. Recalling
                 that {$ {\rm GU}_f $} is completely characterized
                 through minimums of sums of energies, involving a set
                 of applied strains, and complementary energies,
                 involving a set of applied stresses, we provide
                 descriptions of microgeometries that in appropriate
                 limits achieve the minimums in many cases. In these
                 cases the calculation of the minimum is reduced to a
                 finite dimensional minimization problem that can be
                 done numerically. Each microgeometry consists of a
                 union of walls in appropriate directions, where the
                 material in the wall is an appropriate p-mode material,
                 that is almost rigid to $ 6 - p \leq 5 $ independent
                 applied stresses, yet is compliant to any strain in the
                 orthogonal space. Thus the walls, by themselves, can
                 support stress with almost no deformation. The region
                 outside the walls contains ``Avellaneda material'' that
                 is a hierarchical laminate which minimizes an
                 appropriate sum of elastic energies.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "13",
  subject =      "Materials Science (cond-mat.mtrl-sci)",
}

@InCollection{Milton:2016:VPC,
  author =       "Graeme W. Milton",
  title =        "Variational principles and {$ Q_C^* $}-convex
                 functions for {Schr{\"o}dinger}'s equation",
  crossref =     "Milton:2016:ETC",
  chapter =      "13",
  pages =        "337--354",
  year =         "2016",
  bibdate =      "Thu Aug 17 18:16:17 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Bardsley:2017:CGB,
  author =       "Patrick Bardsley and Michael S. Primrose and Michael
                 Zhao and Jonathan Boyle and Nathan Briggs and Zoe Koch
                 and Graeme W. Milton",
  title =        "Criteria for guaranteed breakdown in two-phase
                 inhomogeneous bodies",
  journal =      j-INVERSE-PROBLEMS,
  volume =       "33",
  number =       "8",
  pages =        "085006",
  month =        aug,
  year =         "2017",
  CODEN =        "INPEEY",
  DOI =          "https://doi.org/10.1088/1361-6420/aa76c5",
  ISSN =         "0266-5611 (print), 1361-6420 (electronic)",
  ISSN-L =       "0266-5611",
  MRclass =      "78A48",
  MRnumber =     "3668806",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Inverse Problems. An International Journal on the
                 Theory and Practice of Inverse Problems, Inverse
                 Methods and Computerized Inversion of Data",
  journal-URL =  "http://iopscience.iop.org/0266-5611/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "31",
}

@Article{Cassier:2017:BHF,
  author =       "Maxence Cassier and Graeme W. Milton",
  title =        "Bounds on {Herglotz} functions and fundamental limits
                 of broadband passive quasistatic cloaking",
  journal =      j-J-MATH-PHYS,
  volume =       "58",
  number =       "7",
  pages =        "071504",
  month =        jul,
  year =         "2017",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.4989990",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "81V19",
  MRnumber =     "3671165",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "27",
}

@Article{Harutyunyan:2017:RBE,
  author =       "Davit Harutyunyan and Graeme Walter Milton",
  title =        "On the relation between extremal elasticity tensors
                 with orthotropic symmetry and extremal polynomials",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "223",
  number =       "1",
  pages =        "199--212",
  month =        jan,
  year =         "2017",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/s00205-016-1034-7",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  MRclass =      "74B05",
  MRnumber =     "3590372",
  MRreviewer =   "Haigang Li",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for Rational Mechanics and Analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Harutyunyan:2017:TCA,
  author =       "Davit Harutyunyan and Graeme Walter Milton",
  title =        "Towards characterization of all $ 3 \times 3 $
                 extremal quasiconvex quadratic forms",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "70",
  number =       "11",
  pages =        "2164--2190",
  month =        nov,
  year =         "2017",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.21699",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "74H55 (49Q12)",
  MRnumber =     "3707491",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Mattei:2017:FPB,
  author =       "Ornella Mattei and Graeme W. Milton",
  title =        "Field patterns without blow up",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "27",
  month =        apr,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1088/1367-2630/aa847d",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1705.00539",
  abstract =     "Field patterns, first proposed by the authors in
                 [Milton, Mattei. Proc R Soc A. 2017], are orderly
                 patterns of characteristic lines that arise in specific
                 space-time microstructures whose geometry in one
                 spatial dimension plus time is somehow commensurate to
                 the slope of the characteristic lines. In particular,
                 in [Milton, Mattei. Proc R Soc A. 2017] the authors
                 propose two examples of space-time geometries in which
                 field patterns occur: they are two-phase
                 microstructures in which rectangular space-time
                 inclusions of one material are embedded in another
                 material. After a sufficient large period of time, the
                 field patterns in both microstructures have local
                 periodicity both in time and space, due to the
                 PT-symmetry of the chosen space-time geometries. This
                 allows one to focus only on solving the problem on a
                 discrete network and to define a suitable transfer
                 matrix that, given the solution at a certain time,
                 provides the solution after one time period. Many of
                 the eigenvalues of this transfer matrix have unit norm
                 and hence the corresponding eigenvectors correspond to
                 propagating modes. However, there are also modes that
                 blow up exponentially with time coupled with modes that
                 decrease exponentially with time. The question as to
                 whether there are space-time microstructures such that
                 the transfer matrix only has eigenvalues on the unit
                 circle finds answer in this paper where we see that
                 certain space-time checkerboards have the property that
                 all the modes are propagating modes, within a certain
                 range of the material parameters. Interestingly, when
                 there is no blow-up, the waves generated by an
                 instantaneous disturbance at a point look like shocks
                 with a wake of oscillatory waves. This sets an arrow of
                 time in the sense that it would be extremely difficult
                 to produce the initial conditions necessary to create
                 the corresponding time-reversed waves.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "20",
  subject =      "Classical Physics (physics.class-ph); Mathematical
                 Physics (math-ph); Optics (physics.optics)",
}

