%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Graeme W. Milton", %%% version = "2.02", %%% date = "24 April 2019", %%% time = "18:26:05 MDT", %%% filename = "milton-graeme-w.bib", %%% address = "University of Utah %%% Department of Mathematics, 310 JWB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 6495", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~milton", %%% checksum = "12642 9906 46301 458603", %%% email = "milton at math.utah.edu", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; cloaking; composite %%% materials", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a very rough preliminary unreleased %%% bibliography of publications by, and about, %%% Graeme W. Milton. %%% %%% At version 2.02, the year coverage looked %%% like this: %%% %%% 1979 ( 1) 1993 ( 4) 2007 ( 9) %%% 1980 ( 1) 1994 ( 4) 2008 ( 10) %%% 1981 ( 6) 1995 ( 3) 2009 ( 23) %%% 1982 ( 6) 1996 ( 1) 2010 ( 12) %%% 1983 ( 2) 1997 ( 6) 2011 ( 14) %%% 1984 ( 2) 1998 ( 5) 2012 ( 11) %%% 1985 ( 4) 1999 ( 4) 2013 ( 18) %%% 1986 ( 5) 2000 ( 3) 2014 ( 16) %%% 1987 ( 5) 2001 ( 2) 2015 ( 12) %%% 1988 ( 5) 2002 ( 4) 2016 ( 32) %%% 1989 ( 4) 2003 ( 5) 2017 ( 18) %%% 1990 ( 4) 2004 ( 4) 2018 ( 3) %%% 1991 ( 6) 2005 ( 6) %%% 1992 ( 3) 2006 ( 9) %%% %%% Article: 243 %%% Book: 2 %%% InCollection: 19 %%% InProceedings: 21 %%% Misc: 3 %%% PhdThesis: 1 %%% Proceedings: 1 %%% TechReport: 1 %%% Unpublished: 1 %%% %%% Total entries: 292 %%% %%% Data for this bibliography have been %%% collected and merged from numerous sources, %%% including the author's personal bibliographic %%% records, the TeX User Group and BibNet %%% Project bibliography archives, the MathSciNet %%% database, the Crossref database, Google %%% Scholar, and many different publisher Web %%% sites. %%% %%% At version 2.00 on 12 April 2018, 71 entries %%% from arXiv.org where merged into this %%% bibliography with abstracts and DOI values, %%% labels were regenerated to correct several %%% mismatches in years or three-letter %%% abbreviations, and newly-exposed duplicate %%% entries were merged. In addition, ORCID %%% numbers have been added to all entries where %%% GWM is an author or editor. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

%%% ==================================================================== %%% Preamble material for TeX/LaTeX:

@Preamble{ "\ifx \bblindex \undefined \def \bblindex #1{} \fi" # "\ifx \bbljournal \undefined \def \bbljournal #1{{\em #1}\index{#1@{\em #1}}} \fi" # "\ifx \bblnumber \undefined \def \bblnumber #1{{\bf #1}} \fi" # "\ifx \bblvolume \undefined \def \bblvolume #1{{\bf #1}} \fi" # "\ifx \booktitle \undefined \def \booktitle #1{{{\em #1}}} \fi" # "\ifx \mathbb \undefined \def \mathbb #1{{\bf #1}} \fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

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

%%% ==================================================================== %%% Institution abbreviations:

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

%%% ==================================================================== %%% Journal abbreviations: These are INTENTIONALLY given as full journal %%% names, because abbreviations are often obscure, and sometimes, also %%% ambiguous.

@String{j-AIP-CONF-PROC= "AIP Conference Proceedings"} @String{j-ANAL-MATH-PHYS= "Analysis and Mathematical Physics"} @String{j-APPL-PHYS= "Applied Physics"} @String{j-APPL-PHYS-A= "Applied Physics A: Materials Science \& Processing"} @String{j-APPL-PHYS-LET= "Applied Physics Letters"} @String{j-ARCH-RAT-MECH-ANAL= "Archive for Rational Mechanics and Analysis"} @String{j-ASYMPTOT-ANAL= "Asymptotic Analysis"} @String{j-C-R-MEC= "Comptes Rendus M{'e}canique"} @String{j-C-R-PHYS= "Comptes Rendus Physique"} @String{j-CALC-VAR-PARTIAL-DIFFER-EQU= "Calculus of Variations and Partial Differential Equations"} @String{j-CAN-J-PHYS= "Canadian Journal of Physics = Journal canadien de physique"} @String{j-COMM-PURE-APPL-MATH= "Communications on Pure and Applied Mathematics (New York)"} @String{j-COMMUN-MATH-PHYS= "Communications in Mathematical Physics"} @String{j-COMMUN-MATH-SCI= "Communications in Mathematical Sciences"} @String{j-DOC-MATH= "Documenta Mathematica"} @String{j-EPJ-APPL-PHYS= "European Physical Journal. Applied Physics"} @String{j-EUR-J-MECH-A-SOLIDS= "European Journal of Mechanics, A, Solids"} @String{j-EUROPHYS-LETT= "Europhysics Letters"} @String{j-GEOPHYSICS= "Geophysics"} @String{j-INT-J-ENG-SCI= "International journal of engineering science"} @String{j-INT-J-NUMER-METHODS-ENG= "International Journal for Numerical Methods in Engineering"} @String{j-INVERSE-PROBLEMS= "Inverse Problems"} @String{j-J-APPL-MECH= "Journal of Applied Mechanics"} @String{j-J-APPL-PHYS= "Journal of Applied Physics"} @String{j-J-CHEM-PHYS= "Journal of Chemical Physics"} @String{j-J-ELAST= "Journal of Elasticity"} @String{j-J-ENG-MATER-TECHNOL= "Journal of Engineering Materials and Technology"} @String{j-J-FLUID-MECH= "Journal of Fluid Mechanics"} @String{j-J-MATH-ANAL-APPL= "Journal of Mathematical Analysis and Applications"} @String{j-J-MATH-PHYS= "Journal of Mathematical Physics"} @String{j-J-MATH-PURES-APPL= "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es"} @String{j-J-MECH-PHYS-SOLIDS= "Journal of the Mechanics and Physics of Solids"} @String{j-J-PHYS-D= "Journal of Physics D: Applied Physics"} @String{j-J-REINF-PLAST-COMPOS= "Journal of Reinforced Plastics and Composites"} @String{j-J-STAT-PHYS= "Journal of Statistical Physics"} @String{j-MATER-RES-SOC-SYMP-PROC= "Materials Research Society Symposium Proceedings"} @String{j-MATH-MECH-COMPLEX-SYST= "Mathematics and Mechanics of Complex Systems"} @String{j-MATH-MODEL-NUM-ANA= "Mathematical modelling and numerical analysis = Modelisation math{\'e}matique et analyse num{\'e}rique: $M^2AN$"} @String{j-MECH-MATER= "Mechanics of Materials: An International Journal"} @String{j-METHODS-APPL-ANAL= "Methods and Applications of Analysis"} @String{j-MULTISCALE-MODELING-SIMUL= "Multiscale Modeling \& Simulation"} @String{j-NATURE= "Nature"} @String{j-NETW-HETEROG-MEDIA= "Networks and Heterogeneous Media (NHM)"} @String{j-NEW-J-PHYS= "New Journal of Physics"} @String{j-OPT-EXPRESS= "Optics Express"} @String{j-PHYS-REV-B-CMMP= "Physical Review B: Condensed Matter and Materials Physics"} @String{j-PHYS-REV-LET= "Physical Review Letters"} @String{j-PHYS-STATUS-SOLIDI= "Physica Status Solidi"} @String{j-PHYS-STATUS-SOLIDI-B-BASIC-RES= "Physica Status Solidi. B, Basic Research"} @String{j-PHYS-TODAY= "Physics Today"} @String{j-PHYSICA-A= "Physica A"} @String{j-PHYSICA-B= "Physica. B, Condensed Matter"} @String{j-PHYSICA-D= "Physica. D, Nonlinear Phenomena"} @String{j-PROC-R-SOC-EDINB= "Proceedings of the Royal Society of Edinburgh"} @String{j-PROC-R-SOC-EDINB-SECT-A-MATH= "Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences"} @String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI= "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences"} @String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI= "Proceedings of the Royal Society A: Mathematical, Physical, \& Engineering Sciences"} @String{j-QUART-APPL-MATH= "Quarterly of Applied Mathematics"} @String{j-RHEOL-ACTA= "Rheologica Acta"} @String{j-SIAM-J-APPL-DYN-SYST= "SIAM Journal on Applied Dynamical Systems"} @String{j-SIAM-J-APPL-MATH= "SIAM Journal on Applied Mathematics"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-WAVE-MOTION= "Wave motion"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-AIP= "American Institute of Physics"} @String{pub-AIP:adr= "Woodbury, New York"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-ASME= "American Society of Mechanical Engineers"} @String{pub-ASME:adr= "United Engineering Center, 345 E. 47th St., New York, NY 10017, USA"} @String{pub-BIRKHAUSER= "Birkh{\"a}user Verlag"} @String{pub-BIRKHAUSER:adr= "Basel, Switzerland"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-IOS= "IOS Press"} @String{pub-IOS:adr= "Amsterdam, The Netherlands"} @String{pub-LONGMAN= "Longman Scientific and Technical"} @String{pub-LONGMAN:adr= "Harlow, Essex, UK"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PLENUM= "Plenum Press"} @String{pub-PLENUM:adr= "New York~/ London"} @String{pub-SIAM= "SIAM Press"} @String{pub-SIAM:adr= "Philadelphia"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin~/ Heidelberg~/ London~/ etc."}

%%% ==================================================================== %%% Bibliography entries, sorted in rough publication order with %%% ``bibsort --byyear'':

@TechReport{Milton:1979:TST, author = "Graeme W. Milton", title = "Theoretical studies of the transport properties of inhomogeneous media", type = "Unpublished report", number = "TP/79/1", institution = "University of Sydney", address = "Sydney, Australia", pages = "1--65", year = "1979", DOI = "https://doi.org/10.13140/RG.2.1.2184.8482", bibdate = "Sun Jul 5 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:1980:BCD, author = "Graeme W. Milton", title = "Bounds on the complex dielectric constant of a composite material", journal = j-APPL-PHYS-LET, volume = "37", number = "3", pages = "300--302", day = "1", month = aug, year = "1980", CODEN = "APPLAB", DOI = "https://doi.org/10.1063/1.91895", ISSN = "0003-6951 (print), 1077-3118 (electronic), 1520-8842", ISSN-L = "0003-6951", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0272; GWM0697", originalref = "Milton G. W. 1980 Bounds on the complex dielectric constant of a composite material. {\em Appl. Phys. Lett.} {\bf 37}, 300--302.", texsource = "l-lec4.tex; l-lec15.tex", xxURL = "http://scitation.aip.org/content/aip/journal/apl/37/3/10.1063/1.91895", } @Article{McPhedran:1981:BET, author = "Ross C. McPhedran and Graeme W. Milton", title = "Bounds and exact theories for the transport properties of inhomogeneous media", journal = j-APPL-PHYS-A, volume = "26", number = "4", pages = "207--220", month = dec, year = "1981", CODEN = "APSFDB", DOI = "https://doi.org/10.1007/BF00617840", ISSN = "0721-7250", ISSN-L = "0721-7250", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Applied Physics A: Materials Science \& Processing", journal-URL = "http://link.springer.com/journal/volumesAndIssues/339", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0469", originallab = "GWM0370", originallab = "GWM0129", originalref = "McPhedran R. C. and Milton G. W. 1981 Bounds and exact theories for the transport properties of inhomogeneous media. {\em Appl. Phys. A} {\bf 26}, 207--220.", texsource = "l-lec19.tex", texsource = "l-lec17.tex", texsource = "l-lec10.tex", } @Article{Milton:1981:BCP, author = "Graeme W. Milton", title = "Bounds on the complex permittivity of a two-component composite material", journal = j-J-APPL-PHYS, volume = "52", number = "8", pages = "5286--5293", day = "1", month = aug, year = "1981", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.329385", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Sat Nov 28 20:27:56 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/jap/52/8/10.1063/1.329385", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of Applied Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jap/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0736", originallab = "GWM0698", originallab = "GWM0473", originallab = "GWM0197", originalref = "Milton G. W. 1981 Bounds on the complex permittivity of a two-component composite material, {\em J. Appl. Phys.} {\bf 52}, 5286--5293.", originalref-2 = "Milton G. W. 1981a Bounds on the complex permittivity of a two-component composite material. {\em J. Appl. Phys.} {\bf 52}, 5286--5293.", texsource = "l-lec5.tex", texsource = "l-lec4.tex", texsource = "l-lec19.tex", texsource = "l-lec12.tex", xxURL = "http://scitation.aip.org/content/aip/journal/apl/37/3/10.1063/1.91895", } @Article{Milton:1981:BEE, author = "Graeme W. Milton", title = "Bounds on the electromagnetic, elastic, and other properties of two-component composites", journal = j-PHYS-REV-LET, volume = "46", number = "8", pages = "542--545", day = "23", month = feb, year = "1981", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.46.542", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0475", originallab = "GWM0374", originallab = "GWM0327", originallab = "GWM0214", originallab = "GWM0133", originalref = "Milton G. W. 1981c Bounds on the electromagnetic, elastic, and other properties of two-component composites, {\em Phys. Rev. Lett.} {\bf 46}, 542--545.", originalref-2 = "Milton G. W. 1981b Bounds on the electromagnetic, elastic, and other properties of two-component composites, {\em Phys. Rev. Lett.} {\bf 46}, 542--545.", originalref-3 = "Milton G. W. 1981 Bounds on the electromagnetic, elastic, and other properties of two-component composites, {\em Phys. Rev. Lett.} {\bf 46}, 542--545.", texsource = "l-lec19.tex", texsource = "l-lec17.tex", texsource = "l-lec16.tex", texsource = "l-lec13.tex", texsource = "l-lec10.tex", } @Article{Milton:1981:BTO, author = "Graeme W. Milton", title = "Bounds on the transport and optical properties of a two-component composite material", journal = j-J-APPL-PHYS, volume = "52", number = "8", pages = "5294--5304", month = aug, year = "1981", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.329386", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/jap/52/8/10.1063/1.329386", acknowledgement = ack-gwm, fjournal = "Journal of Applied Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jap/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0547", originallab = "GWM0474", originallab = "GWM0373", originallab = "GWM0198", originalref = "Milton G. W. 1981 Bounds on the transport and optical properties of a two-component composite material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.", originalref-2 = "Milton G. W. 1981b Bounds on the transport and optical properties of a two-component composite material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.", originalref-3 = "Milton G. W. 1981b Bounds on the transport and optical properties of a two-component composite material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.", originalref-4 = "Milton G. W. 1981a Bounds on the transport and optical properties of a two-component composite material. {\em J. Appl. Phys.} {\bf 52}, 5294--5304.", texsource = "l-lec20.tex", texsource = "l-lec19.tex", texsource = "l-lec17.tex", texsource = "l-lec12.tex", } @Article{Milton:1981:CBT, author = "Graeme W. Milton", title = "Concerning bounds on the transport and mechanical properties of multicomponent composite materials", journal = j-APPL-PHYS, volume = "A26", number = "2", pages = "125--130", year = "1981", CODEN = "APAMFC", DOI = "https://doi.org/10.1007/BF00616659", ISSN = "0947-8396 (print), 1432-0630 (electronic)", ISSN-L = "0947-8396", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Applied Physics", journal-URL = "http://link.springer.com/journal/339", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0326", originalref = "Milton G. W. 1981a Concerning bounds on the transport and mechanical properties of multicomponent composite materials. {\em Appl. Phys.} {\bf A26}, 125--130.", texsource = "l-lec16.tex", } @Article{Milton:1981:TPA, author = "Graeme W. Milton and Ross C. McPhedran and D. R. McKenzie", title = "Transport properties of arrays of intersecting cylinders", journal = j-APPL-PHYS, volume = "25", number = "1", pages = "23--30", year = "1981", CODEN = "APAMFC", DOI = "https://doi.org/10.1007/BF00935387", ISSN = "0947-8396 (print), 1432-0630 (electronic)", ISSN-L = "0947-8396", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Applied Physics", journal-URL = "http://link.springer.com/journal/339", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0478", originalref = "Milton G. W., McPhedran R. C., and McKenzie D. R. 1981 Transport properties of arrays of intersecting cylinders. {\em Appl. Phys.} {\bf 25}, 23--30.", texsource = "l-lec19.tex", xxURL = "http://link.springer.com/article/10.1007/BF00935387", } @Article{McPhedran:1982:ESI, author = "Ross C. McPhedran and D. R. McKenzie and Graeme W. Milton", title = "Extraction of structural information from measured transport properties of composites", journal = j-APPL-PHYS-A, volume = "29", number = "1", pages = "19--27", month = sep, year = "1982", CODEN = "APSFDB", DOI = "https://doi.org/10.1007/BF00618111", ISSN = "0721-7250", ISSN-L = "0721-7250", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/BF00618111", acknowledgement = ack-gwm, fjournal = "Applied Physics A: Materials Science \& Processing", journal-URL = "http://link.springer.com/journal/volumesAndIssues/339", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0470", originalref = "McPhedran R. C., McKenzie D. R., and Milton G. W. 1982 Extraction of structural information from measured transport properties of composites. {\em Appl. Phys. A} {\bf 29}, 19--27.", texsource = "l-lec19.tex", } @Article{Milton:1982:BET, author = "Graeme W. Milton", title = "Bounds on the elastic and transport properties of two-component composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "30", number = "3", pages = "177--191", year = "1982", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/0022-5096(82)90022-9", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "73K20", MRnumber = "666510 (83g:73058)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/0022509682900229", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0476", originallab = "GWM0375", originallab = "GWM0134", originalref = "Milton G. W. 1982 Bounds on the elastic and transport properties of two-component composites, {J. Mech. Phys. Solids} {\bf 30}, 177--191.", originalref-2 = "Milton G. W. 1982 Bounds on the elastic and transport properties of two-component composites. {\em J. Mech. Phys. Solids} {\bf 30}, 177--191.", texsource = "l-lec19.tex", texsource = "l-lec17.tex", texsource = "l-lec10.tex", } @InProceedings{Milton:1982:CTM, author = "Graeme W. Milton and Ross C. McPhedran", editor = "Robert Burridge and Stephen Childress and George C. Papanicolaou", booktitle = "Macroscopic Properties of Disordered Media: Proceedings of a Conference Held at the Courant Institute, June 1--3, 1981", title = "A comparison of two methods for deriving bounds on the effective conductivity of composites", volume = "154", publisher = pub-SV, address = pub-SV:adr, bookpages = "vi + 307", pages = "183--193", year = "1982", ISBN = "0-387-11202-2", ISBN-13 = "978-0-387-11202-2", LCCN = "QA911 .M32 1981", MRclass = "73-06", MRnumber = "674958 (83m:73005)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Lecture Notes in Physics", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0479", originalref = "Milton G. W. and McPhedran R. C. 1982 A comparison of two methods for deriving bounds on the effective conductivity of composites. In {\em Macroscopic Properties of Disordered Media}, ed. by R. Burridge, S. Childress, and G. Papanicolaou, {\em Lecture notes in physics}, {\bf 154}, pp. 183--193, Springer Verlag.", rest = "Springer Verlag", texsource = "l-lec19.tex", } @Article{Milton:1982:NBE, author = "Graeme W. Milton and N. Phan-Thien", title = "New bounds on effective elastic moduli of two-component materials", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "380", number = "1779", pages = "305--331", year = "1982", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1982.0044", ISSN = "0080-4630", ISSN-L = "0080-4630", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0376", originallab = "GWM0333", originalref = "Milton G. W. and Phan-Thien N. 1982 New bounds on effective elastic moduli of two-component materials. {\em Proc. Roy. Soc. Lond. A} {\bf 380}, 305--331.", texsource = "l-lec17.tex", texsource = "l-lec16.tex", } @Article{Phan-Thien:1982:NBE, author = "N. Phan-Thien and Graeme W. Milton", title = "New bounds on the effective thermal conductivity of {$N$}-phase materials", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "380", number = "1779", pages = "333--348", year = "1982", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1982.0045", ISSN = "0080-4630", ISSN-L = "0080-4630", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0377", originalref = "Phan-Thien N. and Milton G. W. 1982 New bounds on the effective thermal conductivity of $N$-phase materials. {\em Proc. Roy. Soc. Lond. A} {\bf 380}, 333--348.", texsource = "l-lec17.tex", } @Article{Phan-Thien:1982:PUB, author = "N. Phan-Thien and Graeme W. Milton", title = "A possible use of bounds on effective moduli of composites", journal = j-J-REINF-PLAST-COMPOS, volume = "1", number = "2", pages = "107--114", month = apr, year = "1982", CODEN = "JRPCDW", DOI = "https://doi.org/10.1177/07316844820010020", ISSN = "0731-6844 (print), 1530-7964 (electronic)", ISSN-L = "0731-6844", bibdate = "Fri Aug 12 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://jrp.sagepub.com/content/1/2/107.abstract", acknowledgement = ack-gwm, fjournal = "Journal of Reinforced Plastics and Composites", journal-URL = "http://jrp.sagepub.com/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:1983:CFD, author = "Graeme W. Milton and Michael E. Fisher", title = "Continuum fluids with a discontinuity in the pressure", journal = j-J-STAT-PHYS, volume = "32", number = "2", pages = "413--438", month = aug, year = "1983", CODEN = "JSTPSB", DOI = "https://doi.org/10.1007/BF01012719", ISSN = "0022-4715 (print), 1572-9613 (electronic)", ISSN-L = "0022-4715", MRclass = "82A25 (82A05)", MRnumber = "715034 (85e:82031)", MRreviewer = "O. Penrose", bibdate = "Thu Aug 28 18:33:54 MDT 2014", bibsource = "http://link.springer.com/journal/10955; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=32&issue=2; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib", URL = "http://link.springer.com/article/10.1007/BF01012719", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Physics", journal-URL = "http://link.springer.com/journal/10955", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Phan-Thien:1983:NTO, author = "N. Phan-Thien and Graeme W. Milton", title = "New third-order bounds on the effective moduli of {$N$}-phase composites", journal = j-QUART-APPL-MATH, volume = "41", number = "1", pages = "59--74", year = "1983", CODEN = "QAMAAY", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "73K20 74A40 74A20", MRnumber = "700661 (84i:73058)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", ZMnumber = "0513.73004", acknowledgement = ack-gwm, fjournal = "Quarterly of Applied Mathematics", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0135", originalref = "Phan-Thien N. and Milton G. W. 1983 New third-order bounds on the effective moduli of N-phase composites. {\em Quart. Appl. Math.} {\bf 41}, 59--74.", remark = "AMS journal Web site has data only for 2005--date, so no DOI or URL is known. Not found in JSTOR either.", texsource = "l-lec10.tex", } @InProceedings{Milton:1984:CEEa, author = "Graeme W. Milton", editor = "D. L. Johnson and P. N. Sen", booktitle = "Physics and Chemistry of Porous Media: Papers from a Symposium Held at Schlumberger--Doll Research, Oct. 24--25, 1983", title = "Correlation of the electromagnetic and elastic properties of composities and microgeometries corresponding with effective medium approximations", journal = j-AIP-CONF-PROC, volume = "107", publisher = pub-AIP, address = pub-AIP:adr, bookpages = "223", pages = "52--65", year = "1984", CODEN = "APCPCS", DOI = "https://doi.org/10.1063/1.34305", ISBN = "0-88318-306-4", ISBN-13 = "978-0-88318-306-9", ISSN = "0094-243X (print), 1551-7616 (electronic), 1935-0465", ISSN-L = "0094-243X", LCCN = "TA418.9.P6 P46 1983", bibdate = "Sat Nov 28 20:27:56 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.34305", acknowledgement = ack-nhfb, fjournal = "AIP Conference Proceedings", journal-URL = "http://scitation.aip.org/content/aip/proceeding/aipcp", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Conference date: 24--25 October 1983. Location: Schlumberger- Doll Research", } @InProceedings{Milton:1984:CEEb, author = "Graeme W. Milton", editor = "D. L. Johnson and P. N. Sen", booktitle = "Physics and Chemistry of Porous Media: Papers from a Symposium Held at Schlumberger--Doll Research, Oct. 24--25, 1983", title = "Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium theory", journal = j-AIP-CONF-PROC, volume = "107", publisher = pub-AIP, address = pub-AIP:adr, bookpages = "223", pages = "66--77", year = "1984", CODEN = "APCPCS", DOI = "https://doi.org/10.1063/1.34306", ISBN = "0-88318-306-4", ISBN-13 = "978-0-88318-306-9", ISSN = "0094-243X (print), 1551-7616 (electronic), 1935-0465", ISSN-L = "0094-243X", LCCN = "TA418.9.P6 P46 1983", bibdate = "Sat Nov 28 20:27:56 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "AIP Conference Proceedings", URL = "http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.34306", acknowledgement = ack-gwm # "\slash " # ack-nhfb, fjournal = "AIP Conference Proceedings", journal-URL = "http://scitation.aip.org/content/aip/proceeding/aipcp", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0781", originallab = "GWM0406", originalref = "Milton G. W. 1984 Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium theory. In {\em Physics and Chemistry of Porous Media}, pp. 66--77, ed. by D. L. Johnson and P. N. Sen, American Institute of Physics, New York.", originalref-2 = "Milton G. W. 1984 Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium approximations. In {\em Physics and Chemistry of Porous Media} D. L. Johnson and P. N. Sen, eds., Am. Inst. Phys., New York, pp. 66--77.", remark = "Conference date: 24--25 October 1983. Location: Schlumberger- Doll Research", rest = "ed. by D. L. Johnson and P. N. Sen, American Institute of Physics, New York", texsource = "l-lec6.tex", texsource = "l-lec18.tex", xxtitle = "Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium approximations", } @Article{Berryman:1985:NCV, author = "James G. Berryman and Graeme W. Milton", title = "Normalization constraint for variational bounds on fluid permeability", journal = j-J-CHEM-PHYS, volume = "83", number = "2", pages = "754--760", day = "15", month = jul, year = "1985", CODEN = "JCPSA6", DOI = "https://doi.org/10.1063/1.449489", ISSN = "0021-9606 (print), 1089-7690 (electronic)", ISSN-L = "0021-9606", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/jcp/83/2/10.1063/1.449489", acknowledgement = ack-nhfb, fjournal = "Journal of Chemical Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:1985:CPA, author = "Graeme W. Milton", title = "The coherent potential approximation is a realizable effective medium scheme", journal = j-COMMUN-MATH-PHYS, volume = "99", number = "4", pages = "463--500", year = "1985", CODEN = "CMPHAY", DOI = "https://doi.org/10.1007/BF01215906", ISSN = "0010-3616 (print), 1432-0916 (electronic)", ISSN-L = "0010-3616", MRclass = "82A57 (73B99 82A42)", MRnumber = "796009 (86i:82054)", MRreviewer = "B. Derrida", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/BF01215906; http://projecteuclid.org/euclid.cmp/1103942837", acknowledgement = ack-gwm, fjournal = "Communications in Mathematical Physics", journal-URL = "http://link.springer.com/journal/220", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0782", originalref = "Milton G. W. 1985a The coherent potential approximation is a realizable effective medium scheme. {\em Comm. Math. Phys.