%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Graeme W. Milton", %%% version = "1.12", %%% date = "09 February 2018", %%% time = "07:16:40 MST", %%% 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 = "28973 6877 28796 300425", %%% 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 1.12, the year coverage looked %%% like this: %%% %%% 1979 ( 1) 1992 ( 3) 2005 ( 6) %%% 1980 ( 1) 1993 ( 3) 2006 ( 9) %%% 1981 ( 6) 1994 ( 4) 2007 ( 8) %%% 1982 ( 6) 1995 ( 3) 2008 ( 8) %%% 1983 ( 2) 1996 ( 1) 2009 ( 20) %%% 1984 ( 2) 1997 ( 6) 2010 ( 10) %%% 1985 ( 5) 1998 ( 5) 2011 ( 12) %%% 1986 ( 5) 1999 ( 4) 2012 ( 6) %%% 1987 ( 5) 2000 ( 4) 2013 ( 12) %%% 1988 ( 5) 2001 ( 3) 2014 ( 9) %%% 1989 ( 4) 2002 ( 4) 2015 ( 9) %%% 1990 ( 4) 2003 ( 4) 2016 ( 23) %%% 1991 ( 6) 2004 ( 4) 2017 ( 8) %%% %%% Article: 191 %%% Book: 2 %%% InCollection: 19 %%% InProceedings: 21 %%% Misc: 3 %%% PhdThesis: 1 %%% Proceedings: 1 %%% TechReport: 1 %%% Unpublished: 1 %%% %%% Total entries: 240 %%% %%% Data for this bibliography have been %%% collected and merged from numerous sources, %%% including the author's personal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. %%% %%% 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 \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-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-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-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-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @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, } @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", originallab = "GWM0697", originallab = "GWM0272", 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", texsource = "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", 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", 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", 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", 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", 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", 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", 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", 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, 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", 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", 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/", } @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", } @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", 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", 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", 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", } @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)", MRclass = "82A57 (73B99 82A42)", MRnumber = "796009 (86i:82054)", MRreviewer = "B. Derrida", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/BF01215906", fjournal = "Communications in Mathematical Physics", journal-URL = "http://link.springer.com/journal/220", 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", 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, 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{Milton:1985:TCP, 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 = "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://projecteuclid.org/euclid.cmp/1103942837", acknowledgement = ack-gwm, fjournal = "Communications in Mathematical Physics", journal-URL = "http://link.springer.com/journal/220", 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", } @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", } @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, 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, 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", 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", } @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", } @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", 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", } @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", 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", 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", 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/", 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", 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", 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", 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, 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", } @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", 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, 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", 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, 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", 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", 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", 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, 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", } @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", 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", 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", } @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", } @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", 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", 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", 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, 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", 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", 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", 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", 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", 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", 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", 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", 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", 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", } @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", 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, 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/", } @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", 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", 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, 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/", 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", 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", 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, 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/", 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/", 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", 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, texsource = "l-lec2.tex", } @Article{Eyre:2000: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", texsource = "l-lec6.tex", texsource = "l-lec22.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", 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", 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", 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", 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)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/457/2012/1973", fjournal = "The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", } @Article{Milton:2001:NIC, author = "Graeme W. Milton and S. 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", bibdate = "Fri Oct 20 13:45:09 MST 2000", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", 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/", } @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", } @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", 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{Milton:2002: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", 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{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", } @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", } @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", } @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", } @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/", } @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", 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", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://content.iospress.com/articles/asymptotic-analysis/asy667", fjournal = "Asymptotic Analysis", journal-URL = "http://content.iospress.com/journals/asymptotic-analysis", } @Article{Camar: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", 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", } @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", } @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/", } @Article{Podolskiy:2005:OSM, 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", } @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", } @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.", } @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/", } @Article{Milton:2006:CEM, 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", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/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, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", 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/", } @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", 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/article/10.1088/1367-2630/8/10/248/", acknowledgement = ack-nhfb, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", } @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", } @Article{Milton:2006: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", year = "2007", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2006.1795", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", bibdate = "Wed Aug 23 2006", 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", journal-URL = "http://rspa.royalsocietypublishing.org/", xxyear = "2006", } @Article{Milton:2006: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", xxyear = "2006", } @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", 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://arxiv.org/abs/math/0609374", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", } @Article{Briane:2007:BSF, 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", 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", 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", pagecount = "18", xxURL = "http://scitation.aip.org/content/aip/journal/jmp/52/10/10.1063/1.3644377", xxyear = "2007", } @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", acknowledgement = ack-nhfb, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", } @Article{Cai:2007:NMC, 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 = "Wed Aug 15 2007", 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, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", } @Article{Cai:2007:NMCb, author = "W. Cai and U. K. Chettiar and Graeme W. Milton and A. V. Kildishev", title = "Non-magnetic cloak without reflection", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2007", 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://arxiv.org/abs/0707.3641", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", 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 = "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 of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", xxyear = "2006", } @Article{Milton:2007:NMM, 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", 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{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", } @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", } @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", } @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", } @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", } @Article{Milton:2008:EC, author = "Graeme W. Milton and P. Seppecher", title = "Electromagnetic circuits", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2008", 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://arxiv.org/abs/0805.1079", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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/", } @Article{Milton:2008:SFG, 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", 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", } @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", } @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", } @Article{GuevaraVasquez:2009:AEC, 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 = "7", 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-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", pagecount = "4", } @Article{GuevaraVasquez:2009:AECb, author = "F. {Guevara Vasquez} and Graeme W. Milton", title = "Active Exterior Cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2009", 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/2009arXiv0906.1544G", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", } @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/", } @Article{Vasquez:2009:AEC, 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 = "Fri May 29 2009", 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, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", } @Article{Vasquez:2009:BEC, 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", } @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", } @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", } @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", } @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", } @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", 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 = "??