@Article{Mattei:2017:FPNa,
  author =       "Ornella Mattei and Graeme W. Milton",
  title =        "Field patterns: a new type of wave with infinitely
                 degenerate band structure",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "6",
  month =        jul,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1209/0295-5075/120/54003",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1707.05756",
  abstract =     "Field pattern materials (FP-materials) are space-time
                 composites with PT-symmetry in which the
                 one-dimensional- spatial distribution of the
                 constituents changes in time in such a special manner
                 to give rise to a new type of waves, which we call
                 field pattern waves (FP-waves) [G. W. Milton and O.
                 Mattei, Proc. R. Soc. A 473, 20160819 (2017), O. Mattei
                 and G. W. Milton, arXiv:1705.00539 (2017)].
                 Specifically, due to the special periodic space-time
                 geometry of these materials, when an instantaneous
                 disturbance propagates through the system, the
                 branching of the characteristic lines at the space-time
                 interfaces between phases does not lead to a chaotic
                 cascade of disturbances but concentrates on an orderly
                 pattern of disturbances: this is the field pattern. By
                 applying Bloch--Floquet theory we find that the
                 dispersion diagrams associated with these FP-materials
                 are infinitely degenerate: associated with each point
                 on the dispersion diagram is an infinite space of Bloch
                 functions, a basis for which are generalized functions
                 each concentrated on a field pattern, paramaterized by
                 a variable that we call the launch parameter. The
                 dynamics separates into independent dynamics on the
                 different field patterns, each with the same dispersion
                 relation.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "8",
  subject =      "Classical Physics (physics.class-ph)",
}

@Article{Mattei:2017:FPNb,
  author =       "Ornella Mattei and Graeme W. Milton",
  title =        "Field patterns: A new type of wave with infinitely
                 degenerate band structure",
  journal =      j-EUROPHYS-LETT,
  volume =       "120",
  number =       "5",
  pages =        "54003:1--54003:6",
  year =         "2017",
  CODEN =        "EULEEJ",
  DOI =          "https://doi.org/10.1209/0295-5075/120/54003",
  ISSN =         "0295-5075 (print), 1286-4854 (electronic)",
  ISSN-L =       "0295-5075",
  bibdate =      "Thu Apr 12 10:40:56 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://stacks.iop.org/0295-5075/120/i=5/a=54003",
  abstract =     "Field pattern materials (FP-materials) are space-time
                 composites with PT-symmetry in which the
                 one-dimensional-spatial distribution of the
                 constituents changes in time in such a special manner
                 to give rise to a new type of waves, which we call
                 field pattern waves (FP-waves) (Milton G. W. and Mattei
                 O., Proc. R. Soc. A, 473 (2017) 20160819; Mattei O. and
                 Milton G. W., New J. Phys., 19 (2017) 093022).
                 Specifically, due to the special periodic space-time
                 geometry of these materials, when an instantaneous
                 disturbance propagates through the system, the
                 branching of the characteristic lines at the space-time
                 interfaces between phases does not lead to a chaotic
                 cascade of disturbances but concentrates on an orderly
                 pattern of disturbances: this is the field pattern. In
                 this letter, by applying Bloch--Floquet theory, we show
                 that the dispersion diagrams associated with these
                 FP-materials are infinitely degenerate: associated with
                 each point on the dispersion diagram is an infinite
                 space of Bloch functions. Each generalized function is
                 concentrated on a specific field pattern, each
                 parameterized by a variable that we call the launch
                 parameter. The dynamics separates into independent
                 dynamics on the different field patterns, each with the
                 same dispersion relation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Europhysics Letters",
  journal-URL =  "http://iopscience.iop.org/0295-5075",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "6",
}