} {\bf 99}, 463--500.", texsource = "l-lec6.tex", xxURL = "http://projecteuclid.org/euclid.cmp/1103942837", } @PhdThesis{Milton:1985:SEM, author = "Graeme W. Milton", title = "Some exotic models in statistical physics. {I}. {The} coherent potential approximation is a realizable effective medium scheme. {II}. {Anomalous} first-order transitions", type = "{Ph.D.} thesis", school = inst-CORNELL, address = inst-CORNELL:adr, pages = "x + 164", year = "1985", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://search.proquest.com/dissertations/docview/303393850/", acknowledgement = ack-gwm, advisor = "Michael Ellis Fisher", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0783", originalref = "Milton G. W. 1985b Some exotic models in statistical physics. I The coherent potential approximation is a realizable effective medium scheme. II Anomalous first-order transitions. {\em PhD Thesis} Cornell University.", rest = "Cornell University", texsource = "l-lec6.tex", } @InProceedings{Milton:1985:TCC, author = "Graeme W. Milton and Kenneth M. Golden", editor = "T. Ashworth and D. R. Smith", booktitle = "Thermal Conductivity", title = "Thermal conduction in composites", volume = "18", publisher = pub-PLENUM, address = pub-PLENUM:adr, bookpages = "xix + 764", pages = "571--582", year = "1985", ISBN = "0-306-41918-1", ISBN-13 = "978-0-306-41918-8", LCCN = "QC 320.8 I58 1983", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0550", originallab = "GWM0217", originalref = "Milton G. W. and Golden K. 1985 Thermal conduction in composites. In {\em Thermal Conductivity} {\bf 18}, ed. by T. Ashworth and D. R. Smith, pp. 571-582, Plenum Press, New York.", originalref-2 = "Milton G. W. and Golden K. 1985 Thermal conduction in composites. In {\em Thermal Conductivity} {\bf 18}, ed. by T. Ashworth and D. R. Smith (Plenum Press, New York). pp. 571--582.", rest = "Plenum Press, New York", texsource = "l-lec20.tex", texsource = "l-lec13.tex", xxnote = "Proceedings of the Eighteenth International Conductivity Conference, hosted and organized by the South Dakota School of Mines and Technology, sponsored by RE\slash SPEC Inc. of Rapid City and CINDAS\slash Purdue University, Held October 3--5, 1983, in Rapid City, South Dakota.", } @Article{Fisher:1986:CFO, author = "Michael E. Fisher and Graeme W. Milton", title = "Classifying first-order phase transitions", journal = j-PHYSICA-A, volume = "138", number = "1--2", pages = "22--54", month = sep, year = "1986", CODEN = "PHYSAG", DOI = "https://doi.org/10.1016/0378-4371(86)90172-X", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "82A25 (82A97)", MRnumber = "865235 (87k:82052)", MRreviewer = "V. A. Zagrebnov", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/037843718690172X", fjournal = "Physica A. Statistical and Theoretical Physics", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Kohn:1986:BEC, author = "Robert V. Kohn and Graeme W. Milton", editor = "J. L. Ericksen and David Kinderlehrer and Robert V. Kohn and Jacques-Louis Lions", booktitle = "{Homogenization and Effective Moduli of Materials and Media: Papers presented at a Workshop on Homogenization of Differential Equations and the Determination of Effective Moduli of Materials and Media, Primarily in the Context of Continuum Theory; Minneapolis, MN, October 22--October 26, 1984}", title = "On bounding the effective conductivity of anisotropic composites", volume = "1", publisher = pub-SV, address = pub-SV:adr, bookpages = "x + 263", pages = "97--125", year = "1986", DOI = "https://doi.org/10.1007/978-1-4613-8646-9_5", ISBN = "0-387-96306-5", ISBN-13 = "978-0-387-96306-8", LCCN = "QA808.2 .H661 1986", MRclass = "78A25", MRnumber = "859413 (87k:78005)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "The IMA Volumes in Mathematics and its Applications", URL = "http://link.springer.com/chapter/10.1007/978-1-4613-8646-9_5", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0319", originalref = "Kohn R. V. and Milton G. W. 1986 On bounding the effective conductivity of anisotropic composites. In {\em Homogenization and Effective Moduli of Materials and Media}, ed. by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J.-L. Lions., {\em The IMA volumes in mathematics and its applications} {\bf 1}, pp. 97--125, Springer-Verlag.", rest = "Springer-Verlag", texsource = "l-lec16.tex", } @InProceedings{Milton:1986:APLG, author = "Graeme W. Milton", editor = "George C. Papanicolaou", booktitle = "Advances in Multiphase Flow and Related Problems: Proceedings of the Workshop on Cross Disciplinary Research in Multiphase Flow, Leesburg, Virginia, June 2--4, 1986", title = "A proof that laminates generate all possible effective conductivity functions of two-dimensional, two-phase media", publisher = pub-SIAM, address = pub-SIAM:adr, bookpages = "x + 295", pages = "136--146", year = "1986", ISBN = "0-89871-212-2", ISBN-13 = "978-0-89871-212-4", LCCN = "QA922 .W671 1986", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0200", originalref = "Milton G. W. 1986b A proof that laminates generate all possible effective conductivity functions of two-dimensional, two-phase media. In {\em Advances in multiphase flow and related problems}, ed. G. Papanicolaou {\em S.I.A.M., Philadelphia}, 136--146.", texsource = "l-lec12.tex", xxkey = "xx1986b", xxtitle = "Proof that laminates generate all possible effective conductivity functions of two-dimensional, two-phase media", } @InCollection{Milton:1986:MPC, author = "Graeme W. Milton", editor = "J. L. Ericksen and David Kinderlehrer and Robert V. Kohn and Jacques-Louis Lions", booktitle = "{Homogenization and Effective Moduli of Materials and Media: Papers presented at a Workshop on Homogenization of Differential Equations and the Detemination of Effective Moduli of Materials and Media, Primarily in the Context of Continuum Theory; Minneapolis, MN, October 22--October 26, 1984}", title = "Modeling the properties of composites by laminates", volume = "1", publisher = pub-SV, address = pub-SV:adr, bookpages = "x + 263", pages = "150--174", year = "1986", DOI = "https://doi.org/10.1007/978-1-4613-8646-9_7", ISBN = "0-387-96306-5", ISBN-13 = "978-0-387-96306-8", LCCN = "QA808.2 .H661 1986", MRclass = "73-02 (76-02 78-02) 73K20", MRnumber = "859409 (87i:73006); 859415", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "The IMA Volumes in Mathematics and its Applications", acknowledgement = ack-gwm, book-DOI = "https://doi.org/10.1007/978-1-4613-8646-9", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0737", originallab = "GWM0548", originallab = "GWM0328", originallab = "GWM0199", originalref = "Milton G. W. 1986 Modeling the properties of composites by laminates. In {\em Homogenization and Effective Moduli of Materials and Media}, ed. by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J.-L. Lions., {\em The IMA volumes in mathematics and its applications} {\bf 1}, pp. 150--174, Springer-Verlag.", originalref-2 = "Milton G. W. 1986a Modeling the properties of composites by laminates. In {\em Homogenization and Effective Moduli of Materials and Media}, ed. by J. L. Ericksen, D. Kinderlehrer, R. Kohn, and J.-L. Lions., {\em The IMA volumes in mathematics and its applications} {\bf 1}, pp. 150--174, Springer-Verlag.", rest = "Springer-Verlag", rest = "{\em The IMA volumes in mathematics and its applications}", texsource = "l-lec5.tex", texsource = "l-lec20.tex", texsource = "l-lec16.tex", texsource = "l-lec12.tex", xxkey = "xx1986a", xxtitle = "Modelling the properties of composites by laminates", } @Article{Stroud:1986:AMD, author = "D. Stroud and Graeme W. Milton and B. R. De", title = "Analytical model for the dielectric response of brine-saturated rocks", journal = j-PHYS-REV-B-CMMP, volume = "34", number = "8", pages = "5145--5153", day = "15", month = oct, year = "1986", CODEN = "PRBMDO", DOI = "https://doi.org/10.1103/PhysRevB.34.5145", ISSN = "1098-0121", ISSN-L = "1098-0121", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevB.34.5145", fjournal = "Physical Review B: Condensed Matter and Materials Physics", journal-URL = "http://prb.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Fisher:1987:ECF, author = "Michael E. Fisher and Graeme W. Milton", title = "Erratum: ``{Classifying} first-order phase transitions'' {[Phys. A {\bf 138} (1986), no. 1, 22--54; MR0865235 (87k:82052)]}", journal = j-PHYSICA-A, volume = "142", number = "1-3", pages = "649", year = "1987", CODEN = "PHYSAG", DOI = "https://doi.org/10.1016/0378-4371(87)90048-3", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "82A25 (82A97)", MRnumber = "897288 (88h:82027)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", fjournal = "Physica A. Statistical and Theoretical Physics", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Francfort:1987:OBC, author = "G. A. Francfort and Graeme W. Milton", title = "Optimal bounds for conduction in two-dimensional, multiphase, polycrystalline media", journal = j-J-STAT-PHYS, volume = "46", number = "1--2", pages = "161--177", month = jan, year = "1987", CODEN = "JSTPSB", DOI = "https://doi.org/10.1007/BF01010338", ISSN = "0022-4715 (print), 1572-9613 (electronic)", ISSN-L = "0022-4715", MRclass = "78A25", MRnumber = "887243 (88m:78003)", bibdate = "Thu Aug 28 18:38:02 MDT 2014", bibsource = "http://link.springer.com/journal/10955; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=46&issue=1; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib", URL = "http://link.springer.com/article/10.1007/BF01010338", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of Statistical Physics", journal-URL = "http://link.springer.com/journal/10955", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0264", originalref = "Francfort G. A. and Milton G. W. 1987 Optimal bounds for conduction in two-dimensional, multiphase, polycrystalline media. {\em J. Stat. Phys.} {\bf 46}, 161--177.", texsource = "l-lec15.tex", } @Article{McPhedran:1987:TPT, author = "Ross C. McPhedran and Graeme W. Milton", title = "Transport properties of touching cylinder pairs and of the square array of touching cylinders", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "411", number = "1841", pages = "313--326", day = "8", month = jun, year = "1987", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1987.0069", ISSN = "0080-4630", ISSN-L = "0080-4630", bibdate = "Wed Jun 8 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/411/1841/313", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:1987:MCEa, author = "Graeme W. Milton", title = "Multicomponent composites, electrical networks and new types of continued fraction. {I}", journal = j-COMMUN-MATH-PHYS, volume = "111", number = "2", pages = "281--327", year = "1987", CODEN = "CMPHAY", DOI = "https://doi.org/10.1007/BF01217763", ISSN = "0010-3616 (print), 1432-0916 (electronic)", ISSN-L = "0010-3616", MRclass = "82A55 (73B99)", MRnumber = "899853 (89b:82084)", MRreviewer = "V. Mastrangelo", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://projecteuclid.org/euclid.cmp/1104159541", acknowledgement = ack-gwm, fjournal = "Communications in Mathematical Physics", journal-URL = "http://link.springer.com/journal/220", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0556", originallab = "GWM0215", originalref = "Milton G. W. 1987a Multicomponent composites, electrical networks and new types of continued fraction I. {\em Comm. Math. Phys.} {\bf 111}, 281--327.", originalref-2 = "Milton G. W. 1987 Multicomponent composites, electrical networks and new types of continued fraction I. {\em Comm. Math. Phys.} {\bf 111}, 281--327.", texsource = "l-lec21.tex", texsource = "l-lec13.tex", } @Article{Milton:1987:MCEb, author = "Graeme W. Milton", title = "Multicomponent composites, electrical networks and new types of continued fraction. {II}", journal = j-COMMUN-MATH-PHYS, volume = "111", number = "3", pages = "329--372", year = "1987", CODEN = "CMPHAY", DOI = "https://doi.org/10.1007/BF01238903", ISSN = "0010-3616 (print), 1432-0916 (electronic)", ISSN-L = "0010-3616", MRclass = "82A55 (73B99 73F99 94C05)", MRnumber = "900499 (89b:82085)", MRreviewer = "V. Mastrangelo", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://projecteuclid.org/euclid.cmp/1104159635", acknowledgement = ack-gwm, fjournal = "Communications in Mathematical Physics", journal-URL = "http://link.springer.com/journal/220", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0557", originallab = "GWM0273", originalref = "Milton G. W. 1987b Multicomponent composites, electrical networks and new types of continued fraction II. {\em Comm. Math. Phys.} {\bf 111}, 329--372.", originalref-2 = "Milton G. W. 1987 Multicomponent composites, electrical networks and new types of continued fraction II. {\em Comm. Math. Phys.} {\bf 111}, 329--372.", texsource = "l-lec21.tex", texsource = "l-lec15.tex", } @Article{Avellaneda:1988:ECP, author = "M. Avellaneda and Andrej V. Cherkaev and K. A. Lurie and Graeme W. Milton", title = "On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality", journal = j-J-APPL-PHYS, volume = "63", number = "10", pages = "4989--5003", year = "1988", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.340445", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/jap/63/10/10.1063/1.340445", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of Applied Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jap/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0676", originallab = "GWM0421", originallab = "GWM0389", originallab = "GWM0257", originalref = "Avellaneda M., Cherkaev A. V., Lurie K. A., and Milton G. W. 1988 On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality. {\em J. Appl. Phys.} {\bf 63}, 4989--5003.", texsource = "l-lec4.tex", texsource = "l-lec18.tex", texsource = "l-lec15.tex", } @Article{Berryman:1988:MRC, author = "James G. Berryman and Graeme W. Milton", title = "Microgeometry of random composites and porous media", journal = j-J-PHYS-D, volume = "21", number = "1", pages = "87--94", year = "1988", CODEN = "JPAPBE", DOI = "https://doi.org/10.1088/0022-3727/21/1/013", ISSN = "0022-3727 (print), 1361-6463 (electronic)", ISSN-L = "0022-3727", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/0022-3727/21/1/013", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of Physics D: Applied Physics", journal-URL = "http://iopscience.iop.org/0022-3727/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0391", originallab = "GWM0349", originalref = "Berryman J. G. and Milton G. W. 1988 Microgeometry of random composites and porous media. {\em J. Phys. D: Appl. Phys.} {\bf 21}, 87--94.", texsource = "l-lec18.tex", texsource = "l-lec17.tex", xxURL = "http://iopscience.iop.org/article/10.1088/0022-3727/21/1/013/", } @Article{McPhedran:1988:ASC, author = "Ross C. McPhedran and L. Poladian and Graeme W. Milton", title = "Asymptotic studies of closely spaced, highly conducting cylinders", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "415", number = "1848", pages = "185--196", year = "1988", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1988.0009", ISSN = "0080-4630", ISSN-L = "0080-4630", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0831", originalref = "McPhedran R. C., Poladian L., and Milton G. W. 1988 Asymptotic studies of closely spaced, highly conducting cylinders. {\em Proc. Roy. Soc. Lond. A} {\bf 415}, 185--196.", texsource = "l-lec7.tex", } @Article{Milton:1988:CHE, author = "Graeme W. Milton", title = "Classical {Hall}-effect in two-dimensional composites: a characterization of the set of realizable effective conductivity tensors", journal = j-PHYS-REV-B-CMMP, volume = "38", number = "16", pages = "11296--11303", day = "1", month = dec, year = "1988", CODEN = "PRBMDO", DOI = "https://doi.org/10.1103/PhysRevB.38.11296", ISSN = "1098-0121", ISSN-L = "1098-0121", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.aps.org/prb/abstract/10.1103/PhysRevB.38.11296", acknowledgement = ack-gwm, fjournal = "Physical Review B: Condensed Matter and Materials Physics", journal-URL = "http://prb.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0530", originalref = "Milton G. W. 1988 Classical Hall-effect in two-dimensional composites: a characterization of the set of realizable effective conductivity tensors. {\em Phys. Rev. B} {\bf 38}, 11296--11303.", texsource = "l-lec2.tex", } @Article{Milton:1988:VBE, author = "Graeme W. Milton and Robert V. Kohn", title = "Variational bounds on the effective moduli of anisotropic composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "36", number = "6", pages = "597--629", year = "1988", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/0022-5096(88)90001-4", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "73C40 (73C30 73C60 73K20 73R05)", MRnumber = "969257 (90h:73015)", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/0022509688900014", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0895", originallab = "GWM0739", originallab = "GWM0331", originalref = "Milton G. W. and Kohn R. V., 1988 Variational bounds on the effective moduli of anisotropic composites. {\em J. Mech. Phys. Solids} {\bf 36}, 597--629.", texsource = "l-lec9.tex", texsource = "l-lec5.tex", texsource = "l-lec16.tex", } @InProceedings{Avellaneda:1989:BEE, author = "M. Avellaneda and Graeme W. Milton", editor = "David Hui and Thomas J. Kozik", booktitle = "{Composite material technology 1989: presented at the twelfth Annual Energy-Sources Technology Conference and Exhibition, Houston, Texas January 22--25, 1989}", title = "Bounds on the effective elasticity tensor of composites based on two point correlations", volume = "PD-24", publisher = pub-ASME, address = pub-ASME:adr, bookpages = "vi + 215", pages = "89--93", year = "1989", LCCN = "TA 418.9.C6 C56 1989", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Petroleum Division", acknowledgement = ack-gwm # " and " # ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0723", texsource = "l-lec5.tex", xxaddress = "Houston, Texas", xxpublisher = "American Society of Mechanical Engineers, Petroleum Division", } @Article{Avellaneda:1989:CPP, author = "Marco Avellaneda and A. V. Cherkaev and K. A. Lurie and Graeme Milton", title = "On the conductivity of polycrystals and a phase-interchange inequality", journal = j-PHYSICA-A, volume = "157", number = "1", pages = "148--153", month = may, year = "1989", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/0378-4371(89)90291-4", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Sat Nov 28 18:44:37 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/0378437189902914", acknowledgement = ack-nhfb, fjournal = "Physica A", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Avellaneda:1989:OBE, author = "Marco Avellaneda and Graeme W. Milton", title = "Optimal Bounds on the Effective Bulk Modulus of Polycrystals", journal = j-SIAM-J-APPL-MATH, volume = "49", number = "3", pages = "824--837", month = jun, year = "1989", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/0149048", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "73K20 (73B27 73V25)", MRnumber = "997923 (91e:73088)", bibdate = "Fri Nov 8 18:01:57 MST 2002", bibsource = "ACM Computing Archive CD-ROM database (1991); http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", URL = "http://epubs.siam.org/doi/pdf/10.1137/0149048", acknowledgement = ack-gwm # " and " # ack-nhfb, bibno = "64947", catcode = "G.1.8; J.2; G.1.2; G.1.6", CRclass = "G.1.8 Partial Differential Equations; G.1.8 Difference methods; J.2 Physics; G.1.2 Approximation; G.1.2 Elementary function approximation; G.1.6 Optimization; G.1.6 Constrained optimization", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods; Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics; Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization", fjournal = "SIAM Journal on Applied Mathematics", genterm = "algorithms; theory; experimentation", guideno = "1989-09716", journal-URL = "http://epubs.siam.org/siap", journalabbrev = "SIAM J. Appl. Math.", jrldate = "June 1989", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0419", originallab = "GWM0388", originallab = "GWM0258", originalref = "Avellaneda M. and Milton G. W. 1989 Optimal bounds on the effective bulk modulus of polycrystals. {\em SIAM J. Appl. Math.} {\bf 49}, 824--837.", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS", texsource = "l-lec18.tex", texsource = "l-lec15.tex", } @InProceedings{Tartar:1989:MSA, author = "Luc Tartar", editor = "Robert V. Kohn and Graeme W. Milton", booktitle = "{Proceedings of the SIAM Workshop on Random Media and Composites, Leesburg, Virginia, December 7--10, 1988}", title = "{$H$}-measures and small amplitude homogenization", publisher = pub-SIAM, address = pub-SIAM:adr, bookpages = "214", pages = "89--99", year = "1989", ISBN = "0-89871-246-7", ISBN-13 = "978-0-89871-246-9", LCCN = "TA401.3 .S53 1988", MRclass = "00B25 (35-06 73-06 73B27 73B99 73K20 82B44 82C44)", MRnumber = "1059286 (91b:00052)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0091", originalref = "Tartar L. 1989 $H$-measures and small amplitude homogenization. In {\em Random Media and Composites}, ed. by R. V. Kohn and G. W. Milton, pp. 89--99, Society for Industrial and Applied Mathematics.", rest = "Society for Industrial and Applied Mathematics", texsource = "l-lec10.tex", } @Article{McPhedran:1990:ITP, author = "Ross C. McPhedran and Graeme W. Milton", title = "Inverse transport problems for composite media", journal = j-MATER-RES-SOC-SYMP-PROC, volume = "195", number = "??", pages = "257--274", year = "1990", CODEN = "MRSPDH", DOI = "https://doi.org/10.1557/PROC-195-257", ISSN = "1946-4274", ISSN-L = "1946-4274", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.cambridge.org/abstract_S1946427400554219", acknowledgement = ack-gwm, fjournal = "Materials Research Society Symposium Proceedings", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=OPL", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0471", originalref = "McPhedran R. C. and Milton G. W. 1990 Inverse transport problems for composite media. {\em Mat. Res. Soc. Symp. Proc.} {\bf 195}, 257--274.", texsource = "l-lec19.tex", } @InCollection{Milton:1990:BRT, author = "Graeme W. Milton", editor = "G{\'e}rard A. Maugin", booktitle = "{Continuum models and discrete systems: [contains the texts of most of the short contributions presented at the Sixth International Symposium on Continuum Models and Discrete Systems \ldots{} held on the campus of the University of Bourgogne, Dijon, France, from June 25 to June 29, 1989] Vol. 1}", title = "A brief review of the translation method for bounding effective elastic tensors of composites", volume = "1", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, bookpages = "324", pages = "60--74", year = "1990", ISBN = "0-582-05121-5", ISBN-13 = "978-0-582-05121-8", MRclass = "73K20 (73B27 73V25)", MRnumber = "1100723 (92d:73035)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Interaction of Mechanics and Mathematics Series, Longman, Essex", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0408", originalref = "Milton G. W. 1990 A brief review of the translation method for bounding effective elastic tensors of composites. In {\em Continuum Models and Discrete Systems}, pp. 60--74, ed. by G. A. Maugin, Volume 1, Interaction of Mechanics and Mathematics Series, Longman, Essex.", rest = "ed. by G. A. Maugin, Volume 1, Interaction of Mechanics and Mathematics Series, Longman, Essex", texsource = "l-lec18.tex", } @Article{Milton:1990:CSP, author = "Graeme W. Milton", title = "On characterizing the set of possible effective tensors of composites: {The} variational method and the translation method", journal = j-COMM-PURE-APPL-MATH, volume = "43", number = "1", pages = "63--125", year = "1990", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.3160430104", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "73B27 (49S05 73K20)", MRnumber = "1024190 (91c:73006)", MRreviewer = "John M. Ball", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430104/full", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Communications on Pure and Applied Mathematics (New York)", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0894", originallab = "GWM0871", originallab = "GWM0738", originallab = "GWM0407", originallab = "GWM0329", originallab = "GWM0274", originalref = "Milton G. W. 1990 On characterizing the set of possible effective tensors of composites: The variational method and the translation method. {\em Comm. of Pure and Appl. Math} {\bf XLIII}, 63--125.", originalref-2 = "Milton G. W. 1990 On characterizing the set of possible effective tensors of composites: the variational method and the translation method. {\em Comm. Pure Appl. Math.} {\bf 43}, 63--125.", texsource = "l-lec9.tex", texsource = "l-lec5.tex", texsource = "l-lec18.tex", texsource = "l-lec16.tex", texsource = "l-lec15.tex", xxURL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430104/", xxvolume = "XLIII", } @Article{Milton:1990:RCF, author = "Graeme W. Milton and Kenneth M. Golden", title = "Representations for the conductivity functions of multicomponent composites", journal = j-COMM-PURE-APPL-MATH, volume = "43", number = "5", pages = "647--671", year = "1990", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.3160430504", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "78A30", MRnumber = "1057234 (91c:78009)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0559", originallab = "GWM0275", originallab = "GWM0201", originallab = "GWM0086", originalref = "Milton G. W. and Golden K. 1990 Representations for the conductivity functions of multicomponent composites. {\em Comm. Pure Appl. Math.