--??", month = "????", year = "2010", 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://arxiv.org/abs/1009.2038", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", } @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", } @Article{Milton:2010:MVP, 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/", } @Article{Milton:2010:RMP, 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", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/12/3/033035/", } @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", } @Article{Briane:2011:BSF, 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, 18", 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-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "11 October 2011", pagecount = "18", } @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", 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)", 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", fjournal = "Journal of Elasticity. The Physical and Mathematical Science of Solids", journal-URL = "http://link.springer.com/journal/10659", } @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)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165212511000382", fjournal = "Wave Motion. An International Journal Reporting Research on Wave Phenomena", journal-URL = "http://www.sciencedirect.com/science/journal/01652125", } @Article{GuevaraVasquez:2011:TEA, author = "F. {Guevara Vasquez} and Graeme W. Milton", title = "Transformation elastodynamics and active exterior acoustic cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2011", 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/2011arXiv1105.1221G", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @Article{Helsing:2011:SSR, 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", 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: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", journal-URL = "http://link.springer.com/journal/10659", xxyear = "2011", } @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 = 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://www.springer.com/mathematics/analysis/journal/526", xxyear = "2011", } @Article{Milton:2011:BVF, author = "Graeme W. Milton and Loc H. 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 = "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/S1631072112000393", acknowledgement = ack-gwm, fjournal = "Comptes Rendus M{'e}canique", journal-URL = "http://www.sciencedirect.com/science/journal/16310721", 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: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 = 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", } @Article{Vasquez: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", 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", journal-URL = "http://link.springer.com/journal/10659", } @Article{Vasquez: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", 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", journal-URL = "http://www.sciencedirect.com/science/journal/01652125", } @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, } @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", } @Article{Kadic:2012:RTD, author = "Tiemo B{\"u}ckmann and Muamer Kadic and Graeme 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, remark = "Not found in Web search on 26 November 2015.", } @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", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", fjournal = "Calculus of Variations and Partial Differential Equations", journal-URL = "http://link.springer.com/journal/526", } @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", 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-nhfb, fjournal = "Comptes Rendus M{'e}canique", journal-URL = "http://www.sciencedirect.com/science/journal/16310721", } @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)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", } @Article{Alali:2013:ECT, 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", } @Article{Ammari:2013:ALR, 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/", } @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", } @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 = "????", 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", } @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, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "January 2013", } @Article{Kang:2013:BVF3d, 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", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "January 2013", } @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", 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", 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://arxiv.org/abs/1306.6608", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org/", } @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", } @Article{Milton:2013:SEH, 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", } @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:ATS}.", 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/", pagecount = "18", } @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", } @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", } @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", } @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", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/16/3/033032/", } @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", } @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", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", fjournal = "Journal of Elasticity. The Physical and Mathematical Science of Solids", journal-URL = "http://link.springer.com/journal/10659", } @Article{Kochmann:2014:RBE, 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", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509614001367", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", } @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", 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://arxiv.org/abs/1409.7658", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", 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://arxiv.org/abs/1406.7044", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @Article{Thaler:2014:EDV, 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/", 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", } @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", } @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", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://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/", pagecount = "17", received = "16 November 2014", } @Article{Kochmann:2015:RBE, 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", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", xxyear = "2015", } @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", 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://arxiv.org/abs/1504.08061", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", } @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", 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", URL = "http://rspa.royalsocietypublishing.org/content/471/2176/20140886.abstract", fjournal = "Proceedings A", journal-URL = "http://rspa.royalsocietypublishing.org/", pagecount = "8", } @Article{Milton:2015:ATS, author = "Graeme W. Milton", title = "Addendum to {``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 = "471", number = "2176", 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", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "See \cite{Milton:2013:SIG}.", 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 of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", 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/", } @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", } @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, } @InCollection{Cassier:2016:RAF, 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, } @Article{Harutyunyan:2016:HFH, 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/", pagecount = "18", } @Article{Harutyunyan:2016:IDC, 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, 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, } @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", } @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, } @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, } @Article{Milton:2016:AM, 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/", 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, } @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, } @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, } @Article{Milton:2016:FPN, author = "Graeme W. Milton and Ornella Mattei", title = "Field Patterns: A New Mathematical Object", journal = "arxiv.org", volume = "??", number = "??", pages = "1--31", day = "18", month = nov, year = "2016", bibdate = "Wed Nov 23 05:41:05 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "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, } @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, } @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, } @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, } @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, } @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, } @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, } @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/", 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/", 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", } @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", } @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/", pagecount = "26", } @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/", } @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/", }

%%% ==================================================================== %%% 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:IDC}", 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.", }

%%% ==================================================================== %%% 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)", 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, 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, 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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