@Article{Milton:2017:AET,
  author =       "Graeme W. Milton",
  title =        "Approximating the effective tensor as a function of
                 the component tensors in two-dimensional composites of
                 two anisotropic phases",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "7",
  month =        may,
  year =         "2017",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1705.02633",
  abstract =     "A conducting two-dimensional periodic composite of two
                 anisotropic phases with anisotropic, not necessarily
                 symmetric, conductivity tensors is considered. By
                 finding approximate representations for the relevant
                 operators, an approximation formula is derived for the
                 effective matrix valued conductivity as a function of
                 the two matrix valued conductivity tensors of the
                 phases. This approximation should converge to the exact
                 effective conductivity function as the number of basis
                 fields tends to infinity. Using the approximations for
                 the relevant operators one can also directly obtain
                 approximations, with the same geometry, for the
                 effective tensors of coupled field problems, including
                 elasticity, piezoelectricity, and thermoelectricity. To
                 avoid technical complications we assume that the phase
                 geometry is symmetric under reflection about one of the
                 centerlines of the unit cell.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "56",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2017:BCP,
  author =       "Graeme W. Milton",
  title =        "Bounds on complex polarizabilities and a new
                 perspective on scattering by a lossy inclusion",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "22",
  month =        apr,
  year =         "2017",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Published in Phys. Rev. B 96, 104206 (2017)",
  URL =          "https://arxiv.org/abs/1704.06832",
  abstract =     "Here we obtain explicit formulae for bounds on the
                 complex electrical polarizability at a given frequency
                 of an inclusion with known volume that follow directly
                 from the quasistatic bounds of Bergman and Milton on
                 the effective complex dielectric constant of a
                 two-phase medium. We also describe how analogous bounds
                 on the orientationally averaged bulk and shear
                 polarizabilities at a given frequency can be obtained
                 from bounds on the effective complex bulk and shear
                 moduli of a two-phase medium obtained by Milton,
                 Gibiansky and Berryman, using the quasistatic
                 variational principles of Cherkaev and Gibiansky. We
                 also show how the polarizability problem and the
                 acoustic scattering problem can both be reformulated in
                 an abstract setting as ``Y -problems''. In the acoustic
                 scattering context, to avoid explicit introduction of
                 the Sommerfeld radiation condition, we introduce
                 auxilliary fields at infinity and an appropriate
                 ``constitutive law'' there, which forces the Sommerfeld
                 radiation condition to hold. As a consequence we obtain
                 minimization variational principles for acoustic
                 scattering that can be used to obtain bounds on the
                 complex backwards scattering amplitude. Some explicit
                 elementary bounds are given.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "27",
  subject =      "Mathematical Physics (math-ph)",
}

@Article{Milton:2017:ERG,
  author =       "Graeme W. Milton and Daniel Onofrei",
  title =        "Exact relations for {Green}'s functions in linear
                 {PDE} and boundary field equalities: a generalization
                 of conservation laws",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        dec,
  year =         "2017",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1712.03597",
  abstract =     "Many physics problems have $ J(x) = L(x)E(x) + h(x) $,
                 source $ h(x) $, fields $E$, $J$ satisfying
                 differential constraints, symbolized by $ E \in E$, $ J
                 \in J$ where $E$, $J$ are orthogonal spaces. If L(x)
                 takes values in certain nonlinear manifolds $M$, and
                 coercivity, boundedness hold, then the Green's function
                 satisfies exact identities. We also link Green's
                 functions of different problems. The analysis, based on
                 the theory of exact relations for composites, does not
                 assume microscale variations in $ L(x)$, and allows for
                 other equations, such as for waves in lossy media. For
                 bodies $ \Omega $, in which $ L(x) \in M$, the
                 Dirichlet-to-Neumann map satisfies boundary field
                 equalities. These generalize the notion of conservation
                 laws: the constraints on the fields inside $ \Omega $
                 give identities satisfied by the boundary fields, and
                 provide extra constraints on the interior fields. A
                 consequence is this: if a matrix valued field $ Q(x)$
                 with $ \nabla \cdot Q = 0$ takes values in a set B
                 (independent of x) that lies on a nonlinear manifold,
                 we find conditions on the manifold, and on B, that with
                 appropriate conditions on the boundary fluxes $ q(x) =
                 n(x) \cdot Q(x)$ (where $ n(x)$ is the outwards normal
                 to $ \partial \Omega $) force $ Q(x)$ within $ \Omega $
                 to take values in a subspace $D$. This forces $ q(x)$
                 to take values in $ n(x) \cdot D$. We find there are
                 additional divergence free fields inside $ \Omega $
                 that in turn generate additional boundary field
                 equalities. There exist partial Null-Lagrangians,
                 functionals $ F(w, \nabla w)$ of a vector potential $w$
                 and its gradient, that act as null-Lagrangians when $
                 \nabla w$ is constrained for $ x \in \Omega $ to take
                 values in certain sets $A$, of appropriate non-linear
                 manifolds, and when w satisfies appropriate boundary
                 conditions. The extension to certain non-linear
                 minimization problems is also sketched.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "34",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Milton:2017:FPN,
  author =       "Graeme W. Milton and Ornella Mattei",
  title =        "Field patterns: a new mathematical object",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "473",
  number =       "2198",
  pages =        "20160819",
  month =        feb,
  year =         "2017",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2016.0819",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  MRclass =      "83C10",
  MRnumber =     "3621490",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings A",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "26",
}