} {\bf XLIII}, 647--671.", originalref-2 = "Milton G. W. and Golden K. 1990 Representations for the conductivity functions of multicomponent composites. {\em Comm. Pure Appl. Math.} {\bf 43}, 647-671.", texsource = "l-lec21.tex", texsource = "l-lec15.tex", texsource = "l-lec12.tex", texsource = "l-lec10.tex", xxURL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160430504/", xxvolume = "XLIII", } @Article{Berryman:1991:ERG, author = "James G. Berryman and Graeme W. Milton", title = "Exact results for generalized {Gassman}'s equations in composite porous media with two constituents", journal = j-GEOPHYSICS, volume = "56", number = "12", pages = "1950--1960", month = dec, year = "1991", CODEN = "GPYSA7", DOI = "https://doi.org/10.1190/1.1443006", ISSN = "0016-8033 (print), 1942-2156 (electronic)", ISSN-L = "0016-8033", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://library.seg.org/doi/abs/10.1190/1.1443006", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Geophysics", journal-URL = "http://library.seg.org/loi/gpysa7", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0623", originalref = "Berryman J. G. and Milton G. W. 1991 Exact results for generalized Gassman's equations in composite porous media with two constituents. {\em Geophysics} {\bf 56}, 1950--1960.", texsource = "l-lec3.tex", xxURL = "http://library.seg.org/doi/abs/10.1190/1.1443006", } @Unpublished{Kublanov:1991:REE, author = "L. Kublanov and Graeme W. Milton", title = "Rigorous estimates for the elastic moduli for a two-dimensional two-phase material", pages = "????", year = "1991", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Unpublished manuscript.", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0367", originalref = "Kublanov L. and Milton G. W. 1991 Rigorous estimates for the elastic moduli for a two-dimensional two-phase material. {\em Unpublished manuscript}.", texsource = "l-lec17.tex", } @InProceedings{Milton:1991:EMC, author = "Robert V. Kohn and Graeme W. Milton", editor = "Shun-Chin Chou", booktitle = "Proceedings of [the] 12th Army Symposium on Solid Mechanics: Synergism of Mechanics. Mathematics, and Materials: 4--7 November 1991, Plymouth, Massachusetts", title = "Extremal Microstructures for Composite Materials", publisher = "Defense Technical Information Center", address = "Ft. Belvoir, VA 22060-5606, USA", bookpages = "viii + 644", pages = "75--84", year = "1991", LCCN = "TA349 .P6 1991", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA326997#page=74", acknowledgement = ack-nhfb, book-URL = "http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA326997", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InProceedings{Milton:1991:FER, author = "Graeme W. Milton", editor = "Gianni {Dal Maso} and Gianfausto F. Dell'Antonio", booktitle = "Composite Media and Homogenization Theory: Proceedings of the Workshop on Composite Media and Homogenization Theory Held in Trieste, Italy, from January 15 to 26, 1990", title = "The field equation recursion method", volume = "5", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, bookpages = "xiv + 258", pages = "223--245", year = "1991", DOI = "https://doi.org/10.1007/978-1-4684-6787-1_13", ISBN = "0-8176-3511-4, 3-7643-3511-4", ISBN-13 = "978-0-8176-3511-4, 978-3-7643-3511-3", LCCN = "QA808.2 .C665 1991", MRclass = "73-06 (00B25 49J45 73B27 73K20 76S05) 78A25", MRnumber = "1145753 (93b:73007); 1145740 (92h:73002)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Progress in Nonlinear Differential Equations and Their Applications", URL = "http://link.springer.com/chapter/10.1007/978-1-4684-6787-1_13", acknowledgement = ack-gwm, book-DOI = "https://doi.org/10.1007/978-1-4684-6787-1", book-URL = "http://link.springer.com/book/10.1007/978-1-4684-6787-1", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0558", originallab = "GWM0549", originallab = "GWM0409", originallab = "GWM0216", originalref = "Milton G. W. 1991b The field equation recursion method. In {\em Composite Media and Homogenization Theory}, ed. by G. Dal Maso and G. F. Dell'Antonio, {\em Progress in Nonlinear Differential Equations and Their Applications} {\bf 5}, pp. 223--245, Birkh{\"a}user.", originalref-2 = "Milton G. W. 1991 The field equation recursion method. In {\em Composite Media and Homogenization Theory}, ed. by G. Dal Maso and G. F. Dell'Antonio, {\em Progress in Nonlinear Differential Equations and Their Applications} {\bf 5}, pp. 223--245, Birkh{\"a}user.", originalref-3 = "Milton G. W. 1991 The field equation recursion method. In {\em Composite Media and Homogenization Theory}, pp. 223--245, ed. by G. Dal Maso and G. F. Dell'Antonio, {\em Progress in Nonlinear Differential Equations and Their Applications} {\bf 5}, Birkh{\"a}user.", rest = "Birkh{\"a}user", texsource = "l-lec21.tex", texsource = "l-lec20.tex", texsource = "l-lec18.tex", texsource = "l-lec13.tex", xxbooktitle = "Composite Media and Homogenization Theory: An International Centre for Theoretical Physics workshop, Trieste, Italy, January 1990", } @Article{Nesi:1991:PCM, author = "Vincenzo Nesi and Graeme W. Milton", title = "Polycrystalline configurations that maximize electrical resistivity", journal = j-J-MECH-PHYS-SOLIDS, volume = "39", number = "4", pages = "525--542", year = "1991", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/0022-5096(91)90039-Q", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "73R05 (73B99 73K20 73V25 78A25 82D25)", MRnumber = "1106125 (93a:73070)", MRreviewer = "Philippe Boulanger", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/002250969190039Q", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0607", originallab = "GWM0433", originalref = "Nesi V. and Milton G. W. 1991 Polycrystalline configurations that maximize electrical resistivity. {\em J. Mech. Phys. Solids} {\bf 39}, 525--542.", texsource = "l-lec23.tex", texsource = "l-lec18.tex", xxURL = "http://www.sciencedirect.com/science/article/pii/002250969190039Q", } @Article{Smereka:1991:BFR, author = "Peter Smereka and Graeme W. Milton", title = "Bubbly flow and its relation to conduction in composites", journal = j-J-FLUID-MECH, volume = "233", pages = "65--81", month = dec, year = "1991", CODEN = "JFLSA7", DOI = "https://doi.org/10.1017/S0022112091000393", ISSN = "0022-1120 (print), 1469-7645 (electronic)", ISSN-L = "0022-1120", MRclass = "76T05 (73B27 73K20 76D99)", MRnumber = "1140079 (92i:76097)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.cambridge.org/abstract_S0022112091000393", fjournal = "Journal of Fluid Mechanics", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=FLM", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Berryman:1992:ERL, author = "J. G. Berryman and Graeme W. Milton", title = "Exact results in linear thermomechanics of fluid saturated porous media", journal = j-APPL-PHYS-LET, volume = "61", number = "17", pages = "2030--??", day = "26", month = oct, year = "1992", CODEN = "APPLAB", DOI = "https://doi.org/10.1063/1.108349", ISSN = "0003-6951 (print), 1077-3118 (electronic), 1520-8842", ISSN-L = "0003-6951", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/apl/61/17/10.1063/1.108349", acknowledgement = ack-nhfb, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Cherkaev:1992:IPS, author = "Andrei V. Cherkaev and Konstantin A. Lurie and Graeme W. Milton", title = "Invariant properties of the stress in plane elasticity and equivalence classes of composites", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "438", number = "1904", pages = "519--529", day = "8", month = sep, year = "1992", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1992.0123", ISSN = "0080-4630", ISSN-L = "0080-4630", MRclass = "73B27 (73C99 73K20)", MRnumber = "1183894 (93g:73009)", bibdate = "Thu Dec 16 15:46:41 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/438/1904/519", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0515", originalref = "Cherkaev A. V., Lurie K. A., and Milton G. W. 1992 Invariant properties of the stress in plane elasticity and equivalence classes of composites. {\em Proc. Roy. Soc. London} A {\bf 438}, 519--529.", texsource = "l-lec2.tex", } @Article{Milton:1992:CMP, author = "Graeme W. Milton", title = "Composite materials with {Poisson}'s ratios close to $ - 1 $", journal = j-J-MECH-PHYS-SOLIDS, volume = "40", number = "5", pages = "1105--1137", month = jul, year = "1992", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/0022-5096(92)90063-8", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "73K20 (73B27 73C99)", MRnumber = "1167758 (93c:73074)", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0576", originallab = "GWM0029", originalref = "Milton G. W. 1992 Composite materials with Poisson's ratios close to $-1$. {\em J. Mech. Phys. Solids} {\bf 40}, 1105--1137.", texsource = "l-lec1.tex", texsource = "l-lec22.tex", xxURL = "http://www.sciencedirect.com/science/article/pii/0022509692900638", } @Article{Gibiansky:1993:EVM, author = "Leonid V. Gibiansky and Graeme W. Milton", title = "On the effective viscoelastic moduli of two-phase media. {I}. {Rigorous} bounds on the complex bulk modulus", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "440", number = "1908", pages = "163--188", day = "8", month = jan, year = "1993", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1993.0010", ISSN = "0080-4630", ISSN-L = "0080-4630", MRclass = "73B27 (73F05 73K20 73V25)", MRnumber = "1232831 (94h:73009)", MRreviewer = "Bogdan Vernescu", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0304", originallab = "GWM0213", originalref = "Gibiansky L. V. and Milton G. W. 1993 On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus. {\em Proc. Roy. Soc. Lond. A} {\bf 440}, 163--188.", texsource = "l-lec16.tex", texsource = "l-lec13.tex", xxURL = "http://rspa.royalsocietypublishing.org/content/440/1908/163", } @InProceedings{Gibiansky:1993:VCE, author = "Leonid V. Gibiansky and Roderic S. Lakes and Graeme W. Milton", editor = "J. Herskovits", booktitle = "Structural Optimization 93 (Proceedings of The 1993 World Congress on Optimal Design of Structural Systems)", title = "Viscoelastic composites with extremal properties", volume = "1", publisher = "Federal university of Rio de Janeiro", address = "Rio de Janeiro, Brazil", bookpages = "xvi + 480", pages = "369--376", year = "1993", LCCN = "TA658.8 S928 1993", bibdate = "Sat May 30 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "The World Congress on Optimal Design of Structural Systems Proceedings", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxISBN = "none", xxisbn-13 = "none", } @Article{Milton:1993:MET, author = "G. W. Milton and A. V. Cherkaev", title = "Materials with elastic tensors that range over the entire set compatible with thermodynamics", journal = "Abstracts of the Joint ASCE-ASME-SES Meeting, June, 1993", volume = "??", number = "??", pages = "6--9", month = "????", year = "1993", bibdate = "Thu Feb 28 09:38:03 2019", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-avc, } @Article{Nicorovici:1993:TPT, author = "N. A. Nicorovici and Ross C. McPhedran and Graeme W. Milton", title = "Transport properties of a three-phase composite material: {The} square array of coated cylinders", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "442", number = "1916", pages = "599--620", day = "8", month = sep, year = "1993", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1993.0124", ISSN = "0080-4630", ISSN-L = "0080-4630", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0832", originallab = "GWM0202", originalref = "Nicorovici N. A., McPhedran R. C., and Milton G. W. 1993 Transport properties of a three-phase composite material: the square array of coated cylinders. {\em Proc. Roy. Soc. Lond. A} {\bf 442}, 599--620.", texsource = "l-lec7.tex", texsource = "l-lec12.tex", xxURL = "http://rspa.royalsocietypublishing.org/content/442/1916/599", } @Article{Clark:1994:MEC, author = "Karen E. Clark and Graeme W. Milton", title = "Modeling the effective conductivity function of an arbitrary two-dimensional polycrystal using sequential laminates", journal = j-PROC-R-SOC-EDINB-SECT-A-MATH, volume = "124", number = "4", pages = "757--783", year = "1994", CODEN = "PEAMDU", DOI = "https://doi.org/10.1017/S030821050002864X", ISSN = "0308-2105 (print), 1473-7124 (electronic)", ISSN-L = "0308-2105", MRclass = "73B27 (82D25)", MRnumber = "1298591 (96b:73005)", MRreviewer = "Albert Fannjiang", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of Edinburgh. Section A. Mathematics", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRM", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0179", originalref = "Clark K. E. and Milton G. W. 1994 Modeling the effective conductivity function of an arbitrary two-dimensional polycrystal using sequential laminates, {\em Proc. Roy. Soc. Edinburgh} {\bf 124A}, 757--783.", texsource = "l-lec12.tex", xxtitle = "Modelling the effective conductivity function of an arbitrary two-dimensional polycrystal using sequential laminates", } @Article{Francfort:1994:SCE, author = "Gilles A. Francfort and Graeme W. Milton", title = "Sets of conductivity and elasticity tensors stable under lamination", journal = j-COMM-PURE-APPL-MATH, volume = "47", number = "3", pages = "257--279", year = "1994", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.3160470302", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "73B27 (73K20 78A25)", MRnumber = "1266241 (95c:73004)", MRreviewer = "J. Saint Jean Paulin", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470302/full", acknowledgement = ack-gwm, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0567", originalref = "Francfort G. A. and Milton G. W. 1994 Sets of conductivity and elasticity tensors stable under lamination. {\em Comm. Pure Appl. Math.} {\bf 47}, 257--279.", texsource = "l-lec22.tex", } @Article{Milton:1994:LBS, author = "Graeme W. Milton", title = "A link between sets of tensors stable under lamination and quasiconvexity", journal = j-COMM-PURE-APPL-MATH, volume = "47", number = "7", pages = "959--1003", year = "1994", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.3160470704", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "73B27 (73K20)", MRnumber = "1283879 (95k:73004)", MRreviewer = "Pablo Pedregal", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470704/full", acknowledgement = ack-gwm, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0577", originallab = "GWM0427", originallab = "GWM0410", originalref = "Milton G. W. 1994 A link between sets of tensors stable under lamination and quasiconvexity. {\em Comm. Pure Appl. Math.} {\bf XLVII}, 959--1003.", originalref-2 = "Milton G. W. 1994 A link between sets of tensors stable under lamination and quasiconvexity. {\em Comm. Pure Appl. Math.} {\bf 47}, 959--1003.", texsource = "l-lec22.tex", texsource = "l-lec18.tex", xxURL = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.3160470704/", xxvolume = "XLVII", } @Article{Nicorovici:1994:ODP, author = "N. A. Nicorovici and Ross C. McPhedran and Graeme W. Milton", title = "Optical and dielectric properties of partially resonant composites", journal = j-PHYS-REV-B-CMMP, volume = "49", number = "12", pages = "8479--8482", day = "15", month = mar, year = "1994", CODEN = "PRBMDO", DOI = "https://doi.org/10.1103/PhysRevB.49.8479", ISSN = "1098-0121", ISSN-L = "1098-0121", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Physical Review B: Condensed Matter and Materials Physics", journal-URL = "http://prb.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", texsource = "l-lec7.tex", xxURL = "http://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.8479", } @Article{Clark:1995:OBC, author = "Karen E. Clark and Graeme W. Milton", title = "Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "448", number = "1933", pages = "161--190", day = "8", month = feb, year = "1995", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1995.0011", ISSN = "0080-4630", ISSN-L = "0080-4630", MRclass = "78A30 (73B27 73B30 78-08 78A25)", MRnumber = "1324960 (96a:78004)", MRreviewer = "David J. Bergman", bibdate = "Wed Sep 12 10:43:26 2001", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/448/1933/161", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0543", originalref = "Clark K. E. and Milton G. W. 1995 Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites. {\em Proc. Roy. Soc. Lond. A} {\bf 448}, 161--190.", texsource = "l-lec20.tex", xxnote = "OCLC ArticleFirst has both 1933 and 1934; 1934 is wrong.", xxURL = "http://rspa.royalsocietypublishing.org/content/448/1933/161", } @Article{Milton:1995:CBP, author = "Graeme W. Milton and A. B. Movchan", title = "A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, volume = "450", number = "1939", pages = "293--317", month = aug, year = "1995", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1995.0086", ISSN = "0080-4630", ISSN-L = "0080-4630", MRclass = "73B40 (73C02 73K20 78A25)", MRnumber = "1349509 (96i:73011)", MRreviewer = "J. Saint Jean Paulin", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", abstract = "A correspondence between the two-dimensional complex dielectric equations and those of plane-strain elasticity is established. Specifically, homogeneous orthotropic dielectric media are shown to correspond to orthotropic elastic media, and by making an affine transformation of the elasticity problem, we obtain correspondences between orthotropic dielectric media and non-orthotropic elastic media. We also find a correspondence between the elasticity problem and a pair of dielectric problems in which the dielectric tensors are real. These correspondences are extended to certain classes of inhomogeneous media. Applied to composite materials, they imply exact relations between the effective tensors of associated dielectric and elasticity problems.", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0718", originallab = "GWM0669", originalref = "Milton G. W. and Movchan A. B. 1995 A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media. {\em Proc. Roy. Soc. Lond.} A{\bf 450}, 293--317.", originalref-2 = "Milton G. W. and Movchan A. B. 1995 A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media. {\em Proc. R. Soc. Lond. A} {\bf 450}, 293--317.", texsource = "l-lec4.tex", texsource = "l-lec3.tex", xxCODEN = "PRSLAZ", xxISSN = "0370-1662", xxjournal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI, xxURL = "http://rspa.royalsocietypublishing.org/content/450/1939/293", } @Article{Milton:1995:WET, author = "Graeme W. Milton and Andrej V. Cherkaev", title = "Which elasticity tensors are realizable?", journal = j-J-ENG-MATER-TECHNOL, volume = "117", number = "4", pages = "483--493", day = "1", month = oct, year = "1995", CODEN = "JEMTA8", DOI = "https://doi.org/10.1115/1.2804743", ISSN = "0094-4289 (print), 1528-8889 (electronic)", ISSN-L = "0094-4289", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of engineering materials and technology", journal-URL = "http://materialstechnology.asmedigitalcollection.asme.org/issues.aspx", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0578", originalref = "Milton G. W. and Cherkaev A. V. 1995 Which elasticity tensors are realizable? {\em ASME J. Eng. Mat. Tech.} {\bf 117}, 483--493.", texsource = "l-lec22.tex", texsource = "l-lec01b.tex", xxURL = "http://materialstechnology.asmedigitalcollection.asme.org/article.aspx?articleID=1425346", } @Article{Avellaneda:1996:CCP, author = "M. Avellaneda and Andrej V. Cherkaev and Leonid V. Gibiansky and Graeme W. Milton and M. Rudelson", title = "A complete characterization of the possible bulk and shear moduli of planar polycrystals", journal = j-J-MECH-PHYS-SOLIDS, volume = "44", number = "7", pages = "1179--1218", month = jul, year = "1996", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/0022-5096(96)00018-X", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/002250969600018X", acknowledgement = ack-gwm, fjournal = "Journal of the mechanics and physics of solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0843", originallab = "GWM0420", originallab = "GWM0390", originalref = "Avellaneda M., Cherkaev A. V., Gibiansky L. V., Milton G. W., and Rudelson M. 1996 A complete characterization of the possible bulk and shear moduli of planar polycrystals. {\em J. Mech. Phys. Solids} {\bf 44}, 1179--1218.", texsource = "l-lec8.tex", texsource = "l-lec18.tex", xxURL = "http://www.sciencedirect.com/science/article/pii/002250969600018X", } @Article{Berryman:1997:VBE, author = "J. G. Berryman and Graeme W. Milton", title = "Variational Bounds and Effective Medium Theories for Viscoelastic Composites", journal = "APS March Meeting Abstracts", volume = "??", number = "??", pages = "??--??", month = "????", year = "1997", CODEN = "", ISSN = "", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://adsabs.harvard.edu/abs/1997APS..MAR.B1510B", acknowledgement = ack-nhfb, journal-URL = "http://adsabs.harvard.edu", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Helsing:1997:DRC, author = "Johan Helsing and Graeme W. Milton and A. B. Movchan", title = "Duality relations, correspondences and numerical results for planar elastic composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "45", number = "4", pages = "565--590", year = "1997", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/S0022-5096(96)00083-X", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "73K20 (73B27 73C02 73V20)", MRnumber = "1449232 (98e:73092)", MRreviewer = "Leonid V. Gibiansky", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S002250969600083X", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://www.sciencedirect.com/science/article/pii/S002250969600083X", } @InProceedings{Milton:1997:CMM, author = "Graeme W. Milton", editor = "T. Tatsumi and E. Watanabe and T. Kambe", booktitle = "Theoretical and Applied Mechanics 1996: Proceedings of the XIXth International Congress of Theoretical and Applied Mechanics, Kyoto, Japan, 25--31 August 1996", title = "Composites: {A} myriad of microstructure independent relations", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, bookpages = "xxxix + 623", pages = "443--459", year = "1997", ISBN = "0-444-82446-4", ISBN-13 = "978-0-444-82446-2", LCCN = "QA801 .I39 1996", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0641", originallab = "GWM0055", originalref = "Milton G. W. 1997 Composites: A myriad of microstructure independent relations. In {\em Theoretical and Applied Mechanics 1996}, pp. 443--459, ed. by T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier.", originalref-2 = "Milton G. W. 1997 Composites: A myriad of microstructure independent relations. {\em Theoretical and Applied Mechanics 1996}, pp. 443--459, ed. by T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier.", rest = "ed. by T.Tatsumi, E.Watanabe, and T.Kambe, Elsevier", texsource = "l-lec3.tex", texsource = "l-lec1.tex", } @Article{Milton:1997:ERC, author = "Graeme W. Milton", title = "Exact Relations for Composites: Towards a Complete Solution", journal = j-DOC-MATH, volume = "Extra volume ICM 1998 III", pages = "623--632", year = "1997", ISSN = "1431-0643", ISSN-L = "1431-0635", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.mathunion.org/ICM/ICM1998.3/Main/16/Milton.MAN.ocr.pdf", acknowledgement = ack-nhfb, fjournal = "Documenta mathematica", journal-URL = "http://www.math.uiuc.edu/documenta/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:1997:EVM, author = "Graeme W. Milton and James G. Berryman", title = "On the effective viscoelastic moduli of two-phase media. {II}. {Rigorous} bounds on the complex shear modulus in three dimensions", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "453", number = "1964", pages = "1849--1880", day = "8", month = sep, year = "1997", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1997.0100", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "73B27 (73F05 73K20)", MRnumber = "1478137 (99h:73004)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/453/1964/1849", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/content/current", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0330", originalref = "Milton G. W. and Berryman J. G. 1997 On the effective viscoelastic moduli of two-phase media. II. Rigorous bounds on the complex shear modulus in three dimensions. {\em Proc. Roy. Soc. Lond. A} {\bf 453}, 1849--1880.", texsource = "l-lec16.tex", xxURL = "http://rspa.royalsocietypublishing.org/content/453/1964/1849", } @Article{Milton:1997:FFR, author = "Graeme W. Milton and David J. Eyre and Joseph V. Mantese", title = "Finite frequency range {Kramers--Kronig} relations: {Bounds} on the dispersion", journal = j-PHYS-REV-LET, volume = "79", number = "16", pages = "3062--3065", day = "20", month = oct, year = "1997", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.79.3062", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0477", originalref = "Milton G. W., Eyre D. J., and Mantese J. V. 1997 Finite frequency range Kramers--Kronig relations: Bounds on the dispersion. {\em Phys. Rev. Lett.