@Article{Milton:2017:NOP,
  author =       "Graeme W. Milton and Mohamed Camar-Eddine",
  title =        "Near optimal pentamodes as a tool for guiding stress
                 while minimizing compliance in {3$D$}-printed
                 materials: a complete solution to the weak
                 {$G$}-closure problem for {3$D$}-printed materials",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "6",
  month =        dec,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jmps.2018.02.003",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1712.02292",
  abstract =     "For a composite containing one isotropic elastic
                 material, with positive Lame moduli, and void, with the
                 elastic material occupying a prescribed volume fraction
                 $f$, and with the composite being subject to an average
                 stress, $ \sigma^0$, Gibiansky, Cherkaev, and Allaire
                 provided a sharp lower bound $ W^f(\sigma^0)$ on the
                 minimum compliance energy $ \sigma^0 \colon
                 \epsilon^0$, in which $ \epsilon^0$ is the average
                 strain. Here we show these bounds also provide sharp
                 bounds on the possible $ (\sigma^0, \epsilon^0)$-pairs
                 that can coexist in such composites, and thus solve the
                 weak G-closure problem for 3d-printed materials. The
                 materials we use to achieve the extremal $ (\sigma^0,
                 \epsilon^0)$-pairs are denoted as near optimal
                 pentamodes. We also consider two-phase composites
                 containing this isotropic elasticity material and a
                 rigid phase with the elastic material occupying a
                 prescribed volume fraction $f$, and with the composite
                 being subject to an average strain, $ \epsilon^0$. For
                 such composites, Allaire and Kohn provided a sharp
                 lower bound $ \tilde {W} f(\epsilon^0)$ on the minimum
                 elastic energy $ \sigma^0 \colon \epsilon^0$. We show
                 that these bounds also provide sharp bounds on the
                 possible $ (\sigma^0, \epsilon^0)$-pairs that can
                 coexist in such composites of the elastic and rigid
                 phases, and thus solve the weak $G$-closure problem in
                 this case too. The materials we use to achieve these
                 extremal $ (\sigma^0, \epsilon^0)$-pairs are denoted as
                 near optimal unimodes.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "20",
  subject =      "Analysis of PDEs (math.AP)",
}

@Article{Milton:2017:PEE,
  author =       "Graeme W. Milton and Marc Briane and Davit
                 Harutyunyan",
  title =        "On the possible effective elasticity tensors of
                 2-dimensional and 3-dimensional printed materials",
  journal =      j-MATH-MECH-COMPLEX-SYST,
  volume =       "5",
  number =       "1",
  pages =        "41--94",
  year =         "2017",
  DOI =          "https://doi.org/10.2140/memocs.2017.5.41",
  ISSN =         "2325-3444 (print), 2326-7186 (electronic)",
  ISSN-L =       "2325-3444",
  MRclass =      "74Q20 (35Q74 74B10)",
  MRnumber =     "3677943",
  MRreviewer =   "Carmen Calvo-Jurado",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Mechanics of Complex Systems",
  journal-URL =  "https://msp.org/memocs/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2017:SFI,
  author =       "Graeme W. Milton",
  title =        "The set of forces that ideal trusses, or wire webs,
                 under tension can support",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        apr,
  year =         "2017",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1705.00381",
  abstract =     "The problem of determining those multiplets of forces,
                 or sets of force multiplets, acting at a set of points,
                 such that there exists a truss structure, or wire web,
                 that can support these force multiplets with all the
                 elements of the truss or wire web being under tension,
                 is considered. The two-dimensional problem where the
                 points are at the vertices of a convex polygon is
                 essentially solved: each multiplet of forces must be
                 such that the net anticlockwise torque around any
                 vertex of the forces summed over any number of
                 consecutive points clockwise past the vertex must be
                 non-negative; and one can find a truss structure that
                 supports under tension, and only supports, those force
                 multiplets in a convex polyhedron of force multiplets
                 that is generated by a finite number of force
                 multiplets each satisfying the torque condition.
                 Progress is also made on the problem where only a
                 subset of the points are at the vertices of a convex
                 polygon, and the other points are inside. In
                 particular, in the case where only one point is inside,
                 an explicit procedure is described for constructing a
                 suitable truss, if one exists. An alternative recipe to
                 that provided by Guevara Vasquez, Milton, and Onofrei
                 (2011), based on earlier work of Camar Eddine and
                 Seppecher (2003), is given for constructing a truss
                 structure, with elements under either compression or
                 tension, that supports an arbitrary collection of
                 balanced forces at the vertices of a convex polygon.
                 Finally some constraints are given on the forces that a
                 three-dimension truss, or wire web, under tension must
                 satisfy.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "28",
  subject =      "Mathematical Physics (math-ph); Classical Physics
                 (physics.class-ph)",
}

@Article{Milton:2017:TCC,
  author =       "Graeme W. Milton and Davit Harutyunyan and Marc
                 Briane",
  title =        "Towards a complete characterization of the effective
                 elasticity tensors of mixtures of an elastic phase and
                 an almost rigid phase",
  journal =      j-MATH-MECH-COMPLEX-SYST,
  volume =       "5",
  number =       "1",
  pages =        "95--113",
  year =         "2017",
  DOI =          "https://doi.org/10.2140/memocs.2017.5.95",
  ISSN =         "2325-3444 (print), 2326-7186 (electronic)",
  ISSN-L =       "2325-3444",
  MRclass =      "74Q20 (35Q74)",
  MRnumber =     "3677944",
  bibdate =      "Fri Feb 9 06:34:00 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Mechanics of Complex Systems",
  journal-URL =  "https://msp.org/memocs/",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Moulinec:2017:CIM,
  author =       "Herv{\'e} Moulinec and Pierre Suquet and Graeme W.
                 Milton",
  title =        "Convergence of iterative methods based on {Neumann}
                 series for composite materials: theory and practice",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "16",
  month =        nov,
  year =         "2017",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1711.05880",
  abstract =     "Iterative Fast Fourier Transform methods are useful
                 for calculating the fields in composite materials and
                 their macroscopic response. By iterating back and forth
                 until convergence, the differential constraints are
                 satisfied in Fourier space, and the constitutive law in
                 real space. The methods correspond to series expansions
                 of appropriate operators and to series expansions for
                 the effective tensor as a function of the component
                 moduli. It is shown that the singularity structure of
                 this function can shed much light on the convergence
                 properties of the iterative Fast Fourier Transform
                 methods. We look at a model example of a square array
                 of conducting square inclusions for which there is an
                 exact formula for the effective conductivity (Obnosov).
                 Theoretically some of the methods converge when the
                 inclusions have zero or even negative conductivity.
                 However, the numerics do not always confirm this
                 extended range of convergence and show that accuracy is
                 lost after relatively few iterations. There is little
                 point in iterating beyond this. Accuracy improves when
                 the grid size is reduced, showing that the discrepancy
                 is linked to the discretization. Finally, it is shown
                 that none of the three iterative schemes investigated
                 over-performs the others for all possible
                 microstructures and all contrasts.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "41",
  subject =      "Numerical Analysis (math.NA)",
}

@Article{Milton:2018:NOP,
  author =       "Graeme W. Milton and Mohamed Camar-Eddine",
  title =        "Near optimal pentamodes as a tool for guiding stress
                 while minimizing compliance in {3$D$}-printed
                 materials: a complete solution to the weak
                 {$G$}-closure problem for {3$D$}-printed materials",
  journal =      j-J-MECH-PHYS-SOLIDS,
  volume =       "114",
  pages =        "194--208",
  year =         "2018",
  CODEN =        "JMPSA8",
  DOI =          "https://doi.org/10.1016/j.jmps.2018.02.003",
  ISSN =         "0022-5096 (print), 1873-4782 (electronic)",
  ISSN-L =       "0022-5096",
  MRnumber =     "3783452",
  bibdate =      "Mon Apr 9 16:56:14 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Mechanics and Physics of Solids",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225096",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}

@Article{Milton:2018:NRF,
  author =       "Graeme W. Milton",
  title =        "A new route to finding bounds on the spectrum of many
                 physical operators",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        mar,
  year =         "2018",
  CODEN =        "????",
  ISSN =         "2331-8422",
  ISSN-L =       "2331-8422",
  bibdate =      "Thu Apr 12 10:25:06 MDT 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://arxiv.org/abs/1803.03726",
  abstract =     "Here we obtain bounds on the spectrum of that operator
                 whose inverse, when it exists, gives the Green's
                 function. We consider the wide of physical problems
                 that can be cast in a form where a constitutive
                 equation $ J(x) = L(x)E(x) - h(x) $ with a source term
                 $ h(x) $ holds for all $x$ in some domain $ \Omega $,
                 and relates fields $E$ and $J$ that satisfy appropriate
                 differential constraints, symbolized by $ E \in
                 E_\Omega $ and $ J \in J_\Omega $ where $ E_\Omega $
                 and $ J_\Omega $ are orthogonal spaces that span the
                 space $ H_\Omega $ of square-integrable fields in which
                 $h$ lies. Boundedness and coercivity conditions on the
                 moduli $ L(x)$ ensure there exists a unique $E$ for any
                 given $h$, i.e., $ E = G_\Omega h$ which then
                 establishes the existence of the Green's function $
                 G_\Omega $. We show that the coercivity condition is
                 guaranteed to hold if weaker conditions, involving
                 generalized quasiconvex functions, are satisfied. The
                 advantage is that these weaker conditions are easier to
                 verify, and for multiphase materials they can be
                 independent of the geometry of the phases. For $ L(x)$
                 depending linearly on a vector of parameters $ z =
                 (z_1, z_2, \ldots {}, z_n)$, we obtain constraints on
                 $z$ that ensure the Green's function exists, and hence
                 which provide bounds on the spectrum.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  pagecount =    "30",
  subject =      "Mathematical Physics (math-ph)",
}