} {\bf 79}, 3062--3065.", texsource = "l-lec19.tex", xxURL = "http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.79.3062", } @InProceedings{Berryman:1998:TIP, author = "James G. Berryman", editor = "Kenneth M. Golden and G. R. Grimmett and R. D. James and Graeme W. Milton and P. N. Sen", booktitle = "Mathematics of Multiscale Materials", title = "Transversely isotropic poroelasticity arising from thin isotropic layers", volume = "99", publisher = pub-SV, address = pub-SV:adr, bookpages = "x + 280", pages = "37--50", year = "1998", DOI = "https://doi.org/10.1007/978-1-4612-1728-2_3", ISBN = "0-387-98528-X", ISBN-13 = "978-0-387-98528-2", LCCN = "TA405 .M395 1998", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "IMA Volumes in Mathematics and its Applications", URL = "http://link.springer.com/chapter/10.1007/978-1-4612-1728-2_3", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0726", originalref = "Berryman J. G. 1998 Transversely isotropic poroelasticity arising from thin isotropic layers. In {\em Mathematics of multiscale materials}, ed. by K. M. Golden, G. R. Grimmett, R. D. James, G. W. Milton, and P. N. Sen, IMA Volumes in mathematics and its applications, {\bf 99}, pp.37--50, Springer-Verlag, Berlin.", rest = "Springer-Verlag, Berlin", texsource = "l-lec5.tex", } @Article{Grabovsky:1998:ERC, author = "Yury Grabovsky and Graeme W. Milton", booktitle = "Proceedings of the {International} {Congress} of {Mathematicians}, {Vol}. {III} ({Berlin}, 1998)", title = "Exact relations for composites: towards a complete solution", journal = j-DOC-MATH, volume = "Extra Volume ICM III", number = "Extra Vol. III", pages = "623--632", year = "1998", ISSN = "1431-0635", ISSN-L = "1431-0635", MRclass = "73B27 (35B27 49J45)", MRnumber = "1648193 (99j:73008)", MRreviewer = "David J. Bergman", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.math.uiuc.edu/documenta/xvol-icm/16/Milton.MAN.ps.gz", acknowledgement = ack-gwm, fjournal = "Documenta Mathematica", journal-URL = "http://www.math.uiuc.edu/documenta/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0848", originalref = "Grabovsky Y., and Milton G. W. 1998b Exact relations for composites: towards a complete solution. {\em Doc. Math. J. DMV, Extra volume ICM III} 623--632.", texsource = "l-lec8.tex", xxnote = "ZB has: 896.35013 Grabovsky, Yury; Milton, Graeme W. Exact relations for composites: Towards a complete solution. (English) Doc. Math., J. DMV Extra Vol. ICM III, 623-632 (1998). MSC 1991: *35B27 73B27 73S10.", } @Article{Grabovsky:1998:ROP, author = "Yury Grabovsky and Graeme W. Milton", title = "Rank one plus a null-{Lagrangian} is an inherited property of two-dimensional compliance tensors under homogenisation", journal = j-PROC-R-SOC-EDINB-SECT-A-MATH, volume = "128", number = "2", pages = "283--299", year = "1998", CODEN = "PEAMDU", DOI = "https://doi.org/10.1017/S0308210500012798", ISSN = "0308-2105 (print), 1473-7124 (electronic)", ISSN-L = "0308-2105", MRclass = "73B27 (73C02 73K20)", MRnumber = "1621339 (99b:73005)", MRreviewer = "Leonid V. Gibiansky", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=8240207", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society of Edinburgh. Section A. Mathematics", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRM", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0847", originalref = "Grabovsky Y., and Milton G. W. 1998a Rank one plus a null-Lagrangian is an inherited property of two-dimensional compliance tensors under homogenization. {\em Proc. Roy. Soc. Edin.} {\bf 128A}, 283--299.", texsource = "l-lec8.tex", } @Article{Milton:1998:MCP, author = "Graeme W. Milton and A. B. Movchan", title = "Mapping certain planar elasticity problems to antiplane ones", journal = j-EUR-J-MECH-A-SOLIDS, volume = "17", number = "1", pages = "1--11", year = "1998", CODEN = "EJASEV", DOI = "https://doi.org/10.1016/S0997-7538(98)80060-0", ISSN = "0997-7538 (print), 1873-7285 (electronic)", ISSN-L = "0997-7538", MRclass = "73C02 (73B27 73B40)", MRnumber = "1615969 (99a:73035)", MRreviewer = "Leonid V. Gibiansky", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0997753898800600", acknowledgement = ack-gwm, fjournal = "European Journal of Mechanics. A. Solids", journal-URL = "http://www.sciencedirect.com/science/journal/09977538", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0670", originalref = "Milton G. W. and Movchan A. B. 1998 Mapping certain planar elasticity problems to antiplane ones. {\em Eur. J. Mech., A/Solids} {\bf 17}, 1--11.", texsource = "l-lec3.tex", xxURL = "http://www.sciencedirect.com/science/article/pii/S0997753898800600", } @InProceedings{Nesi:1998:FPS, author = "V. Nesi", editor = "Kenneth M. Golden and G. R. Grimmett and R. D. James and Graeme W. Milton and P. N. Sen", booktitle = "Mathematics of Multiscale Materials", title = "Fine properties of solutions to conductivity equations with applications to composites", volume = "99", publisher = pub-SV, address = pub-SV:adr, bookpages = "x + 280", pages = "179--208", year = "1998", ISBN = "0-387-98528-X", ISBN-13 = "978-0-387-98528-2", LCCN = "TA405 .M395 1998", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "IMA Volumes in Mathematics and its Applications", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0720", originalref = "Nesi V. 1998 Fine properties of solutions to conductivity equations with applications to composites. In {\em Mathematics of multiscale materials}, ed. by K. M. Golden, G. R. Grimmett, R. D. James, G. W. Milton, and P. N. Sen, IMA Volumes in mathematics and its applications, {\bf 99}, pp.179--208, Springer-Verlag, Berlin.", rest = "Springer-Verlag, Berlin", texsource = "l-lec4.tex", } @Article{Eyre:1999:FNS, author = "David J. Eyre and Graeme W. Milton", title = "A fast numerical scheme for computing the response of composites using grid refinement", journal = j-EPJ-APPL-PHYS, volume = "6", number = "1", pages = "41--47", month = apr, year = "1999", CODEN = "EPAPFV", DOI = "https://doi.org/10.1051/epjap:1999150", ISSN = "1286-0042 (print), 1286-0050 (electronic)", ISSN-L = "1286-0042", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.epjap.org/articles/epjap/abs/1999/04/ap8234/ap8234.html", acknowledgement = ack-gwm, fjournal = "European Physical Journal. Applied Physics", journal-URL = "http://www.epjap.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0071", originalref = "Eyre D. J. and Milton G. W. 1999 A fast numerical scheme for computing the response of composites using grid refinement. {\em Eur. Phys. J. Applied Physics} {\bf 6}, 41--47.", texsource = "l-lec10.tex", } @Article{Gibiansky:1999:EVM, author = "Leonid V. Gibiansky and Graeme W. Milton and James G. Berryman", title = "On the effective viscoelastic moduli of two-phase media: {III}. {Rigorous} bounds on the complex shear modulus in two dimensions", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "455", number = "1986", pages = "2117--2149", day = "8", month = jun, year = "1999", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.1999.0395", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74Q20 (74D99 74E30)", MRnumber = "1702750 (2000e:74095)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0305", originalref = "Gibiansky L. V., Milton G. W., and Berryman J. G. 1999 On the effective viscoelastic moduli of two-phase media: III. Rigorous bounds on the complex shear modulus in two dimensions. {\em Proc. Roy. Soc. Lond. A} {\bf 455}, 2117--2149.", texsource = "l-lec16.tex", xxURL = "http://rspa.royalsocietypublishing.org/content/455/1986/2117", } @Article{Milton:1999:OCB, author = "Graeme W. Milton and V. Nesi", title = "Optimal {$G$}-closure bounds via stability under lamination", journal = j-ARCH-RAT-MECH-ANAL, volume = "150", number = "3", pages = "191--207", month = dec, year = "1999", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s002050050186", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "74Q05 (49J45 74Q15)", MRnumber = "1738117 (2001k:74085)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s002050050186", acknowledgement = ack-gwm, fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0784", originallab = "GWM0579", originallab = "GWM0332", originalref = "Milton G. W. and Nesi V. 1999 Optimal $G$-closure bounds via stability under lamination. {\em Arch. Rat. Mech. Anal.} ****to appear", rest = "****to appear", texsource = "l-lec6.tex", texsource = "l-lec22.tex", texsource = "l-lec16.tex", } @InProceedings{Suquet:1999:NSE, author = "Pierre M. Suquet and H. Moulinec", editor = "Kenneth M. Golden and G. R. Grimmett and R. D. James and Graeme W. Milton and P. N. Sen", booktitle = "Mathematics of Multiscale Materials", title = "Numerical simulation of the effective elastic properties of a class of cell materials", volume = "99", publisher = pub-SV, address = pub-SV:adr, bookpages = "x + 280", pages = "271--280", year = "1999", ISBN = "0-387-98528-X", ISBN-13 = "978-0-387-98528-2", LCCN = "TA405.M395 1998", bibdate = "Fri Mar 31 13:45:09 MST 2000", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "The IMA Volumes in Mathematics and its Applications", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", texsource = "l-lec2.tex", } @Article{Grabovsky:2000:ERE, author = "Yury Grabovsky and Graeme W. Milton and Daniel S. Sage", title = "Exact relations for effective tensors of composites: {Necessary} conditions and sufficient conditions", journal = j-COMM-PURE-APPL-MATH, volume = "53", number = "3", pages = "300--353", month = mar, year = "2000", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/d8k4vw", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "74Q05 (74A40 74F15 78A48 78M40)", MRnumber = "1725610 (2001m:74060)", MRreviewer = "Konstantin A. Lurie", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://math.cst.temple.edu/~yury/exact.pdf", acknowledgement = ack-gwm, fjournal = "Communications on Pure and Applied Mathematics (New York)", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0849", originalref = "Grabovsky Y., Milton G. W., and Sage D. S. 1999(?***) Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions. {\em Comm. Pure Appl. Math.} submitted.", remark = "Short punctuation-free permanent DOI supplied by http://shortdoi.org on Sun Nov 22 11:04:45 2015.", texsource = "l-lec8.tex", xxDOI = "https://doi.org/10.1002/(SICI)1097-0312(200003)53:3<300::AID-CPA2>3.0.CO%3B2-D", } @Article{Milton:2000:BCN, author = "Graeme W. Milton and Sergey K. Serkov", title = "Bounding the current in nonlinear conducting composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "48", number = "6--7", pages = "1295--1324", day = "1", month = jun, year = "2000", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/S0022-5096(99)00083-6", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74Q20 (74E30 78A48)", MRnumber = "1766404 (2001c:74074)", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "The J. R. Willis 60th anniversary volume", URL = "http://www.sciencedirect.com/science/article/pii/S0022509699000836", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0428", originalref = "Milton G. W. and Serkov S. K. 2000 Bounding the current in nonlinear conducting composites. {\rm J. Mech. Phys. Solids} to appear.", texsource = "l-lec18.tex", } @Article{Solna:2000:BGV, author = "Knut S{\o}lna and Graeme W. Milton", title = "Bounds for the group velocity of electromagnetic signals in two phase materials", journal = j-PHYSICA-B, volume = "279", number = "1--3", pages = "9--12", month = apr, year = "2000", CODEN = "PHYBE3", DOI = "https://doi.org/10.1016/S0921-4526(99)00654-7", ISSN = "0921-4526 (print), 1873-2135 (electronic)", ISSN-L = "0921-4526", bibdate = "Fri Nov 5 13:45:09 MST 1999", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0921452699006547", acknowledgement = ack-gwm, fjournal = "Physica. B, Condensed matter", journal-URL = "http://www.sciencedirect.com/science/journal/09214526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", originallab = "GWM0837", originalref = "Solna K. and Milton G. W. 1999 Bounds for the group velocity of electromagnetic signals in two phase materials. {\em Physica B}, ***to appear", rest = "***to appear", texsource = "l-lec7.tex", } @Article{Milton:2001:NCI, author = "Graeme W. Milton and Sergey K. Serkov", title = "Neutral coated inclusions in conductivity and anti-plane elasticity", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "457", number = "2012", pages = "1973--1997", day = "8", month = jul, year = "2001", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2001.0796", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74F15 (74E05 74Q05 78A48)", MRnumber = "1852434 (2002f:74021)", bibdate = "Fri Oct 20 13:45:09 MST 2000", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/457/2012/1973", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences", fjournal = "The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", texsource = "l-lec04.tex", xxURL = "http://rspa.royalsocietypublishing.org/content/457/2012/1973", } @Article{Milton:2001:PCC, author = "Graeme W. Milton", title = "Proof of a conjecture on the conductivity of checkerboards", journal = j-J-MATH-PHYS, volume = "42", number = "10", pages = "4873--4882", month = oct, year = "2001", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.1385564", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "82B20 (78A48)", MRnumber = "1855103 (2003a:82013)", MRreviewer = "E. J. Janse van Rensburg", bibdate = "Thu Mar 28 19:47:19 MST 2002", bibsource = "http://www.aip.org/ojs/jmp.html; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib", URL = "http://scitation.aip.org/content/aip/journal/jmp/42/10/10.1063/1.1385564", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Eyre:2002:BIC, author = "David J. Eyre and Graeme W. Milton and Roderic S. Lakes", title = "Bounds for interpolating complex effective moduli of viscoelastic materials from measured data", journal = j-RHEOL-ACTA, volume = "41", number = "5", pages = "461--470", year = "2002", CODEN = "RHEAAK", DOI = "https://doi.org/10.1007/s003970100172", ISSN = "0035-4511 (print), 1435-1528 (electronic)", ISSN-L = "0035-4511", bibdate = "Mon Apr 30 13:45:09 MST 2001", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s003970100172", acknowledgement = ack-gwm, fjournal = "Rheologica acta", journal-URL = "http://link.springer.com/journal/397", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", texsource = "l-lec6.tex", texsource = "l-lec22.tex", } @InCollection{Lukkassen:2002:HSR, author = "Dag Lukkassen and Graeme W. Milton", booktitle = "Function spaces, interpolation theory and related topics ({Lund}, 2000)", title = "On hierarchical structures and reiterated homogenization", publisher = "de Gruyter", address = "Berlin, Germany", pages = "355--368", year = "2002", MRclass = "35B27 (49J45 74Q05)", MRnumber = "1943293 (2003k:35019)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2002:CMM, author = "Graeme W. Milton and Knut S{\o}lna", title = "Can Mixing Materials Make Electromagnetic Signals Travel Faster?", journal = j-SIAM-J-APPL-MATH, volume = "62", number = "6", pages = "2064--2091 (electronic)", year = "2002", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/S0036139901385084", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "78A48 (35B27 35Q60 78M40)", MRnumber = "1918307 (2003i:78007)", MRreviewer = "Philip Huddleston", bibdate = "Fri Jul 02 09:53:22 2004", bibsource = "http://epubs.siam.org/toc/smjmap/62/6; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/38508", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", texsource = "l-lec7.tex", xxauthor = "Knut S{\o}lna and Graeme W. Milton", xxnote = "Check author order in PDF of original paper??", xxURL = "http://epubs.siam.org/doi/abs/10.1137/S0036139901385084", } @Article{Benveniste:2003:NER, author = "Y. Benveniste and Graeme W. Milton", title = "New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages", journal = j-J-MECH-PHYS-SOLIDS, volume = "51", number = "10", pages = "1773--1813", month = oct, year = "2003", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/S0022-5096(03)00074-7", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74Q15 (74A60 74E30 78A48 78A55)", MRnumber = "1993514 (2004f:74080)", bibdate = "Fri Apr 15 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509603000747", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2003:EBS, author = "Graeme W. Milton", title = "Exact band structure for the scalar wave equation with periodic complex moduli", journal = j-PHYSICA-B, volume = "338", number = "1--4", pages = "186--189", month = oct, year = "2003", CODEN = "PHYBE3", DOI = "https://doi.org/10.1016/S0921-4526(03)00484-8", ISSN = "0921-4526 (print), 1873-2135 (electronic)", ISSN-L = "0921-4526", bibdate = "Mon Mar 31 13:45:09 MST 2003", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0921452603004848", fjournal = "Physica. B, Condensed matter", journal-URL = "http://www.sciencedirect.com/science/journal/09214526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Proceedings of the Sixth International Conference on Electrical Transport and Optical Properties of Inhomogeneous Media Snowbird, UT, USA 15--19 July 2002.", texsource = "l-lec7.tex", } @Article{Milton:2003:RAS, author = "Graeme W. Milton and S. K. Serkov and A. B. Movchan", title = "Realizable (Average Stress, Average Strain) Pairs in a Plate with Holes", journal = j-SIAM-J-APPL-MATH, volume = "63", number = "3", pages = "987--1028", year = "2003", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/S0036139901395717", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "74Q20 (74K20 74P10)", MRnumber = "1969685 (2005a:74084)", MRreviewer = "Yury Grabovsky", bibdate = "Fri Aug 15 05:31:40 MDT 2003", bibsource = "http://epubs.siam.org/toc/smjmap/63/3; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/39571", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Movchan:2003:RAS, author = "A. B. Movchan and Graeme W. Milton and S. K. Serkov", title = "Realizable (Average Stress, Average Strain) Pairs in a Plate with Holes", journal = j-SIAM-J-APPL-MATH, volume = "63", number = "3", pages = "987--1028", year = "2003", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/S0036139901395717", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Fri Aug 15 05:31:40 MDT 2003", bibsource = "http://epubs.siam.org/toc/smjmap/63/3; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/39571", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2004:CSC, author = "Marc Briane and Graeme W. Milton and Vincenzo Nesi", title = "Change of sign of the corrector's determinant for homogenization in three-dimensional conductivity", journal = j-ARCH-RAT-MECH-ANAL, volume = "173", number = "1", pages = "133--150", year = "2004", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s00205-004-0315-8", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "49J45 (74Q05)", MRnumber = "2073507 (2005i:49015)", MRreviewer = "Alexander A. Pankov", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s00205-004-0315-8", fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2004:EPB, author = "Graeme W. Milton", title = "The exact photonic band structure for a class of media with periodic complex moduli", journal = j-METHODS-APPL-ANAL, volume = "11", number = "3", pages = "413--421", year = "2004", ISSN = "1073-2772 (print), 1945-0001 (electronic)", ISSN-L = "1073-2772", MRclass = "78A48 (35P05 35Q60)", MRnumber = "2214684 (2006m:78013)", MRreviewer = "Alexandre Fedorov", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://projecteuclid.org/euclid.maa/1147353063", ajournal = "Methods Appl. Anal.", fjournal = "Methods and Applications of Analysis", journal-URL = "http://www.intlpress.com/MAA/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InProceedings{Milton:2004:ERP, author = "Graeme W. Milton", editor = "J. S. Yang", booktitle = "{The 41st annual technical meeting of the Society of Engineering Science (SES-2004) held at the Cornhusker Hotel in downtown Lincoln, Nebraska during October 10--13, 2004}", title = "Exact Results for the Piezoelectric Properties of Composite Ellipsoid Assemblages (keynote lecture)", publisher = pub-IOS, address = pub-IOS:adr, pages = "??--??", month = "????", year = "2004", ISBN = "????", ISBN-13 = "????", ISSN = "1383-5416 (print), 1875-8800 (electronic)", ISSN-L = "1383-5416", LCCN = "????", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "International journal of applied electromagnetics and mechanics", URL = "https://ses.confex.com/ses/2004tm/techprogram/P1230.HTM", acknowledgement = ack-nhfb, book-URL = "http://ses.confex.com/ses/2004tm/", journal-URL = "http://ses.confex.com", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", series-URL = "http://www.iospress.nl/journal/international-journal-of-applied-electromagnetics-and-mechanics/", } @InProceedings{Vinogradov:2004:BCC, author = "Vladimir Vinogradov and Graeme W. Milton", editor = "J. S. Yang", booktitle = "{The 41st annual technical meeting of the Society of Engineering Science (SES-2004) held at the Cornhusker Hotel in downtown Lincoln, Nebraska during October 10--13, 2004}", title = "Bounds on the creep of composites under hydrostatic loading", publisher = pub-IOS, address = pub-IOS:adr, bookpages = "????", pages = "??--??", year = "2004", ISBN = "????", ISBN-13 = "????", ISSN = "1383-5416 (print), 1875-8800 (electronic)", ISSN-L = "1383-5416", LCCN = "????", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "International journal of applied electromagnetics and mechanics", URL = "https://ses.confex.com/ses/2004tm/techprogram/P1085.HTM", acknowledgement = ack-nhfb, book-URL = "http://ses.confex.com/ses/2004tm/", book-URL = "https://ses.confex.com/ses/2004tm/techprogram/MEETING.HTM", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", series-URL = "http://www.iospress.nl/journal/international-journal-of-applied-electromagnetics-and-mechanics/", } @Article{Camar-Eddine:2005:NLI, author = "M. Camar-Eddine and Graeme W. Milton", title = "Non-local interactions in the homogenization closure of thermoelectric functionals", journal = j-ASYMPTOT-ANAL, volume = "41", number = "3--4", pages = "259--276", year = "2005", CODEN = "ASANEZ", ISSN = "0921-7134 (print), 1875-8576 (electronic)", ISSN-L = "0921-7134", MRclass = "35Q60 (35A15 78A99)", MRnumber = "2127998 (2005k:35393)", MRreviewer = "Norbert Weck", bibdate = "Tue Nov 14 2006", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://content.iospress.com/articles/asymptotic-analysis/asy667", acknowledgement = ack-gwm, fjournal = "Asymptotic Analysis", journal-URL = "http://content.iospress.com/journals/asymptotic-analysis", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2005:OPH, author = "Graeme W. Milton", title = "On Optimizing the Properties of Hierarchical Laminates Using {Pontryagin}'s Maximum Principle", journal = j-MULTISCALE-MODELING-SIMUL, volume = "3", number = "3", pages = "658--679 (electronic)", year = "2005", CODEN = "MMSUBT", DOI = "https://doi.org/10.1137/030602368", ISSN = "1540-3459 (print), 1540-3467 (electronic)", ISSN-L = "1540-3459", MRclass = "74P10 (49K20 49N90 65K10 74N15 74Q20)", MRnumber = "2136808 (2006d:74067)", MRreviewer = "Yury Grabovsky", bibdate = "Sat Apr 16 10:58:26 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/MMS/3/3; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siammms.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/60236", acknowledgement = ack-nhfb, fjournal = "Multiscale Modeling and Simulation", journal-URL = "http://epubs.siam.org/mms", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2005:PSQ, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici and Ross C. McPhedran and Viktor A. Podolskiy", title = "A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "461", number = "2064", pages = "3999--4034", day = "8", month = dec, year = "2005", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2005.1570", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "78A10", MRnumber = "2186014 (2006h:78001)", bibdate = "Mon Dec 12 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/461/2064/3999", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Podolskiy:2005:OSMa, author = "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme W. Milton", title = "Optimizing the {Superlens}: manipulating geometry to enhance the resolution", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = sep, year = "2005", CODEN = "APRHCB", DOI = "https://doi.org/10.1063/1.2139620", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Applied Physics Letters, v.87, p.231113 (2005)", URL = "https://arxiv.org/abs/physics/0509067", abstract = "We analyze the performance of a planar lens based on realistic negative index material in a generalized geometry. We demonstrate that the conventional superlens design (where the lens is centered between the object and the image) is not optimal from the resolution point-of-view, develop an analytical expression for the resolution limit of a generalized lens, use it to find the optimum lens configuration, and calculate the maximum absorption practical nearfield superlenses may have. We demonstrate that in contrast to the conventional superlens picture, planar imaging is typically accompanied by excitation of surface waves at both interfaces of the lens.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Optics (physics.optics); General Physics (physics.gen-ph)", } @Article{Podolskiy:2005:OSMb, author = "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme W. Milton", title = "Optimizing the superlens: manipulating geometry to enhance the resolution", journal = j-APPL-PHYS-LET, volume = "87", number = "23", pages = "231113", day = "5", month = dec, year = "2005", CODEN = "APPLAB", DOI = "https://doi.org/10.1063/1.2139620", ISSN = "0003-6951 (print), 1077-3118 (electronic), 1520-8842", ISSN-L = "0003-6951", bibdate = "Mon Dec 12 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/apl/87/23/10.1063/1.2139620", acknowledgement = ack-gwm, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Vinogradov:2005:TCV, author = "V. Vinogradov and Graeme W. Milton", title = "The total creep of viscoelastic composites under hydrostatic or antiplane loading", journal = j-J-MECH-PHYS-SOLIDS, volume = "53", number = "6", pages = "1248--1279", month = jun, year = "2005", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2005.01.005", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74Q20 (74D99 74E30)", MRnumber = "2137063 (2006a:74071)", MRreviewer = "Sergio Guti{\'e}rrez", bibdate = "Sun Jul 5 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509605000244", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Kang:2006:CPS, author = "Hyeonbae Kang and Graeme W. Milton", booktitle = "Inverse problems, multi-scale analysis and effective medium theory", title = "On conjectures of {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}", volume = "408", publisher = pub-AMS, address = pub-AMS:adr, pages = "75--80", year = "2006", DOI = "https://doi.org/10.1090/conm/408/07687", MRclass = "35R30 (35J25)", MRnumber = "2262351 (2007i:35244)", MRreviewer = "Enno Pais", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Contemp. Math.", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Kang:2006:SCP, author = "Hyeonbae Kang and Graeme W. Milton", title = "Solutions to the conjectures of {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "13", month = sep, year = "2006", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/math/0609374", abstract = "Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, i.e., that if the field inside an inclusion is uniform for all uniform loadings, then the inclusion is of elliptic or ellipsoidal shape. We call this the weak Eshelby conjecture. In this paper we prove this conjecture in three dimensions. In two dimensions, a stronger conjecture, which we call the strong Eshelby conjecture, has been proved: If the field inside an inclusion is uniform for a single uniform loading, then the inclusion is of elliptic shape. We give an alternative proof of Eshelby's conjecture in two dimensions using a hodographic transformation. As a consequence of the weak Eshelby's conjecture, we prove in two and three dimensions a conjecture of P{\'o}lya and Szeg{\H{o}} on the isoperimetric inequalities for the polarization tensors. The P{\'o}lya--Szeg{\H{o}} conjecture asserts that the inclusion whose electrical polarization tensor has the minimal trace takes the shape of a disk or a ball.