%%% ====================================================================
%%% Publications about Graeme W. Milton and his works:
@Article{Berryman:2009:FDT,
  author =       "James G. Berryman",
  title =        "Frequency dependent thermal expansion in binary
                 viscoelastic composites",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "463--480",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.013",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000106",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Berryman:2009:ISI,
  author =       "James G. Berryman and Elena Cherkaev and Igor
                 Sevostianov",
  title =        "Introduction to the Special Issue in Honor of {Graeme
                 W. Milton, 2007 Winner of the William Prager Medal of
                 the Society of Engineering Science}",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "355--355",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2008.11.005",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016766360800166X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Cherkaev:2009:BEP,
  author =       "Andrej V. Cherkaev",
  title =        "Bounds for effective properties of multimaterial
                 two-dimensional conducting composites",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "411--433",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.027",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000052",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Francfort:2009:POB,
  author =       "Gilles A. Francfort and Fran{\c{c}}ois Murat",
  title =        "The proofs of the optimal bounds for mixtures of two
                 anisotropic conducting materials in two dimensions",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "448--455",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.020",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000039",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Grabovsky:2009:AGT,
  author =       "Yury Grabovsky",
  title =        "An application of the general theory of exact
                 relations to fiber-reinforced conducting composites
                 with {Hall} effect",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "456--462",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.012",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000064",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Jasiuk:2009:SIE,
  author =       "Iwona Jasiuk",
  title =        "Stress invariance and exact relations in the mechanics
                 of composite materials: Extensions of the {CLM} result:
                 a review",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "394--404",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.001",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016766360900009X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Kang:2009:CPS,
  author =       "Hyeonbae Kang",
  title =        "Conjectures of {P{\'o}lya--Szeg{\H{o}}} and {Eshelby},
                 and the {Newtonian} potential problem: A review",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "405--410",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.019",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000131",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Lopez-Pamies:2009:MEH,
  author =       "O. Lopez-Pamies and P. {Ponte Casta{\~n}eda}",
  title =        "Microstructure evolution in hyperelastic laminates and
                 implications for overall behavior and macroscopic
                 stability",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "364--374",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.006",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000040",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{McPhedran:2009:PCB,
  author =       "R. C. McPhedran and A. B. Movchan and N. V. Movchan",
  title =        "Platonic crystals: Bloch bands, neutrality and
                 defects",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "356--363",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.005",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000027",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Sevostianov:2009:ECC,
  author =       "Igor Sevostianov and Mark Kachanov",
  title =        "Elasticity-conductivity connections for contacting
                 rough surfaces: An overview",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "375--384",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.002",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000076",
  acknowledgement = ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Smyshlyaev:2009:PLE,
  author =       "Valery P. Smyshlyaev",
  title =        "Propagation and localization of elastic waves in
                 highly anisotropic periodic composites via two-scale
                 homogenization",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "434--447",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.009",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Mon May 30 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000088",
  acknowledgement = ack-gwm,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Article{Willis:2009:EER,
  author =       "John R. Willis",
  title =        "Exact effective relations for dynamics of a laminated
                 body",
  journal =      j-MECH-MATER,
  volume =       "41",
  number =       "4",
  pages =        "385--393",
  month =        apr,
  year =         "2009",
  CODEN =        "MSMSD3",
  DOI =          "https://doi.org/10.1016/j.mechmat.2009.01.010",
  ISSN =         "0167-6636 (print), 1872-7743 (electronic)",
  ISSN-L =       "0167-6636",
  bibdate =      "Thu Nov 26 08:41:39 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.sciencedirect.com/science/journal/01676636/41/4",
  note =         "Special Issue in Honor of Graeme W. Milton, 2007
                 Winner of the William Prager Medal of the Society of
                 Engineering Science.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167663609000118",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  fjournal =     "Mechanics of Materials: an International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676636",
}

@Misc{Anonymous:2016:GWM,
  author =       "Anonymous",
  title =        "{Graeme W. Milton}",
  howpublished = "Press release by the Scientific Committee of the
                 International Research Center MEMOCS",
  pages =        "2",
  day =          "25",
  month =        may,
  year =         "2016",
  bibdate =      "Wed Jul 06 09:52:04 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Announcement of the award of the 2015 International
                 Tullio Levi-Civit{\`a} Prize.",
  URL =          "http://memocs.univaq.it/wp-content/uploads/2016/05/MiltonLaudatio.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2016:NMT,
  author =       "Anonymous",
  title =        "New math tools for new materials",
  howpublished = "Press releases.",
  day =          "21",
  month =        nov,
  year =         "2016",
  bibdate =      "Wed Nov 23 05:43:50 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "https://www.eurekalert.org/pub_releases/2016-11/uou-nmt112116.php",
  abstract =     "University of Utah mathematician Graeme Milton
                 presents a new tool for understanding how energy waves
                 move through complex materials, opening up
                 possibilities to design materials that absorb or bend
                 energy as desired. His solution for so-called
                 ``analytic materials'' was published November 15 in
                 Proceedings of the Royal Society A.",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2016:TCR,
  author =       "Anonymous",
  title =        "Theoretical climbing rope could brake falls: Now
                 mathematicians need material to make it a reality",
  howpublished = "University of Utah Web site.",
  day =          "6",
  month =        jul,
  year =         "2016",
  bibdate =      "Wed Jul 06 09:49:05 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "Describes work published in
                 \cite{Harutyunyan:2016:IDCb}",
  URL =          "unews.utah.edu/theoretical-climbing-rope-could-brake-falls/Boyee",
  acknowledgement = ack-nhfb,
  keywords =     "David Harutyunyan; Graeme W. Milton; Justin Boyer;
                 Trevor J. Dick",
}

@Article{Miller:2017:SMF,
  author =       "Johanna L. Miller",
  title =        "Semiconductor metamaterial fools the {Hall} effect",
  journal =      j-PHYS-TODAY,
  volume =       "70",
  number =       "2",
  pages =        "21--23",
  month =        feb,
  year =         "2017",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/pt.3.3453",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Mon Jul 31 17:15:13 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  note =         "The journal issue cover image is based on work by
                 Graeme Milton and colleagues.",
  URL =          "http://physicstoday.scitation.org/na101/home/literatum/publisher/aip/journals/content/pto/2017/pto.2017.70.issue-2/pto.2017.70.issue-2/20170202/pto.2017.70.issue-2.cover.jpg;
                 https://doi.org/10.1063/pt.3.3453",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
  remark =       "This article describes work by Graeme Milton and
                 colleagues on a 3D materials design that contradicts
                 standard textbook discussions of the Hall effect. Such
                 a material has now been manufactured in a laboratory,
                 and is pictured in the article.",
}

@Article{Sharma:2017:BRE,
  author =       "Pradeep Sharma",
  title =        "Book Review: {{\booktitle{Extending the Theory of
                 Composites to Other Areas of Science}}, edited by
                 Graeme W. Milton}",
  journal =      j-J-APPL-MECH,
  volume =       "84",
  number =       "3",
  pages =        "036501--1",
  day =          "25",
  month =        jan,
  year =         "2017",
  CODEN =        "JAMCAV",
  DOI =          "https://doi.org/10.1115/1.4035525",
  ISSN =         "0021-8936 (print), 1528-9036 (electronic)",
  bibdate =      "Mon Jun 04 09:33:11 2018",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
  URL =          "http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=2594947",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Mechanics",
  journal-URL =  "http://appliedmechanics.asmedigitalcollection.asme.org/issues.aspx",
  pagecount =    "1",
  papernumber =  "JAM-16-1598",
}

@Article{Grabovsky:2018:BRE,
  author =       "Yury Grabovsky",
  title =        "Book Review: {{\booktitle{Extending the Theory of
                 Composites to Other Areas of Science}}, edited and
                 authored by Graeme W. Milton}",
  journal =      j-SIAM-REVIEW,
  volume =       "60",
  number =       "2",
  pages =        "475--481",
  month =        "????",
  year =         "2018",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/18N97456X",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Mon Jun 4 09:14:47 MDT 2018",
  bibsource =    "http://epubs.siam.org/toc/siread/60/2;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 2018",
}

%%% ====================================================================
%%% Cross-referenced entries and conference proceedings must come last.
%%% They are sorted in publication order with ``bibsort --byyear''.
@Book{Milton:2002:TC,
  author =       "Graeme W. Milton",
  booktitle =    "The Theory of Composites",
  title =        "The Theory of Composites",
  volume =       "6",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxviii + 719",
  year =         "2002",
  DOI =          "https://doi.org/10.1017/CBO9780511613357",
  ISBN =         "0-521-78125-6",
  ISBN-13 =      "978-0-521-78125-1",
  LCCN =         "TA418.9.C6 M58 2001",
  MRclass =      "74Qxx (74A40 74E30 74Pxx 78A48 82B99 82D20)",
  MRnumber =     "1899805 (2003d:74077)",
  MRreviewer =   "Gr{\'e}goire Allaire",
  bibdate =      "Sat May 04 06:33:55 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  note =         "Series editors: P. G. Ciarlet, A. Iserles, Robert V.
                 Kohn, and M. H. Wright.",
  price =        "US\$80",
  series =       "Cambridge Monographs on Applied and Computational
                 Mathematics",
  URL =          "http://www.math.utah.edu/books/tcbook",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  keywords =     "composite materials; differential equations, partial;
                 homogenization (differential equations)",
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "NHFB was the chief technical editor for this book, and
                 wrote the author/editor indexing software, the {\TeX}
                 DVI-to-PostScript driver and the initial Web site for
                 the book, at
                 \path=http://www.math.utah.edu/books/tcbook/index.html=.",
  tableofcontents = "1. Introduction \\
                 2. Some equations of interest and numerical approaches
                 to solving them \\
                 3. Duality transformations in two-dimensional media \\
                 4. Translations and equivalent media \\
                 5. Some microstructure-independent exact relations \\
                 6. Exact relations for coupled equations \\
                 7. Assemblages of spheres, ellipsoids, and other
                 neutral inclusions \\
                 8. Tricks for generating other exactly solvable
                 microgeometries \\
                 9. Laminate materials \\
                 10. Approximations and asymptotic formulas \\
                 11. Wave propagation in the quasistatic limit \\
                 12. Reformulating the problem of finding effective
                 tensors \\
                 13. Variational principles and inequalities \\
                 14. Series expansions for the fields and effective
                 tensors \\
                 15. Correlation functions and how they enter series
                 expansions \\
                 16. Other perturbation solutions \\
                 17. General theory of exact relations and links between
                 effective tensors \\
                 18 Analytic properties \\
                 19. Y -tensors \\
                 20. Y -tensors and effective tensors in electrical
                 circuits \\
                 21. Bounds on the properties of composites \\
                 22. Classical variational principle bounds \\
                 23. Bounds from the Hashin--Shtrikman variational
                 inequalities \\
                 24. Bounds using the compensated compactness or
                 translation method \\
                 25. Choosing the translations and finding
                 microgeometries that attain the bounds \\
                 26. Bounds incorporating three-point correlation
                 functions \\
                 27. Bounds using the analytic method \\
                 28. Fractional linear transformations as a tool for
                 generating bounds \\
                 29. Field equation recursion method \\
                 30. Properties of the G-closure and extremal families
                 of composites \\
                 31. Bounding of effective moduli as a
                 quasiconvexification problem",
}