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "22", subject = "Analysis of PDEs (math.AP); Optimization and Control (math.OC)", } @Article{Milton:2006:CEA, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici", title = "On the cloaking effects associated with anomalous localized resonance", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "462", number = "2074", pages = "3027--3059", month = oct, year = "2006", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2006.1715", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "78A55", MRnumber = "2263683 (2008e:78018)", bibdate = "Mon Jul 3 2006", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/462/2074/3027", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2006:CEP, author = "Graeme W. Milton and Marc Briane and John R. Willis", title = "On cloaking for elasticity and physical equations with a transformation invariant form", journal = j-NEW-J-PHYS, volume = "8", number = "10", pages = "248", month = oct, year = "2006", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/8/10/248", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Mon Nov 27 2006", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/1367-2630/8/10/248; http://iopscience.iop.org/article/10.1088/1367-2630/8/10/248/", abstract = "In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only with the velocity but also with the strain. These are a special case of equations which describe the elastodynamic response of composite materials, and which it has been argued should apply to any material which has microstructure below the scale of continuum modelling. If composites could be designed with the required moduli then it could be possible to design elastic cloaking devices where an object is cloaked from elastic waves of a given frequency. To an outside observer it would appear as though the waves were propagating in a homogeneous medium, with the object and surrounding cloaking shell invisible. Other new elastodynamic equations also retain their form under curvilinear transformations. The question is raised as to whether all equations of microstructured continua have a form which is invariant under curvilinear space or space-time coordinate transformations. We show that the non-local bianisotropic electrodynamic equations have this invariance under space-time transformations and that the standard non-local, time-harmonic, electromagnetic equations are invariant under space transformations.", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://stacks.iop.org/1367-2630/8/i=10/a=248", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/8/10/248/", } @InProceedings{Milton:2006:CSF, author = "Graeme W. Milton and N. A. P. Nicorovici", editor = "Anonymous", booktitle = "{Photonic metamaterials: from random to periodic, technical digest: June 5--8, 2006, Westin Grand Bahama Island Our Lucaya Resort, Grand Island, the Bahamas}", title = "Cloaking: Science Fiction or Reality?", publisher = "OSA Publishing", address = "Washington, DC, USA", pages = "??--??", year = "2006", DOI = "https://doi.org/10.1364/META.2006.TuA3", ISBN = "1-55752-808-X", ISBN-13 = "978-1-55752-808-7", LCCN = "QC759.6 .P46 2006", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.osapublishing.org/abstract.cfm?uri=META-2006-TuA3", acknowledgement = ack-nhfb, journal-URL = "http://osapublishing.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2006:OPL, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici and Ross C. McPhedran", title = "Opaque perfect lenses", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "23", month = aug, year = "2006", CODEN = "APRHCB", DOI = "https://doi.org/10.1016/j.physb.2006.12.010", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Presented at The 7th International Conference on the Electrical transport and Optical Properties of Inhomogeneous Media (ETOPIM7).", URL = "https://arxiv.org/abs/physics/0608225", abstract = "The response of the ``perfect lens'', consisting of a slab of lossless material of thickness $d$ with $ \epsilon = \mu = - 1$ at one frequency $ \omega_0$ is investigated. It is shown that as time progresses the lens becomes increasingly opaque to any physical TM line dipole source located a distance $ d_0 < d / 2$ from the lens and which has been turned on at time $ t = 0$. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is an exact correspondence between the response of the perfect lens in the long time constant limit and the response of lossy lenses in the low loss limit. Contrary to the usual picture where the field intensity has a minimum at the front interface we find that the field diverges to infinity there in the long time constant limit.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Optics (physics.optics); Classical Physics (physics.class-ph)", } @Article{Milton:2006:SCP, author = "Graeme W. Milton and H. Kang", title = "Solutions to the conjectures of {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2006", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/math/0609374", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Nicorovici:2006:PRT, author = "N. A. Nicorovici and R. C. McPhedran and G. W. Milton and L. C. Botten", title = "Partial Resonances of Three-Phase Composites at Long Wavelengths", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "25", month = aug, year = "2006", CODEN = "APRHCB", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/physics/0608247", abstract = "We investigate the behaviour of a three-phase composite, structured as a hexagonal array of coated cylinders, when the sum of the dielectric constants of the core and shell equals zero. In such cases, the absorption of the composite is the same as the absorption of a periodic array of solid cylinders of core material and radius equal to the outer radius of the original coated cylinder. When the sum of the dielectric constants of the shell and matrix equals zero, the composite has the same absorption as a periodic array of solid cylinders of core material, and radius exceeding the shell radius.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "11", subject = "Optics (physics.optics); Classical Physics (physics.class-ph)", } @InProceedings{Podolskiy:2006:OSG, author = "Viktor A. Podolskiy and Nicholas A. Kuhta and Graeme W. Milton", editor = "Anonymous", booktitle = "{CLEO/QELS 06: PhAST: Conference on Lasers and Electro-optics: Quantum Electronics and Laser Science Conference: Conference on Photonic Applications, Systems and Technologies: technical digest CD-ROM, Long Beach Convention Center, Long Beach, California, USA, CLEO/QELS Conference: May 21-26, 2006: PhAST Conference, May 22-25, 2006.: Lasers and Electro-optics and 2006 Quantum Electronics and Laser Science Conference, CLEO}", title = "Optimizing the superlens geometry", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "??--??", month = "????", year = "2006", ISBN = "1-55752-813-6", ISBN-13 = "978-1-55752-813-1", LCCN = "TA1673 .C63 2006", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.osapublishing.org/abstract.cfm?uri=QELS-2006-JWB84", acknowledgement = ack-nhfb, journal-URL = "http://osapublishing.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Cai:2007:NCM, author = "Wenshan Cai and Uday K. Chettiar and Alexander V. Kildishev and Vladimir M. Shalaev and Graeme W. Milton", title = "Nonmagnetic cloak with minimized scattering", journal = j-APPL-PHYS-LET, volume = "91", number = "11", pages = "111105", day = "10", month = sep, year = "2007", CODEN = "APPLAB", DOI = "https://doi.org/10.1063/1.2783266", ISSN = "0003-6951 (print), 1077-3118 (electronic), 1520-8842", ISSN-L = "0003-6951", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://scitation.aip.org/content/aip/journal/apl/91/11/10.1063/1.2783266", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Applied Physics Letters", journal-URL = "http://scitation.aip.org/content/aip/journal/apl", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Cai:2007:NMC, author = "Wenshan Cai and Uday K. Chettiar and Alexander V. Kildishev and Graeme W. Milton and Vladimir M. Shalaev", title = "Non-Magnetic Cloak without Reflection", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "24", month = jul, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1063/1.2783266", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0707.3641", abstract = "In an electromagnetic cloak based on a transformation approach, reduced sets of material properties are generally favored due to their easier implementation in reality, although a seemingly inevitable drawback of undesired reflection exists in such cloaks. Here we suggest using high-order transformations to create smooth moduli at the outer boundary of the cloak, therefore completely eliminating the detrimental scattering within the limit of geometric optics. We apply this scheme to a non-magnetic cylindrical cloak and demonstrate that the scattered field is reduced substantially in a cloak with optimal quadratic transformation as compared to its linear counterpart.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "8", subject = "Optics (physics.optics)", } @InProceedings{Milton:2007:CNP, author = "Graeme W. Milton", editor = "Anonymous", booktitle = "{Photonic metamaterials: from random to periodic: 4--7 June 2007, Jackson Hole, Wyoming, United States}", title = "Cloaking: A New Phenomenon in Electromagnetism and Elasticity", publisher = "OSA Publishing", address = "Washington, DC, USA", pages = "??--??", year = "2007", DOI = "https://doi.org/10.1364/META.2007.TuD1", ISBN = "1-55752-839-X", ISBN-13 = "978-1-55752-839-1", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.osapublishing.org/abstract.cfm?uri=META-2007-TuD1", acknowledgement = ack-nhfb, journal-URL = "http://osapublishing.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "2", } @Article{Milton:2007:MNS, author = "Graeme W. Milton and John R. Willis", title = "On modifications of {Newton}'s second law and linear continuum elastodynamics", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "463", number = "2079", pages = "855--880", month = mar, year = "2007", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2006.1795", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74Q10 (74A40 74H45 74Q99)", MRnumber = "2293080 (2007m:74118)", MRreviewer = "Paolo Maria Mariano", bibdate = "Wed Aug 23 2006", bibdate = "Sat Nov 21 09:12:03 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/463/2079/855", abstract = "In this paper, we suggest a new perspective, where Newton{\textquoteright}s second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies. We confirm a finding of Willis that the density of a body at a given frequency of oscillation can be anisotropic. The relation between the force and the acceleration is non-local (but causal) in time. Conversely, for every response function satisfying these properties, and having the appropriate high-frequency limit, there is a model which realizes that response function. In many circumstances, the differences between Newton{\textquoteright}s second law and the new law are small, but there are circumstances, such as in specially designed composite materials, where the difference is enormous. For bodies which are not seemingly rigid, the continuum equations of elastodynamics govern behaviour and also need to be modified. The modified versions of these equations presented here are a generalization of the equations proposed by Willis to describe elastodynamics in composite materials. It is argued that these new sets of equations may apply to all physical materials, not just composites. The Willis equations govern the behaviour of the average displacement field whereas one set of new equations governs the behaviour of the average-weighted displacement field, where the weighted displacement field may attach zero weight to {\textquoteleft}hidden{\textquoteright} areas in the material where the displacement may be unobservable or not defined. From knowledge of the average-weighted displacement field, one obtains an approximate formula for the ensemble averaged energy density. Two other sets of new equations govern the behaviour when the microstructure has microinertia, i.e. where there are internal spinning masses below the chosen scale of continuum modelling. In the first set, the average displacement field is assumed to be observable, while in the second set an average-weighted displacement field is assumed to be observable.", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, \& Engineering Sciences", fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxyear = "2006", } @Article{Milton:2007:NMMa, author = "Graeme W. Milton", title = "New metamaterials with macroscopic behavior outside that of continuum elastodynamics", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "14", month = jun, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/9/10/359", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0706.2202", abstract = "Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally depends not only on the strain, but also on the local rotation, and the stress is generally not symmetric. A variant is constructed for which, at a fixed frequency, the momentum density is independent of the local rotation (but still depends on the strain) and the stress is symmetric (but still depends on the velocity). Generalizations of these metamaterials may be useful in the design of elastic cloaking devices.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "14", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2007:NMMb, author = "Graeme W. Milton", title = "New metamaterials with macroscopic behavior outside that of continuum elastodynamics", journal = j-NEW-J-PHYS, volume = "9", number = "10", pages = "359", year = "2007", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/9/10/359", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Tue Nov 6 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/1367-2630/9/10/359", abstract = "Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient and the stress depends on the local acceleration. In these models the momentum density generally depends not only on the strain, but also on the local rotation, and the stress is generally not symmetric. A variant is constructed for which, at a fixed frequency, the momentum density is independent of the local rotation (but still depends on the strain) and the stress is symmetric (but still depends on the acceleration). Generalizations of these metamaterials may be useful in the design of elastic cloaking devices.", acknowledgement = ack-gwm, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://stacks.iop.org/1367-2630/9/i=10/a=359", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/9/10/359/", } @Article{Milton:2007:OPL, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici and Ross C. McPhedran", title = "Opaque perfect lenses", journal = j-PHYSICA-B, volume = "394", number = "2", pages = "171--175", day = "15", month = may, year = "2007", CODEN = "PHYBE3", DOI = "https://doi.org/10.1016/j.physb.2006.12.010", ISSN = "0921-4526 (print), 1873-2135 (electronic)", ISSN-L = "0921-4526", bibdate = "Fri Mar 21 2008", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0921452606018941", acknowledgement = ack-gwm, fjournal = "Physica. B, Condensed matter", journal-URL = "http://www.sciencedirect.com/science/journal/09214526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxyear = "2006", } @Article{Milton:2007:RRM, author = "Graeme W. Milton and Pierre Seppecher", title = "Realizable response matrices of multiterminal electrical, acoustic, and elastodynamic networks at a given frequency", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "7", month = dec, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2007.0345", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0712.1066", abstract = "We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in the three-dimensional case and in the two-dimensional case. Specifically we construct networks which realize any response matrix which is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Due to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "22", subject = "Materials Science (cond-mat.mtrl-sci)", } @Article{Nicorovici:2007:QCT, author = "Nicolae-Alexandru P. Nicorovici and Graeme W. Milton and Ross C. McPhedran and Lindsay C. Botten", title = "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance", journal = j-OPT-EXPRESS, volume = "15", number = "10", pages = "6314--6323", day = "14", month = may, year = "2007", CODEN = "OPEXFF", DOI = "https://doi.org/10.1364/OE.15.006314", ISSN = "1094-4087", ISSN-L = "1094-4087", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://www.osapublishing.org/oe/abstract.cfm?uri=oe-15-10-6314", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Optics Express", journal-URL = "http://opticsexpress.org/Issue.cfm", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2008:GHE, author = "Marc Briane and Graeme W. Milton", title = "Giant {Hall} effect in composites", journal = j-MULTISCALE-MODELING-SIMUL, volume = "7", number = "3", pages = "1405--1427", year = "2008", CODEN = "MMSUBT", DOI = "https://doi.org/10.1137/08073189X", ISSN = "1540-3459 (print), 1540-3467 (electronic)", ISSN-L = "1540-3459", MRclass = "35B27 (74Q15 78A55 81V70)", MRnumber = "2496707 (2010m:35021)", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/08073189X", fjournal = "Multiscale Modeling \& Simulation. A SIAM Interdisciplinary Journal", journal-URL = "http://epubs.siam.org/mms", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2008:HTD, author = "M. Briane and D. Manceau and Graeme W. Milton", title = "Homogenization of the two-dimensional {Hall} effect", journal = j-J-MATH-ANAL-APPL, volume = "339", number = "2", pages = "1468--1484", day = "15", month = mar, year = "2008", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/j.jmaa.2007.07.044", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "81V70 (35B27 49J45)", MRnumber = "2377101 (2008k:81378)", MRreviewer = "Alain Brillard", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022247X07009055", fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Kang:2008:IPS, author = "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton", title = "Inclusion Pairs Satisfying {Eshelby}'s Uniformity Property", journal = j-SIAM-J-APPL-MATH, volume = "69", number = "2", pages = "577--595", month = "????", year = "2008", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/070691358", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "74M25 (30C20 35J25 74P99 74Q05)", MRnumber = "2465857 (2009i:74077)", MRreviewer = "Pham Duc Chinh", bibdate = "Mon May 17 18:38:59 MDT 2010", bibsource = "http://epubs.siam.org/toc/smjmap/69/2; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2000.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/070691358", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Kang:2008:SPS, author = "Hyeonbae Kang and Graeme W. Milton", title = "Solutions to the {P{\'o}lya--Szeg{\H{o}}} Conjecture and the {Weak Eshelby Conjecture}", journal = j-ARCH-RAT-MECH-ANAL, volume = "188", number = "1", pages = "93--116", month = apr, year = "2008", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s00205-007-0087-z", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "74G40 (35J55 35Q72 49Q05 74B05)", MRnumber = "2379654 (2009j:74046)", bibdate = "Mon Nov 7 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s00205-007-0087-z", acknowledgement = ack-gwm, fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2008:EC, author = "Graeme W. Milton and Pierre Seppecher", title = "Electromagnetic Circuits", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = may, year = "2008", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0805.1079", abstract = "The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of them. They consist of thin triangular magnetic components joined at the edges by cylindrical dielectric components. (There are also dual electromagnetic circuits consisting of thin triangular dielectric components joined at the edges by cylindrical magnetic components.) Some of the edges can be terminal edges to which electric fields are applied. The response is measured in terms of the real or virtual free currents that are associated with the terminal edges. The relation between the terminal electric fields and the terminal free currents is governed by a symmetric complex matrix $ \BW $. In the case where all the terminal edges are disjoint, and the frequency is fixed, a complete characterization is obtained of all possible response matrices $ \BW $ both in the lossless and lossy cases. This is done by introducing a subclass of electromagnetic circuits, called electromagnetic ladder networks. It is shown that an electromagnetic ladder network, structured as a cubic network, can have a macroscopic electromagnetic continuum response which is non-Maxwellian, and novel.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "33", subject = "Classical Physics (physics.class-ph); Optics (physics.optics)", } @Article{Milton:2008:MVP, author = "Graeme W. Milton and Pierre Seppecher and Guy Bouchitte", title = "Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = jul, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2008.0195", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Proc. R. Soc. A 465 (2009) 367-396", URL = "https://arxiv.org/abs/0807.1336", abstract = "The classical energy minimization principles of Dirichlet and Thompson are extended as minimization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. This is done by building upon ideas of Cherkaev and Gibiansky, who derived minimization variational principles for quasistatics. In the absence of free current the primary electromagnetic minimization variational principles have a minimum which is the time-averaged electrical power dissipated in the body. The variational principles provide constraints on the boundary values of the fields when the moduli are known. Conversely, when the boundary values of the fields have been measured, then they provide information about the values of the moduli within the body. This should have application to electromagnetic tomography. We also derive saddle point variational principles which correspond to variational principles of Gurtin, Willis, and Borcea.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "32", subject = "Mathematical Physics (math-ph); Materials Science (cond-mat.mtrl-sci); Analysis of PDEs (math.AP); Classical Physics (physics.class-ph); Optics (physics.optics)", } @Article{Milton:2008:RRM, author = "Graeme W. Milton and Pierre Seppecher", title = "Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "464", number = "2092", pages = "967--986", month = apr, year = "2008", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2007.0345", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "94C05 (74E30)", MRnumber = "2379501 (2009d:94171)", MRreviewer = "D. Stanomir", bibdate = "Tue May 6 2008", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/464/2092/967", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2008:SFGa, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici and Ross C. McPhedran and Kirill Cherednichenko and Zubin Jacob", title = "Solutions in folded geometries, and associated cloaking due to anomalous resonance", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "24", month = apr, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/10/11/115021", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0804.3903", abstract = "Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite collections of polarizable line dipoles lying within a critical region surrounding the hyperlens are shown to be cloaked having vanishingly small dipole moments. This cloaking, which occurs both in the folded geometry and the equivalent unfolded one, is due to anomalous resonance, where the collection of dipoles generates an anomalously resonant field, which acts back on the dipoles to essentially cancel the external fields acting on them.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "23", subject = "Optics (physics.optics)", } @Article{Milton:2008:SFGb, author = "Graeme W. Milton and Nicolae-Alexandru P. Nicorovici and Ross C. McPhedran and Kirill Cherednichenko and Zubin Jacob", title = "Solutions in folded geometries, and associated cloaking due to anomalous resonance", journal = j-NEW-J-PHYS, volume = "10", number = "11", pages = "115021", month = nov, year = "2008", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/10/11/115021", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://stacks.iop.org/1367-2630/10/i=11/a=115021", abstract = "Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular, the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite collections of polarizable line dipoles lying within a critical region surrounding the hyperlens are shown to be cloaked having vanishingly small dipole moments. This cloaking, which occurs both in the folded geometry and the equivalent unfolded one, is due to anomalous resonance, where the collection of dipoles generates an anomalously resonant field, which acts back on the dipoles to essentially cancel the external fields acting on them.", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/10/11/115021/", } @Article{Vinogradov:2008:AFA, author = "V. Vinogradov and Graeme W. Milton", title = "An accelerated {FFT} algorithm for thermoelastic and non-linear composites", journal = j-INT-J-NUMER-METHODS-ENG, volume = "76", number = "11", pages = "1678--1695", year = "2008", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/nme.2375", ISSN = "0029-5981 (print), 1097-0207 (electronic)", ISSN-L = "0029-5981", MRclass = "74S30 (74A40)", MRnumber = "2468562 (2009m:74099)", MRreviewer = "Stan Chiri{\c{t}}{\u{a}}", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", fjournal = "International Journal for Numerical Methods in Engineering", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Ammari:2009:PSE, author = "Habib Ammari and Yves Capdeboscq and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton and Habib Zribi", title = "Progress on the Strong {Eshelby}'s Conjecture and Extremal Structures for the Elastic Moment Tensor", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "10", month = sep, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1016/j.matpur.2010.01.003", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in J. Math. Pures Appl. (9) 94(1):93--106, 2010", URL = "https://arxiv.org/abs/0909.1969", abstract = "We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two linearly independent loadings the strains inside the inclusions are uniform, then the inclusion must be of ellipsoidal shape. We then use this result to address a problem of determining the shape of an inclusion when the elastic moment tensor (elastic polarizability tensor) is extremal. We show that the shape of inclusions, for which the lower Hashin--Shtrikman bound either on the bulk part or on the shear part of the elastic moment tensor is attained, is an ellipse in two dimensions and an ellipsoid in three dimensions.