@Proceedings{Milton:2003:PSI,
  editor =       "Graeme W. Milton and K. M. Golden and D. Dobson and Z.
                 V. Vardeny",
  booktitle =    "Proceedings of the {Sixth International Conference on
                 Electrical Transport and Optical Properties of
                 Inhomogeneous Media: ETOPIM 6, held in Snowbird, UT,
                 USA, 15--19 July 2002}",
  title =        "Proceedings of the {Sixth International Conference on
                 Electrical Transport and Optical Properties of
                 Inhomogeneous Media: ETOPIM 6, held in Snowbird, UT,
                 USA, 15--19 July 2002}",
  volume =       "338(1--4)",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xiii + 374",
  year =         "2003",
  ISBN =         "",
  ISBN-13 =      "",
  ISSN =         "0921-4526 (print), 1873-2135 (electronic)",
  LCCN =         "",
  bibdate =      "Sat Jul 03 12:05:44 2004",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  series =       "Physica B, Condensed Matter",
  URL =          "http://www.elseview.com/locate/physb;
                 http://www.math.utah.edu/etopim/",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  remark =       "Technical editing by Nelson H. F. Beebe and Eleen
                 Collins. No ISBN assigned: this is a combined journal
                 issue.",
  xxnote =       "Book cover page has incorrect A. Z. Vardeny instead of
                 V. Z. Vardeny.",
}

@Book{Milton:2016:ETC,
  editor =       "Graeme W. Milton",
  booktitle =    "Extending the Theory of Composites to Other Areas of
                 Science",
  title =        "Extending the Theory of Composites to Other Areas of
                 Science",
  publisher =    "Milton--Patton Publishers",
  address =      "P.O. Box 581077, Salt Lake City, UT 85148, USA",
  pages =        "xx + 422",
  year =         "2016",
  ISBN =         "1-4835-6919-5 (print), 1-4835-6920-9 (e-book)",
  ISBN-13 =      "978-1-4835-6919-2 (print), 978-1-4835-6920-8
                 (e-book)",
  LCCN =         "????",
  bibdate =      "Wed Jul 06 09:36:32 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  URL =          "http://www.math.utah.edu/books/milton",
  acknowledgement = ack-gwm # " and " # ack-nhfb,
  ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
  tableofcontents = "1: Canonical forms for linear physics equations and
                 key identities / Graeme W. Milton / 1 \\
                 2: Composites and the associated abstract theory /
                 Graeme W. Milton / 47 \\
                 3: A new perspective on boundary value problems /
                 Graeme W. Milton / 77 \\
                 4: Analyticity of the Dirichlet-to-Neumann map for the
                 time-harmonic Maxwell's equations / Maxence Cassier,
                 Aaron Welters and Graeme W. Milton / 95 \\
                 5: The inverse problem / Graeme W. Milton / 123 \\
                 6: Bounds for the transient response of viscoelastic
                 composites / Ornella Mattei and Graeme W. Milton / 149
                 \\
                 7: Superfunctions and the algebra of subspace
                 collections / Graeme W. Milton / 179 \\
                 8: Accelerating FFT methods for conducting composites /
                 Graeme W. Milton / 235 \\
                 9: The response of systems with coupled fields /
                 Mordehai Milgrom and Graeme W. Milton / 255 \\
                 10: A rigorous approach to the field recursion method /
                 Maxence Cassier, Aaron Welters and Graeme W. Milton /
                 287 \\
                 11: Projection Functional Theory for finding excited
                 states / Graeme W. Milton / 309 \\
                 12: The desymmetrization method for solving the
                 Schr{\"o}dinger equation / Graeme W. Milton / 319 \\
                 13: Variational principles and $Q_C^*$-convex functions
                 for Schr{\"o}dinger's equation / Graeme W. Milton / 337
                 \\
                 14: Green's functions for self-adjoint and
                 non-self-adjoint operators / Graeme W. Milton / 355 \\
                 Bibliography / / 369 \\
                 Author/editor index / / 401 \\
                 Index / / 413",
}

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