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Analysis of PDEs (math.AP)", } @Article{Briane:2009:GHE, author = "Marc Briane and Graeme W. Milton", title = "Giant {Hall} Effect in Composites", journal = j-MULTISCALE-MODELING-SIMUL, volume = "7", number = "3", pages = "1405--1427", month = "????", year = "2009", CODEN = "MMSUBT", DOI = "https://doi.org/10.1137/08073189X", ISSN = "1540-3459 (print), 1540-3467 (electronic)", ISSN-L = "1540-3459", bibdate = "Wed May 19 17:34:41 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/MMS/7/3; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siammms.bib", acknowledgement = ack-nhfb, fjournal = "Multiscale Modeling and Simulation", journal-URL = "http://epubs.siam.org/mms", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2009:HTD, author = "Marc Briane and Graeme W. Milton", title = "Homogenization of the three-dimensional {Hall} effect and change of sign of the {Hall} coefficient", journal = j-ARCH-RAT-MECH-ANAL, volume = "193", number = "3", pages = "715--736", month = sep, year = "2009", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s00205-008-0200-y", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "78A48 (35B27 35C20 74E10 74Q05)", MRnumber = "2525116 (2010d:78025)", MRreviewer = "Alain Brillard", bibdate = "Sat Oct 31 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s00205-008-0200-y", acknowledgement = ack-gwm, fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{GuevaraVasquez:2009:AECa, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Active Exterior Cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = jun, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1103/PhysRevLett.103.073901", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Physical Review Letters, 103, 073901 (2009)", URL = "http://adsabs.harvard.edu/abs/2009arXiv0906.1544G; https://arxiv.org/abs/0906.1544", abstract = "A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "4", subject = "Mathematical Physics (math-ph); Optics (physics.optics)", } @Article{GuevaraVasquez:2009:AECb, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Active exterior cloaking for the {$2$D} {Laplace} and {Helmholtz} equations", journal = j-PHYS-REV-LET, volume = "103", number = "7", pages = "073901", day = "14", month = aug, year = "2009", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.103.073901", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.073901", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "4", } @Article{GuevaraVasquez:2009:BECa, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Broadband Exterior Cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "1", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1364/OE.17.014800", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Optics Express, Vol. 17, pp. 14800-14805 (2009)", URL = "https://arxiv.org/abs/0907.0263", abstract = "It is shown how a recently proposed method of cloaking is effective over a broad range of frequencies. The method is based on three or more active devices. The devices, while not radiating significantly, create a ``quiet zone'' between the devices where the wave amplitude is small. Objects placed within this region are virtually invisible. The cloaking is demonstrated by simulations with a broadband incident pulse.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Mathematical Physics (math-ph)", } @Article{GuevaraVasquez:2009:BECb, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Broadband exterior cloaking", journal = j-OPT-EXPRESS, volume = "17", number = "17", pages = "14800--14805", day = "17", month = aug, year = "2009", CODEN = "OPEXFF", DOI = "https://doi.org/10.1364/OE.17.014800", ISSN = "1094-4087", ISSN-L = "1094-4087", bibdate = "Fri May 29 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://www.osapublishing.org/oe/abstract.cfm?uri=oe-17-17-14800", acknowledgement = ack-gwm, fjournal = "Optics Express", journal-URL = "http://opticsexpress.org/Issue.cfm", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{GuevaraVasquez:2009:CCS, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Complete characterization and synthesis of the response function of elastodynamic networks", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = nov, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1007/s10659-010-9260-y", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Journal of Elasticity, 102, no. 1 (2011), 31--54, 2011", URL = "https://arxiv.org/abs/0911.1501", abstract = "The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function $ W(\omega) $, depending on the frequency $ \omega $, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function $ W(\omega) $ to be the response function of an elastodynamic network, assuming there is no damping. In particular we construct an elastodynamic network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks in three dimensions and also for planar networks, which are networks where all the elements, displacements and forces are in a plane. The network we design can fit within an arbitrarily small neighborhood of the convex hull of the terminal nodes, provided the springs and masses occupy an arbitrarily small volume. Additionally, we prove stability of the network response to small changes in the spring constants and/or addition of springs with small spring constants.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "23", subject = "Mathematical Physics (math-ph)", } @Article{McPhedran:2009:CPR, author = "Ross C. McPhedran and Nicolae-Alexandru P. Nicorovici and Lindsay C. Botten and Graeme W. Milton", title = "Cloaking by plasmonic resonance among systems of particles: cooperation or combat?", journal = j-C-R-PHYS, volume = "10", number = "5", pages = "391--399", month = jun, year = "2009", CODEN = "CRPOBN", DOI = "https://doi.org/10.1016/j.crhy.2009.03.007", ISSN = "1631-0705 (print), 1878-1535 (electronic)", ISSN-L = "1631-0705", bibdate = "Sat Nov 28 18:44:37 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1631070509000413", acknowledgement = ack-nhfb, fjournal = "Comptes Rendus Physique", journal-URL = "http://www.sciencedirect.com/science/journal/16310705", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2009:HEC, author = "Graeme W. Milton and Pierre Seppecher", title = "Hybrid electromagnetic circuits", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "5", month = oct, year = "2009", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/0910.0798", abstract = "Electromagnetic circuits are the electromagnetic analog at fixed frequency of mass-spring networks in elastodynamics. By interchanging the roles of epsilon and mu in electromagnetic circuits one obtains magnetoelectric circuits. Here we show that by introducing tetrahedral connectors having epsilon=mu=0 one can join electromagnetic and magnetoelectric circuits to obtain hybrid circuits. Their response is governed by a symmetric matrix with negative semidefinite imaginary part. Conversely given any such matrix a recipe is given for constructing a hybrid circuit which has that matrix as its response matrix.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "5", subject = "Optics (physics.optics)", } @Article{Milton:2009:MVP, author = "Graeme W. Milton and Pierre Seppecher and Guy Bouchitt{\'e}", title = "Minimization variational principles for acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "465", number = "2102", pages = "367--396", day = "8", month = feb, year = "2009", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2008.0195", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74B05 (49S05 76Q05 78A25)", MRnumber = "2471764 (2009m:74013)", MRreviewer = "Sven Ivansson", bibdate = "Thu May 28 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/465/2102/367", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Ammari:2010:PSE, author = "Habib Ammari and Yves Capdeboscq and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton and Habib Zribi", title = "Progress on the strong {Eshelby}'s conjecture and extremal structures for the elastic moment tensor", journal = j-J-MATH-PURES-APPL, volume = "94", number = "1", pages = "93--106", year = "2010", CODEN = "JMPAAM", DOI = "https://doi.org/10.1016/j.matpur.2010.01.003", ISSN = "0021-7824 (print), 1776-3371 (electronic)", ISSN-L = "0021-7824", MRclass = "74G55 (74B05 74Q05)", MRnumber = "2653981 (2011h:74049)", bibdate = "Thu Apr 16 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021782410000115", acknowledgement = ack-gwm, fjournal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es", journal-URL = "http://www.sciencedirect.com/science/journal/00217824", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Benveniste:2010:EMAa, author = "Y. Benveniste and Graeme W. Milton", title = "The effective medium and the average field approximations vis-{\`a}-vis the {Hashin--Shtrikman} bounds. {I}. {The} self-consistent scheme in matrix-based composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "58", number = "7", pages = "1026--1038", month = jul, year = "2010", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2010.04.014", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74A40 (74B05 74M25)", MRnumber = "2642449", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509610000839", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Benveniste:2010:EMAb, author = "Y. Benveniste and Graeme W. Milton", title = "The effective medium and the average field approximations vis-{\`a}-vis the {Hashin--Shtrikman} bounds. {II}. {The} generalized self-consistent scheme in matrix-based composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "58", number = "7", pages = "1039--1056", month = jul, year = "2010", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2010.04.013", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74A40 (74B05 74M25)", MRnumber = "2642450", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509610000827", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2010:AEH, author = "Marc Briane and Graeme W. Milton", title = "An Antisymmetric Effective {Hall} Matrix", journal = j-SIAM-J-APPL-MATH, volume = "70", number = "6", pages = "1810--1820", month = "????", year = "2010", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/09075901X", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "35B27 (35Q74 74Q15 78A48 81V70)", MRnumber = "2596502 (2011b:35031)", MRreviewer = "Nicolas Charalambakis", bibdate = "Mon May 17 18:39:21 MDT 2010", bibsource = "http://epubs.siam.org/toc/smjmap/70/6; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/09075901X", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2010:NBS, author = "Marc Briane and Graeme W. Milton", title = "New Bounds on Strong Field Magneto-Transport in Multiphase Columnar Composites", journal = j-SIAM-J-APPL-MATH, volume = "70", number = "8", pages = "3272--3286", month = "????", year = "2010", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/100798090", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "35B27 (74Q20 78A48)", MRnumber = "2763504 (2012j:35015)", MRreviewer = "A. K. Nandakumaran", bibdate = "Fri Mar 4 09:51:08 MST 2011", bibsource = "http://epubs.siam.org/toc/smjmap/70/8; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/100798090", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "December 14, 2010", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://epubs.siam.org/siap/resource/1/smjmap/v70/i8/p3272_s1", } @Article{GuevaraVasquez:2010:ECA, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Exterior cloaking with active sources in two dimensional acoustics", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "10", month = sep, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1007/s10659-010-9260-y", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Wave Motion, 48, no. 6 (2011), 515--524", URL = "https://arxiv.org/abs/1009.2038", abstract = "We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the cloaked region, the scattered field is small and the scatterers are for all practical purposes undetectable. The devices are multipolar point sources that can be determined from Green's formula and an addition theorem for Hankel functions. The cloaking devices are exterior to the cloaked region.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2010:EC, author = "Graeme W. Milton and Pierre Seppecher", title = "Electromagnetic Circuits", journal = j-NETW-HETEROG-MEDIA, volume = "5", number = "2", pages = "335--360", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.3934/nhm.2010.5.335", ISSN = "1556-1801 (print), 1556-181X (electronic)", ISSN-L = "1556-1801", MRclass = "35Q60, 78A48, 94C05", MRnumber = "2661411 (2011i:94129)", MRreviewer = "Alain Brillard", bibdate = "Tue Sep 15 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://aimsciences.org/journals/redirecting.jsp?paperID=5217", acknowledgement = ack-gwm, fjournal = "Networks and Heterogeneous Media (NHM)", journal-URL = "http://aimsciences.org/journals/home.jsp?journalID=9", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2010:HEC, author = "Graeme W. Milton and Pierre Seppecher", title = "Hybrid electromagnetic circuits", journal = j-PHYSICA-B, volume = "405", number = "14", pages = "2935--2937", day = "15", month = jul, year = "2010", CODEN = "PHYBE3", DOI = "https://doi.org/10.1016/j.physb.2010.01.007", ISSN = "0921-4526 (print), 1873-2135 (electronic)", ISSN-L = "0921-4526", bibdate = "Tue Sep 15 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0921452610000098", acknowledgement = ack-gwm, fjournal = "Physica. B, Condensed matter", journal-URL = "http://www.sciencedirect.com/science/journal/09214526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2010:MVPa, author = "Graeme W. Milton and John R. Willis", title = "Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of {Hashin--Shtrikman} type", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "15", month = jan, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2010.0006", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1001.2773", abstract = "Minimization variational principles for linear elastodynamic, acoustic, or electromagnetic time-harmonic waves in dissipative media were obtained by Milton, Seppecher and Bouchitt{\'e} generalizing the quasistatic variational principles of Cherkaev and Gibiansky. Here a further generalization is made to allow for a much wider variety of boundary conditions, and in particular Dirichlet and Neumann boundary conditions. In addition minimization or maximization principles of the Hashin--Shtrikman type, incorporating ``polarization fields'', are developed.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "23", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2010:MVPb, author = "Graeme W. Milton and John R. Willis", title = "Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of {Hashin--Shtrikman} type", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "466", number = "2122", pages = "3013--3032", year = "2010", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2010.0006", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74Q10", MRnumber = "2684717 (2011k:74098)", bibdate = "Tue Nov 1 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/early/2010/04/15/rspa.2010.0006", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2010:RMPa, author = "Graeme W. Milton", title = "Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "15", month = jan, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/12/3/033035", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1001.2761", abstract = "We show that any pair of real symmetric tensors $ \BGve $ and $ \BGm $ can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{\'e} and Bourel and Bouchitt{\'e} and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "12", subject = "Optics (physics.optics)", } @Article{Milton:2010:RMPb, author = "Graeme W. Milton", title = "Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors", journal = j-NEW-J-PHYS, volume = "12", number = "3", pages = "033035", year = "2010", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/12/3/033035", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Wed Dec 22 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://stacks.iop.org/1367-2630/12/i=3/a=033035", acknowledgement = ack-gwm, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/12/3/033035/", } @Article{Ammari:2011:STN, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Spectral theory of a {Neumann--Poincar{\'e}}-type operator and analysis of cloaking due to anomalous localized resonance", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "2", month = sep, year = "2011", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1109.0479", abstract = "The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a critical radius CALR does not take place, and for sources located inside the critical radius satisfying certain conditions CALR does take place as the loss parameter goes to zero.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "24", subject = "Analysis of PDEs (math.AP); Materials Science (cond-mat.mtrl-sci); Optics (physics.optics)", } @Article{Benveniste:2011:EMT, author = "Y. Benveniste and Graeme W. Milton", title = "An effective medium theory for multi-phase matrix-based dielectric composites with randomly oriented ellipsoidal inclusions", journal = j-INT-J-ENG-SCI, volume = "49", number = "1", pages = "2--16", month = jan, year = "2011", CODEN = "IJESAN", DOI = "https://doi.org/10.1016/j.ijengsci.2010.06.019", ISSN = "0020-7225 (print), 1879-2197 (electronic)", ISSN-L = "0020-7225", bibdate = "Sat Nov 28 18:44:37 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0020722510001266", acknowledgement = ack-nhfb, fjournal = "International journal of engineering science", journal-URL = "http://www.sciencedirect.com/science/journal/00207225", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2011:BSFa, author = "Marc Briane and Graeme W. Milton", title = "Bounds on strong field magneto-transport in three-dimensional composites", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1063/1.3644377", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1105.3858", abstract = "This paper deals with bounds satisfied by the effective non-symmetric conductivity of three-dimensional composites in the presence of a strong magnetic field. On the one hand, it is shown that for general composites the antisymmetric part of the effective conductivity cannot be bounded solely in terms of the antisymmetric part of the local conductivity, contrary to the columnar case. So, a suitable rank-two laminate the conductivity of which has a bounded antisymmetric part together with a high-contrast symmetric part, may generate an arbitrarily large antisymmetric part of the effective conductivity. On the other hand, bounds are provided which show that the antisymmetric part of the effective conductivity must go to zero if the upper bound on the antisymmetric part of the local conductivity goes to zero, and the symmetric part of the local conductivity remains bounded below and above. Elementary bounds on the effective moduli are derived assuming the local conductivity and effective conductivity have transverse isotropy in the plane orthogonal to the magnetic field. New Hashin--Shtrikman type bounds for two-phase three-dimensional composites with a non-symmetric conductivity are provided under geometric isotropy of the microstructure. The derivation of the bounds is based on a particular variational principle symmetrizing the problem, and the use of Y-tensors involving the averages of the fields in each phase.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "21", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Briane:2011:BSFb, author = "Marc Briane and Graeme W. Milton", title = "Bounds on strong field magneto-transport in three-dimensional composites", journal = j-J-MATH-PHYS, volume = "52", number = "10", pages = "103705:1--103705:118", month = oct, year = "2011", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.3644377", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "82D40 (35B27)", MRnumber = "2894615 (2012m:82059)", MRreviewer = "Alain Brillard", bibdate = "Thu Oct 27 16:57:30 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v52/i10/p103705_s1", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "11 October 2011", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "18", xxURL = "http://scitation.aip.org/content/aip/journal/jmp/52/10/10.1063/1.3644377", xxyear = "2007", } @Article{GuevaraVasquez:2011:CCS, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Complete characterization and synthesis of the response function of elastodynamic networks", journal = j-J-ELAST, volume = "102", number = "1", pages = "31--54", month = jan, year = "2011", CODEN = "JELSAY", DOI = "https://doi.org/10.1007/s10659-010-9260-y", ISSN = "0374-3535 (print), 1573-2681 (electronic)", ISSN-L = "0374-3535", MRclass = "74K10 (35Q74 74B05 74H45)", MRnumber = "2746911 (2011k:74064)", bibdate = "Wed Dec 22 2010", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s10659-010-9260-y", acknowledgement = ack-gwm, fjournal = "Journal of Elasticity", fjournal = "Journal of Elasticity. The Physical and Mathematical Science of Solids", journal-URL = "http://link.springer.com/journal/10659", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{GuevaraVasquez:2011:ECA, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Exterior cloaking with active sources in two dimensional acoustics", journal = j-WAVE-MOTION, volume = "48", number = "6", pages = "515--524", year = "2011", CODEN = "WAMOD9", DOI = "https://doi.org/10.1016/j.wavemoti.2011.03.005", ISSN = "0165-2125 (print), 1878-433X (electronic)", ISSN-L = "0165-2125", MRclass = "76Q05", MRnumber = "2811880 (2012g:76141)", bibdate = "Fri May 29 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165212511000382", acknowledgement = ack-gwm, fjournal = "Wave Motion. An International Journal Reporting Research on Wave Phenomena", journal-URL = "http://www.sciencedirect.com/science/journal/01652125", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{GuevaraVasquez:2011:MAT, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "16", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1007/s13324-012-0031-8", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Analysis and Mathematical Physics, 2 (2012), no. 3, pp 231-246", URL = "https://arxiv.org/abs/1109.3526", abstract = "We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach remains valid in the quasistatic regime in a homogeneous medium. We start by relating the problem of designing an exterior cloak in the quasistatic regime to the classic problem of approximating a harmonic function with harmonic polynomials. An explicit polynomial solution to the problem was given earlier in [Phys. Rev. Lett. 103 (2009), 073901]. Here we show convergence of the device field to the field needed to perfectly cloak an object. The convergence region limits the size of the cloaked region, and the size and position of the device.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Mathematical Physics (math-ph)", } @Article{GuevaraVasquez:2011:TEA, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei and Pierre Seppecher", title = "Transformation elastodynamics and active exterior acoustic cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "6", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1007/978-94-007-4813-2_12", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Submitted as a chapter for the volume \booktitle{Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking}, Craster and Guenneau ed., Springer.", URL = "http://adsabs.harvard.edu/abs/2011arXiv1105.1221G; https://arxiv.org/abs/1105.1221", abstract = "This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with ``torque springs'', which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Mathematical Physics (math-ph)", } @Article{Helsing:2011:SSRa, author = "Johan Helsing and Ross C. McPhedran and Graeme W. Milton", title = "Spectral super-resolution in metamaterial composites", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "25", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/13/11/115005", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1105.5012", abstract = "We investigate the optical properties of periodic composites containing metamaterial inclusions in a normal material matrix. We consider the case where these inclusions have sharp corners, and following Hetherington and Thorpe, use analytic results to argue that it is then possible to deduce the shape of the corner (its included angle) by measurements of the absorptance of such composites when the scale size of the inclusions and period cell is much finer than the wavelength. These analytic arguments are supported by highly accurate numerical results for the effective permittivity function of such composites as a function of the permittivity ratio of inclusions to matrix. The results show that this function has a continuous spectral component with limits independent of the area fraction of inclusions, and with the same limits for both square and staggered square arrays.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "17", subject = "Optics (physics.optics); Materials Science (cond-mat.mtrl-sci); Analysis of PDEs (math.AP)", } @Article{Helsing:2011:SSRb, author = "Johan Helsing and Ross C. McPhedran and Graeme W. Milton", title = "Spectral super-resolution in metamaterial composites", journal = j-NEW-J-PHYS, volume = "13", number = "11", pages = "115005", year = "2011", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/13/11/115005", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Wed Oct 21 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/1367-2630/13/11/115005", acknowledgement = ack-gwm, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://stacks.iop.org/1367-2630/13/i=11/a=115005", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/13/11/115005/", } @Article{Kang:2011:SBV, author = "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton", title = "Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "4", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1007/s00526-011-0462-3", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1105.0949", abstract = "We deal with the problem of estimating the volume of inclusions using a finite number of boundary measurements in electrical impedance tomography. We derive upper and lower bounds on the volume fractions of inclusions, or more generally two phase mixtures, using two boundary measurements in two dimensions. These bounds are optimal in the sense that they are attained by certain configurations with some boundary data. We derive the bounds using the translation method which uses classical variational principles with a null Lagrangian. We then obtain necessary conditions for the bounds to be attained and prove that these bounds are attained by inclusions inside which the field is uniform. When special boundary conditions are imposed the bounds reduce to those obtained by Milton and these in turn are shown here to reduce to those of Capdeboscq-Vogelius in the limit when the volume fraction tends to zero. The bounds of this paper, and those of Milton, work for inclusions of arbitrary volume fractions. We then perform some numerical experiments to demonstrate how good these bounds are.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "34", subject = "Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Medical Physics (physics.med-ph)", } @Article{Milton:2011:BVF, author = "Graeme Walter Milton and Loc Hoang Nguyen", title = "Bounds on the volume fraction of $2$-phase, $2$-dimensional elastic bodies and on (stress, strain) pairs in composites", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "29", month = aug, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1016/j.crme.2012.02.002", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1108.5764", abstract = "Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy, determinant of the stress, and determinant of the displacement gradient, which can be determined from measurements of the traction and displacement at the boundary. The bounds are sharp if in each phase certain displacement field components are constant. The inequalities we obtain also directly give bounds on the possible (average stress, average strain) pairs in a two-phase, two-dimensional, periodic or statistically homogeneous composite", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "16", subject = "Analysis of PDEs (math.AP); Materials Science (cond-mat.mtrl-sci); Classical Physics (physics.class-ph)", } @Article{Milton:2011:MHF, author = "Graeme Milton and Pierre Seppecher", title = "A metamaterial having a frequency dependent elasticity tensor and a zero effective mass density", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "4", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1002/pssb.201084214", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1105.0941", abstract = "Within the context of linear elasticity we show that a two-terminal network of springs and masses, can respond exactly the same as a normal spring, but with a frequency dependent spring constant. As a consequence a network of such springs can have a frequency dependent effective elasticity tensor but zero effective mass density. The internal masses influence the elasticity tensor, but do not contribute to the effective mass density at any frequency.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "5", subject = "Classical Physics (physics.class-ph); Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)", } @Article{Milton:2011:UBE, author = "Graeme W. Milton", title = "Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "4", month = may, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1016/j.jmps.2011.09.007", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1105.0954", abstract = "Universal bounds on the electrical and elastic response of two-phase (and multiphase) ellipsoidal or parallelopipedic bodies have been obtained by Nemat-Nasser and Hori. Here we show how their bounds can be improved and extended to bodies of arbitrary shape. Although our analysis is for two-phase bodies with isotropic phases it can easily be extended to multiphase bodies with anisotropic constituents. Our two-phase bounds can be used in an inverse fashion to bound the volume fractions occupied by the phases, and for electrical conductivity reduce to those of Capdeboscq and Vogelius when the volume fraction is asymptotically small. Other volume fraction bounds derived here utilize information obtained from thermal, magnetic, dielectric or elastic responses. One bound on the volume fraction can be obtained by simply immersing the body in a water filled cylinder with a piston at one end and measuring the change in water pressure when the piston is displaced by a known small amount. This bound may be particularly effective for estimating the volume of cavities in a body. We also obtain new bounds utilizing just one pair of (voltage, flux) electrical measurements at the boundary of the body.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "5", subject = "Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Classical Physics (physics.class-ph)", } @Article{Ammari:2012:STN, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Spectral theory of a {Neumann--Poincar{\'e}}-type operator and analysis of anomalous localized resonance {II}", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "20", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1007/s00205-012-0605-5", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1212.5066", abstract = "If a body of dielectric material is coated by a plasmonic structure of negative dielectric constant with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. The aim of this paper is to investigate this phenomenon in two and three dimensions when the coated structure is radial, and the core, shell and matrix are isotropic materials. In two dimensions, we show that if the real part of the permittivity of the shell is -1 (under the assumption that the permittivity of the background is 1), then CALR takes place. If it is different from -1, then CALR does not occur. In three dimensions, we show that CALR does not occur. The analysis of this paper reveals that occurrence of CALR is determined by the eigenvalue distribution of the Neumann--Poincar{\'e}-type operator associated with the structure.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Analysis of PDEs (math.AP)", } @Article{Buckmann:2012:RTD, author = "Tiemo B{\"u}ckmann and Muamer Kadic and Graeme W. Milton and Michael Thiel and Martin Wegener", title = "Realizability of three-dimensional dilational materials", journal = "????", volume = "??", number = "??", pages = "??--??", year = "2012", bibdate = "Fri May 25 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "In preparation.", acknowledgement = ack-gwm, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Not found in Web search on 26 November 2015.", } @Article{GuevaraVasquez:2012:MAT, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei", title = "Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime", journal = j-ANAL-MATH-PHYS, volume = "2", number = "3", pages = "231--246", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1007/s13324-012-0031-8", ISSN = "1664-235X (print), 1664-2368 (electronic)", ISSN-L = "1664-2368", MRclass = "35J05 (30E10 31A05 35J25)", MRnumber = "2958358", bibdate = "Sat Apr 27 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s13324-012-0031-8", acknowledgement = ack-gwm, ajournal = "Anal. Math. Phys.", fjournal = "Analysis and Mathematical Physics", journal-URL = "http://link.springer.com/journal/13324", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Kang:2012:BVFa, author = "Hyeonbae Kang and Graeme W. Milton and Jenn-Nan Wang", title = "Bounds on the volume fraction of the two-phase shallow shell using one measurement", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "23", month = apr, year = "2012", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1204.4962", abstract = "We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in this paper is based on the translation method. One of the key steps is to connect the shallow shell equations to the thin plate equation.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Analysis of PDEs (math.AP)", } @Article{Kang:2012:BVFb, author = "Hyeonbae Kang and Graeme W. Milton", title = "Bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "4", month = jun, year = "2012", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1206.0631", abstract = "Using the translation method of Tartar, Murat, Lurie, and Cherkaev bounds are derived on the volume occupied by an inclusion in a three-dimensional conducting body. They assume electrical impedance tomography measurements have been made for three sets of pairs of current flux and voltage measurements around the boundary. Additionally the conductivity of the inclusion and surrounding medium are assumed to be known. If the boundary data (Dirichlet or Neumann) is special, i.e. such that the fields inside the body would be uniform were the body homogeneous, then the bounds reduce to those of Milton and thus when the volume fraction is small to those of Capdeboscq and Vogelius.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "13", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Kang:2012:EIP, author = "Hyeonbae Kang and Graeme Milton and Jenn-Nan Wang", title = "Equivalence of inverse problems for {$2$D} elasticity and for the thin plate with finite measurements and its applications", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "17", month = mar, year = "2012", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1203.3833", abstract = "In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation with boundary data by solving the corresponding inverse problems for 2D elasticity, and vice versa. For example, we can derive bounds on the volume fraction of the two-phase thin plate from the knowledge of one pair of boundary measurements using the known result for 2D elasticity \cite{ml}. Similarly, we give another approach to the size estimate problem for the thin plate studied by Morassi, Rosset, and Vessella \cite{mrv07, mrv09}.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "9", subject = "Analysis of PDEs (math.AP)", } @Article{Kang:2012:SBV, author = "Hyeonbae Kang and Eunjoo Kim and Graeme W. Milton", title = "Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method", journal = j-CALC-VAR-PARTIAL-DIFFER-EQU, volume = "45", number = "3--4", pages = "367--401", month = nov, year = "2012", DOI = "https://doi.org/10.1007/s00526-011-0462-3", ISSN = "0944-2669 (print), 1432-0835 (electronic)", ISSN-L = "0944-2669", MRclass = "35R30", MRnumber = "2984137", bibdate = "Thu Apr 28 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s00526-011-0462-3", acknowledgement = ack-gwm, fjournal = "Calculus of Variations and Partial Differential Equations", journal-URL = "http://link.springer.com/journal/526; http://www.springer.com/mathematics/analysis/journal/526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxyear = "2011", } @Article{Milton:2012:ANB, author = "Graeme Walter Milton", title = "Adaptable nonlinear bimode metamaterials with rigid bars, pivots, and actuators", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "1", month = jun, year = "2012", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1206.0325", abstract = "A large family of periodic planar non-linear bimode metamaterials are constructed from rigid bars and pivots. They are affine materials in the sense that their macroscopic deformations are only affine deformations: at large distances any deformation must be close to an affine deformation. Bimode means that the paths of all possible deformations of Bravais lattices that preserve the periodicity of the lattice lie on a two dimensional surface in the three dimensional space of invariants describing the deformation (excluding translations and rotations). By adding two actuators inside a single microscopic cell one can control the macroscopic deformation, which may be useful for the design of adaptive structures. The design of adaptable nonlinear affine trimode metamaterials (for which the macroscopic deformations lie within a three-dimensional region in the space of invariants) is discussed, although their realization remains an open problem. Examples are given of non-affine unimode and non-affine bimode materials. In these materials the deformation can vary from cell to cell in such a way that the macroscopic deformation is non-affine.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "13", subject = "Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Algebraic Geometry (math.AG)", } @Article{Milton:2012:BVF, author = "Graeme W. Milton and Loc Hoang Nguyen", title = "Bounds on the volume fraction of $2$-phase, $2$-dimensional elastic bodies and on (stress, strain) pairs in composites", journal = j-C-R-MEC, volume = "340", number = "4--5", pages = "193--204", year = "2012", CODEN = "CRMOC9", DOI = "https://doi.org/10.1016/j.crme.2012.02.002", ISSN = "1631-0721 (print), 1873-7234 (electronic)", ISSN-L = "1631-0721", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1631072112000393", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Comptes Rendus M{'e}canique", journal-URL = "http://www.sciencedirect.com/science/journal/16310721", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Recent Advances in Micromechanics of Materials, Edited by M. Bornert, R. Brenner, O. Castelnau, P. Ponte Casta{\~n}eda and P. Suquet.", } @Article{Milton:2012:CCM, author = "Graeme Walter Milton", title = "Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "28", month = may, year = "2012", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1205.6213", abstract = "A complete characterization is given of the possible macroscopic deformations of periodic nonlinear affine unimode metamaterials constructed from rigid bars and pivots. The materials are affine in the sense that their macroscopic deformations can only be affine deformations: on a local level the deformation may vary from cell to cell. Unimode means that macroscopically the material can only deform along a one dimensional trajectory in the six dimensional space of invariants describing the deformation (excluding translations and rotations). We show by explicit construction that any continuous trajectory is realizable to an arbitrarily high degree of approximation provided at all points along the trajectory the geometry does not collapse to a lower dimensional one. In particular, we present two and three dimensional dilational materials having an arbitrarily large flexibility window. These are perfect auxetic materials for which a dilation is the only easy mode of deformation. They are free to dilate to arbitrarily large strain with zero bulk modulus.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "34", subject = "Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Algebraic Geometry (math.AG)", } @Article{Milton:2012:UBE, author = "Graeme W. Milton", title = "Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements", journal = j-J-MECH-PHYS-SOLIDS, volume = "60", number = "1", pages = "139--155", year = "2012", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2011.09.007", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74F15 (78A30 78A45)", MRnumber = "2907437 (2012j:74058)", bibdate = "Wed Aug 17 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509611001748", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Alali:2013:ECTa, author = "Bacim Alali and Graeme W. Milton", title = "Effective Conductivities of Thin-Interphase Composites", journal = "arXiv.org", volume = "????", number = "??", pages = "??--??", day = "12", month = feb, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1016/j.jmps.2013.08.022", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1302.2943", abstract = "A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the fields need to be computed only in a reference composite in which the interphases have been replaced by perfect interfaces. The results apply whether any two phases of the composite are separated by a single interphase or multiple interphases, whether the conductivities of the composite phases are isotropic or anisotropic, and whether the thickness of an interphase is uniform or varies as a function of position. It is assumed that the conductivities of the interphase materials have intermediate values as opposed to very high or very low conductivities.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "", subject = "Analysis of PDEs (math.AP); Materials Science (cond-mat.mtrl-sci)", } @Article{Alali:2013:ECTb, author = "Bacim Alali and Graeme W. Milton", title = "Effective conductivities of thin-interphase composites", journal = j-J-MECH-PHYS-SOLIDS, volume = "61", number = "12", pages = "2680--2691", year = "2013", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2013.08.022", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74A50 (74F15)", MRnumber = "3111584", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509613001750", fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Ammari:2013:ALRa, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Anomalous localized resonance using a folded geometry in three dimensions", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "24", month = jan, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2013.0048", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1301.5712", abstract = "If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. It was proved in other papers by authors that if the coated structure is circular (2D) and dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (3D), then CALR does not occur. The aim of this paper is to show that the CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding a folded geometry.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Mathematical Physics (math-ph); Analysis of PDEs (math.AP)", } @Article{Ammari:2013:ALRb, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Anomalous localized resonance using a folded geometry in three dimensions", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "469", number = "2154", pages = "20130048", day = "8", month = jun, year = "2013", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2013.0048", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Also available as arXiv:1301.5712 [math-ph].", URL = "http://rspa.royalsocietypublishing.org/content/469/2154/20130048", abstract = "If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. If the coated structure is circular (two dimensions) and the dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (three dimensions), then CALR does not occur. The aim of this paper is to show that CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding a folded geometry.", acknowledgement = ack-gwm, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Ammari:2013:STN, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Spectral theory of a {Neumann--Poincar{\'e}}-type operator and analysis of cloaking due to anomalous localized resonance", journal = j-ARCH-RAT-MECH-ANAL, volume = "208", number = "2", pages = "667--692", month = may, year = "2013", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s00205-012-0605-5", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "78A46 (35A08 35J25 78M22)", MRnumber = "3035988", MRreviewer = "Yoichi Miyazaki", bibdate = "Fri Jan 25 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "See also arXiv:1109.0479 [math.AP].", URL = "http://link.springer.com/article/10.1007/s00205-012-0605-5", acknowledgement = ack-gwm, fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Ammari:2013:STNII, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", title = "Spectral theory of a {Neumann--Poincar{\'e}}-type operator and analysis of cloaking due to anomalous localized resonance {II}", journal = "arXiv.org", volume = "", number = "", pages = "", year = "2013", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Fri Jan 25 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Submitted. Available as arXiv:1212.5066 [math.AP].", acknowledgement = ack-gwm, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2013:WEF, author = "Marc Briane and (IRMAR, INSA Rennes), Graeme W. Milton and Andrejs Treibergs", title = "Which electric fields are realizable in conducting materials?", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "8", month = jan, year = "2013", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1301.1613", abstract = "In this paper we study the realizability of a given smooth periodic gradient field $ \nabla u $ defined in $ \RR^d $, in the sense of finding when one can obtain a matrix conductivity $ \si $ such that $ \si \nabla u $ is a divergence free current field. The construction is shown to be always possible locally in $ \RR^d $ provided that $ \nabla u $ is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot be both periodic and isotropic. However, using a dynamical systems approach the isotropic realizability is proved to hold in the whole space (without periodicity) under the assumption that the gradient does not vanish anywhere. Moreover, a sharp condition is obtained to ensure the isotropic realizability in the torus. The realizability of a matrix field is also investigated both in the periodic case and in the laminate case. In this context the sign of the matrix field determinant plays an essential role according to the space dimension.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "19", subject = "Analysis of PDEs (math.AP); Classical Physics (physics.class-ph)", } @Article{Kang:2013:BSI, author = "Hyeonbae Kang and Kyoungsun Kim and Hyundae Lee and Xiaofei Li and Graeme W. Milton", title = "Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "9", month = oct, year = "2013", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1310.2439", abstract = "The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the body are derived in terms of two pairs of voltage and current data measured on the boundary of the body. These bounds are derived using the translation method. We also provide numerical examples to show that these bounds are quite tight and stable under measurement noise.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "15", subject = "Analysis of PDEs (math.AP)", } @Article{Kang:2013:BVF, author = "Hyeonbae Kang and Graeme W. Milton", title = "Bounds on the Volume Fractions of Two Materials in a Three-Dimensional Body from Boundary Measurements by the Translation Method", journal = j-SIAM-J-APPL-MATH, volume = "73", number = "1", pages = "475--492", month = "????", year = "2013", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/120879713", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "65N21 (35J25 35R30 45Q05)", MRnumber = "3033159", MRreviewer = "Mansur I. Ismailov", bibdate = "Thu Mar 7 10:00:39 MST 2013", bibsource = "http://epubs.siam.org/toc/smjmap/73/1; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/120879713", acknowledgement = ack-nhfb, acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "January 2013", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2013:ANB, author = "Graeme Walter Milton", title = "Adaptable nonlinear bimode metamaterials using rigid bars, pivots, and actuators", journal = j-J-MECH-PHYS-SOLIDS, volume = "61", number = "7", pages = "1561--1568", year = "2013", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2012.08.012", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74N15 (74B20)", MRnumber = "3063487", bibdate = "Mon Oct 13 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxtitle = "Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots", } @Article{Milton:2013:BVI, author = "Graeme W. Milton and A. E. Thaler", title = "Bounds on the volume of an inclusion in a body from a complex conductivity measurement", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2013", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1306.6608", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2013:CCM, author = "Graeme Walter Milton", title = "Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots", journal = j-J-MECH-PHYS-SOLIDS, volume = "61", number = "7", pages = "1543--1560", year = "2013", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2012.08.011", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74N15 (74B20 74K10)", MRnumber = "3063486", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2013:SEHa, author = "Graeme W. Milton and Ross C. McPhedran and Ari Sihvola", title = "The searchlight effect in hyperbolic materials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "25", month = feb, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1364/OE.21.014926", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1302.5980", abstract = "The quasistatic field around a circular hole in a two-dimensional hyperbolic medium is studied. As the loss parameter goes to zero, it is found that the electric field diverges along four lines each tangent to the hole. In this limit, the power dissipated by the field in the vicinity of these lines, per unit length of the line, goes to zero but extends further and further out so that the net power dissipated remains finite. Additionally the interaction between polarizable dipoles in a hyperbolic medium is studied. It is shown that a dipole with small polarizability can dramatically influence the dipole moment of a distant polarizable dipole, if it is appropriately placed. We call this the searchlight effect, as the enhancement depends on the orientation of the line joining the polarizable dipoles and can be varied by changing the frequency. For some particular polarizabilities the enhancement can actually increase the further the polarizable dipoles are apart.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "21", subject = "Optics (physics.optics); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)", } @Article{Milton:2013:SEHb, author = "Graeme W. Milton and Ross C. McPhedran and Ari Sihvola", title = "The searchlight effect in hyperbolic materials", journal = j-OPT-EXPRESS, volume = "21", number = "12", pages = "14926--14942", day = "17", month = jun, year = "2013", CODEN = "OPEXFF", DOI = "https://doi.org/10.1364/OE.21.014926", ISSN = "1094-4087", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.osapublishing.org/abstract.cfm?uri=oe-21-12-14926", acknowledgement = ack-nhfb, fjournal = "Optics Express", journal-URL = "http://opticsexpress.org/Issue.cfm", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2013:SIG, author = "Graeme W. Milton", title = "Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "469", number = "2157", pages = "20130075, 18", year = "2013", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2013.0075", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "49J45 (49N15)", MRnumber = "3078206", MRreviewer = "Jos{\'e} Carlos Pedro Cardoso Matias", bibdate = "Tue Nov 4 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "See addendum \cite{Milton:2015:ASI}.", URL = "http://rspa.royalsocietypublishing.org/content/469/2157/20130075", acknowledgement = ack-gwm, fjournal = "Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "18", } @Article{Milton:2013:SIW, author = "Graeme W. Milton", title = "Sharp inequalities which generalize the divergence theorem --- an extension of the notion of quasiconvexity, with an addendum", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "5", month = feb, year = "2013", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1302.0942", abstract = "Subject to suitable boundary conditions being imposed, sharp inequalities are obtained on integrals over a region $ \Omega $ of certain special quadratic functions $ f(E) $ where $ E(x) $ derives from a potential $ U(x) $. With $ E = \nabla U $ it is known that such sharp inequalities can be obtained when $ f(E) $ is a quasiconvex function and when $U$ satisfies affine boundary conditions (i.e., for some matrix $D$, $ U = D x$ on $ \partial \Omega $). Here we allow for other boundary conditions and for fields $E$ that involve derivatives of a variety orders of $U$. We define a notion of convexity that generalizes quasiconvexity. $ Q_*$-convex quadratic functions are introduced, characterized and an algorithm is given for generating sharply $ Q_*$-convex functions. We emphasize that this also solves the outstanding problem of finding an algorithm for generating extremal quasiconvex quadratic functions. We also treat integrals over $ \Omega $ of special quadratic functions $ g(J)$ where $ J(x)$ satisfies a differential constraint involving derivatives with, possibly, a variety of orders. The results generalize an example of Kang and the author in three spatial dimensions where $ J(x)$ is a $ 3 \times 3$ matrix valued field satisfying $ \nabla \cdot J = 0$. In the addendum the paper is clarified. Notably, much more general boundary conditions are given under which sharp lower bounds on the integrals of certain quadratic functions of the fields can be obtained. As a consequence, strict $ Q_*$-convexity is found to be an appropriate condition to ensure uniqueness of the solutions of a wide class of partial differential equations with constant coefficients, in a given domain $ \Omega $ with appropriate boundary conditions.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "23 + 7", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Thaler:2013:BVI, author = "Andrew E. Thaler and Graeme W. Milton", title = "Bounds on the volume of an inclusion in a body from a complex conductivity measurement", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "27", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.4310/CMS.2015.v13.n4.a2", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Communications in Mathematical Sciences 13(4): 863--892, 2015", URL = "https://arxiv.org/abs/1306.6608", abstract = "We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of the electric field, current, and certain products of the electric field and current. All of these average values are computed from a single electrical impedance tomography measurement of the voltage and current on the boundary of the body. Additionally, the bounds are tight in the sense that at least one of the bounds gives the exact volume of the inclusion for certain geometries and boundary conditions.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Analysis of PDEs (math.AP)", } @InProceedings{Vasquez:2013:SRP, author = "Fernando {Guevara Vasquez} and Graeme W. Milton and Daniel Onofrei and Pierre Seppecher", editor = "Richard V. Craster and S{\'e}bastien Guenneau", booktitle = "Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking", title = "Transformation elastodynamics and active exterior acoustic cloaking", volume = "166", publisher = pub-SV, address = pub-SV:adr, pages = "289--318", year = "2013", DOI = "https://doi.org/10.1007/978-94-007-4813-2_12", ISBN = "94-007-4813-2", ISBN-13 = "978-94-007-4813-2", LCCN = "????", bibdate = "Sat Apr 27 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Springer Series in Materials Science", URL = "http://link.springer.com/chapter/10.1007/978-94-007-4813-2_12", acknowledgement = ack-gwm, book-DOI = "https://doi.org/10.1007/978-94-007-4813-2", book-URL = "http://www.springerlink.com/content/978-94-007-4813-2", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InProceedings{Ammari:2014:STN, author = "Habib Ammari and Giulio Ciraolo and Hyeonbae Kang and Hyundae Lee and Graeme W. Milton", editor = "Plamen Stefanov and Andr{\'a}s Vasy and Maciej Zworski", booktitle = "{Inverse problems and applications: Conference in honor of Gunther Uhlmann on Inverse Problems, June 18--22, 2012, University of California, Irvine, CA: International Conference in honor of Gunther Uhlmann's 60th birthday on Inverse Problems and applications, September 17--21, 2012, Yuquan Campus, Zhejiang University, Hangzhou, China}", title = "Spectral theory of a {Neumann--Poincar{\'e}}-type operator and analysis of cloaking by anomalous localized resonance {II}", volume = "615", publisher = pub-AMS, address = pub-AMS:adr, bookpages = "vii + 309", pages = "1--14", year = "2014", DOI = "https://doi.org/10.1090/conm/615/12244", ISBN = "978-147-041-0-7-9-7 (print), 978-147-041-6-5-9-1 (online)", ISBN-13 = "978-1-4704-1079-7 (print), 978-1-4704-1659-1 (online)", LCCN = "QA378.5 .C665 2014", MRclass = "35J25 (35A08 35B30 35Q60 35R30 78A48)", MRnumber = "3221596", MRreviewer = "Yoichi Miyazaki", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", series = "Contemporary Mathematics", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1090/conm/615", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Briane:2014:IRC, author = "Marc Briane and Graeme W. Milton", title = "Isotropic realizability of current fields in {$ R^3 $}", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "26", month = sep, year = "2014", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1409.7658", abstract = "This paper deals with the isotropic realizability of a given regular divergence free field $j$ in $ R^3$ as a current field, namely to know when $j$ can be written as $ \sigma D_u$ for some isotropic conductivity $ \sigma $, and some gradient field $ D_u$. The local isotropic realizability in $ R^3$ is obtained by Frobenius' theorem provided that $j$ and $ \curl j$ are orthogonal in $ R^3$. A counter-example shows that Frobenius' condition is not sufficient to derive the global isotropic realizability in $ R^3$. However, assuming that ($j$, $ \curl j$, $ \j \times c u r l j$) is an orthogonal basis of $ R^3$, an admissible conductivity sigma is constructed from a combination of the three dynamical flows along the directions $ j / |j|$, $ \curl j / | \curl j|$ and $ (j / |j|^2) \times \curl j$. When the field $j$ is periodic, the isotropic realizability in the torus needs in addition a boundedness assumption satisfied by the flow along the third direction $ (j / |j|^2) \times \curl j$. Several examples illustrate the sharpness of the realizability conditions.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "22", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Briane:2014:WEF, author = "Marc Briane and Graeme W. Milton and Andrejs Treibergs", title = "Which electric fields are realizable in conducting materials?", journal = j-MATH-MODEL-NUM-ANA, volume = "48", number = "2", pages = "307--323", month = mar # "\slash " # apr, year = "2014", CODEN = "RMMAEV", DOI = "https://doi.org/10.1051/m2an/2013109", ISSN = "0764-583X (print), 1290-3841 (electronic)", ISSN-L = "0764-583X", MRclass = "65N21 (78A30)", MRnumber = "3177847", MRreviewer = "Mansur I. Ismailov", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://journals.cambridge.org/abstract_S0764583X1300109X", acknowledgement = ack-nhfb, fjournal = "ESAIM. Mathematical Modelling and Numerical Analysis", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=MZA; http://www.esaim-m2an.org/component/issues", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Buckmann:2014:TDD, author = "Tiemo B{\"u}ckmann and Robert Schittny and Michael Thiel and Muamer Kadic and Graeme W. Milton and Martin Wegener", title = "On three-dimensional dilational elastic metamaterials", journal = j-NEW-J-PHYS, volume = "16", number = "3", pages = "033032", month = mar, year = "2014", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/16/3/033032", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Sun Oct 12 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://stacks.iop.org/1367-2630/16/i=3/a=033032", abstract = "Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poisson's ratio of 1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial material, a metamaterial, which approaches the ideal of a dilational material. The main novelty of our work is that we also fabricate and characterize corresponding metamaterial samples. To reveal all modes in the design, we calculate the phonon band structures. On this basis, using cubic symmetry we can unambiguously retrieve all different non-zero elements of the rank-four effective metamaterial elasticity tensor from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches 1 in the limit of small internal connections. This finding is also supported by independent, static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as 0.8 in good agreement with the theory. Microscopic samples are also presented.", acknowledgement = ack-gwm, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxURL = "http://iopscience.iop.org/article/10.1088/1367-2630/16/3/033032/", } @Article{Harutyunyan:2014:EEE, author = "Davit Harutyunyan and Graeme Walter Milton", title = "Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "14", month = mar, year = "2014", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1403.3718", abstract = "We prove that if the associated fourth order tensor of a quadratic form has a linear elastic cubic symmetry then it is quasiconvex if and only if it is polyconvex, i.e., a sum of convex and null-Lagrangian quadratic forms. We prove that allowing for slightly less symmetry, namely only cyclic and axis-reflection symmetry, gives rise to a class of extremal quasiconvex quadratic forms, that are not polyconvex. Non-affine boundary conditions on the potential are identified which allow one to obtain sharp bounds on the integrals of these extremal quasiconvex quadratic forms of $ \nabla u $ over an arbitrary region.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "17", subject = "Analysis of PDEs (math.AP)", } @Article{Harutyunyan:2014:RBE, author = "Davit Harutyunyan and Graeme Walter Milton", title = "On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "16", month = nov, year = "2014", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1411.4216", abstract = "We prove that an elasticity tensor with orthotropic symmetry is extremal if the determinant of its acoustic tensor is an extremal polynomial that is not a perfect square.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "17", subject = "Analysis of PDEs (math.AP)", } @Article{Kang:2014:BSI, author = "Hyeonbae Kang and Kyoungsun Kim and Hyundae Lee and Xiaofei Li and Graeme W. Milton", title = "Bounds on the Size of an Inclusion Using the Translation Method for Two-Dimensional Complex Conductivity", journal = j-SIAM-J-APPL-MATH, volume = "74", number = "4", pages = "939--958", month = "????", year = "2014", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/130940426", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "65N21 (45Q05)", MRnumber = "3229662", MRreviewer = "Barbara Zubik-Kowal", bibdate = "Sat Sep 13 08:30:15 MDT 2014", bibsource = "http://epubs.siam.org/toc/smjmap/74/4; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/130940426", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "January 2014", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Kang:2014:BVF, author = "Hyeonbae Kang and Graeme W. Milton and Jenn-Nan Wang", title = "Bounds on the volume fraction of the two-phase shallow shell using one measurement", journal = j-J-ELAST, volume = "114", number = "1", pages = "41--53", month = jan, year = "2014", CODEN = "JELSAY", DOI = "https://doi.org/10.1007/s10659-012-9425-y", ISSN = "0374-3535 (print), 1573-2681 (electronic)", ISSN-L = "0374-3535", MRclass = "74K25 (74E30 74G45 74G75 74K20)", MRnumber = "3144824", MRreviewer = "Victor A. Eremeyev", bibdate = "Sat Apr 11 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://link.springer.com/article/10.1007/s10659-012-9425-y", acknowledgement = ack-gwm, fjournal = "Journal of Elasticity. The Physical and Mathematical Science of Solids", journal-URL = "http://link.springer.com/journal/10659", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxyear = "2011", } @Article{Kochmann:2014:RBEa, author = "Dennis M. Kochmann and Graeme W. Milton", title = "Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "16", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1016/j.jmps.2014.06.010", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1401.4142", abstract = "We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness phases). We show that for statically stable bodies the classical displacement-based variational principles for Dirichlet and Neumann boundary problems hold but that the dual variational principle for traction boundary problems does not apply. We illustrate our findings by the example of a coated spherical inclusion whose stability conditions are obtained from the variational principles. We further show that the classical Voigt upper bound on the linear elastic moduli in multi-phase inhomogeneous bodies and composites applies and that it imposes a stability condition: overall stability requires that the effective moduli do not surpass the Voigt upper bound. This particularly implies that, while the geometric constraints among constituents in a composite can stabilize negative-stiffness phases, the stabilization is insufficient to allow for extreme overall static elastic moduli (exceeding those of the constituents). Stronger bounds on the effective elastic moduli of isotropic composites can be obtained from the Hashin--Shtrikman variational inequalities, which are also shown to hold in the presence of negative stiffness.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Materials Science (cond-mat.mtrl-sci)", } @Article{Kochmann:2014:RBEb, author = "Dennis M. Kochmann and Graeme W. Milton", title = "Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases", journal = j-J-MECH-PHYS-SOLIDS, volume = "71", pages = "46--63", month = nov, year = "2014", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2014.06.010", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRclass = "74Q15 (74A40 74B05)", MRnumber = "3255662", MRreviewer = "Alain Brillard", bibdate = "Sat Jul 4 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022509614001367", acknowledgement = ack-gwm, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", xxyear = "2015", } @Article{Meklachi:2014:SAL, author = "Taoufik Meklachi and Graeme W. Milton and Daniel Onofrei and Andrew E. Thaler and Gregory Funchess", title = "Sensitivity of anomalous localized resonance phenomena with respect to dissipation", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "26", month = jun, year = "2014", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1406.7044", abstract = "We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. If the charge density distribution is within a critical distance of the slab, then the power dissipation within the slab blows up as certain electrical dissipation parameters go to zero. The potential remains bounded far away from the slab in this limit, which leads to cloaking due to anomalous localized resonance. On the other hand, if the charge density distribution is further than this critical distance from the slab, then the power dissipation within the slab remains bounded and cloaking due to anomalous localized resonance does not occur. The critical distance is shown to strongly depend on the the rate at which the dissipation outside of the slab goes to zero.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "34", subject = "Analysis of PDEs (math.AP)", } @Article{Milton:2014:IRC, author = "Graeme W. Milton and M. Briane", title = "Isotropic realizability of current fields in {$ \mathbb {R}^3 $}", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2014", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1409.7658", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2014:NET, author = "Graeme Walter Milton", title = "New examples of three-dimensional dilational materials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "15", month = oct, year = "2014", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1410.4143", abstract = "Two-dimensional dilational materials, for which the only easy mode of deformation is a dilation are reviewed and connections are drawn between models previously proposed in the literature. Some models which appear to be dilational materials, but which in fact are not, are also discussed. Finally, four new examples of three-dimensional dilational materials are given.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "11", subject = "Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph)", } @Article{Milton:2014:SAL, author = "Graeme W. Milton and T. Meklachi and D. Onofrei and A. E. Thaler", title = "Sensitivity of anomalous localized resonance phenomena with respect to dissipation", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2014", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1406.7044", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Thaler:2014:EDVa, author = "Andrew E. Thaler and Graeme W. Milton", title = "Exact determination of the volume of an inclusion in a body having constant shear modulus", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "25", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1088/0266-5611/30/12/125008", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Inverse Problems 30 (2014) 1250008", URL = "https://arxiv.org/abs/1406.6656", abstract = "We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus. Our formula depends on an appropriate measurement of the displacement and traction around the boundary of the body. In particular, the boundary conditions around the boundary of the body must be such that they mimic the body being placed in an infinite medium with an appropriate displacement applied at infinity.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "16", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Thaler:2014:EDVb, author = "Andrew E. Thaler and Graeme W. Milton", title = "Exact determination of the volume of an inclusion in a body having constant shear modulus", journal = j-INVERSE-PROBLEMS, volume = "30", number = "12", pages = "125008, 16", month = dec, year = "2014", CODEN = "INPEEY", DOI = "https://doi.org/10.1088/0266-5611/30/12/125008", ISSN = "0266-5611 (print), 1361-6420 (electronic)", ISSN-L = "0266-5611", MRclass = "74B05 (35Q74 74G05)", MRnumber = "3291122", MRreviewer = "Rui Li", bibdate = "Sat Apr 11 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://iopscience.iop.org/0266-5611/30/12/125008", abstract = "We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus. Our formula depends on an appropriate measurement of the displacement and traction around the boundary of the body. In particular, the boundary conditions around the boundary of the body must be such that they mimic the body being placed in an infinite medium with an appropriate displacement applied at infinity.", acknowledgement = ack-gwm, fjournal = "Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data", journal-URL = "http://iopscience.iop.org/0266-5611/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "16", xxURL = "http://stacks.iop.org/0266-5611/30/i=12/a=125008", xxURL = "http://iopscience.iop.org/article/10.1088/0266-5611/30/12/125008/", } @Article{Briane:2015:IRC, author = "M. Briane and Graeme W. Milton", title = "Isotropic Realizability of Current Fields in {$ \mathbb {R}^3 $}", journal = j-SIAM-J-APPL-DYN-SYST, volume = "14", number = "2", pages = "1165--1188", month = "????", year = "2015", CODEN = "SJADAY", DOI = "https://doi.org/10.1137/140989121", ISSN = "1536-0040", MRclass = "35B27 (35F40 37C10 78A30)", MRnumber = "3359673", MRreviewer = "Simon Labrunie", bibdate = "Sat Aug 8 07:10:05 MDT 2015", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIADS/14/2; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamjappldynsyst.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Dynamical Systems", journal-URL = "http://epubs.siam.org/siads", onlinedate = "January 2015", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Buckmann:2015:TDD, author = "Tiemo B{\"u}ckmann and Robert Schittny and Michael Thiel and Muamer Kadic and Graeme W. Milton and Martin Wegener", title = "On three-dimensional dilational elastic metamaterials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "11", month = oct, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/16/3/033032", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1310.3719", abstract = "Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we calculate the phonon band structures. On this basis, using cubic symmetry, we can unambiguously retrieve all different non-zero elements of the rank-4 effective metamaterial elasticity tensor, from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes isotropic and approaches -1 in the limit of small internal connections. This finding is also supported by independent static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poisson's ratios as low as -0.8 in good agreement with theory. Microscopic samples are also presented.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "??", subject = "Materials Science (cond-mat.mtrl-sci)", } @Article{Cassier:2015:ADN, author = "Maxence Cassier and Aaron Welters and Graeme W. Milton", title = "Analyticity of the {Dirichlet}-to-{Neumann} map for the time-harmonic {Maxwell}'s equations", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "15", month = dec, year = "2015", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "This is a copy of chapter 4 in the book \booktitle{Extending the Theory of Composites to Other Areas of Science} edited by Graeme W. Milton, 2016, Milton-Patton Publishers, ISBN-13 978-1-4835-6919-2.", URL = "https://arxiv.org/abs/1512.05838", abstract = "In this chapter of the book entitled, \booktitle{0Extending the Theory of Composites to Other Areas of Science} [edited by Graeme W. Milton, 2016] we derive the analyticity properties of the electromagnetic Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations for passive linear multicomponent media. Moreover, we discuss the connection of this map to Herglotz functions for isotropic and anisotropic multicomponent composites.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "33", subject = "Analysis of PDEs (math.AP); Mathematical Physics (math-ph)", } @Article{Harutyunyan:2015:EEE, author = "Davit Harutyunyan and Graeme Walter Milton", title = "Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex", journal = j-CALC-VAR-PARTIAL-DIFFER-EQU, volume = "54", number = "2", pages = "1575--1589", month = oct, year = "2015", DOI = "https://doi.org/10.1007/s00526-015-0836-z", ISSN = "0944-2669 (print), 1432-0835 (electronic)", ISSN-L = "0944-2669", MRclass = "26B25 (35A23 49J40 74B05)", MRnumber = "3396424", MRreviewer = "Hans Arwed Keller", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "See also arXiv:1403.3718 [math.AP].", acknowledgement = ack-gwm, fjournal = "Calculus of variations and partial differential equations", journal-URL = "http://www.springer.com/mathematics/analysis/journal/526", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Harutyunyan:2015:RBE, author = "Davit Harutyunyan and Graeme W. Milton", title = "On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials", journal = "arXiv.org", year = "2015", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Nov 26 16:58:19 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1411.4216", abstract = "We prove that an elasticity tensor with orthotropic symmetry is extremal if the determinant of its acoustic tensor is an extremal polynomial that is not a perfect square.", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "17", received = "16 November 2014", } @Article{Harutyunyan:2015:TCA, author = "Davit Harutyunyan and Graeme W. Milton", title = "Towards characterization of all $ 3 \times 3 $ extremal quasiconvex quadratic forms", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "14,", month = dec, year = "2015", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1512.04174", abstract = "Given a $ d \times d $ quasiconvex quadratic form, $ d \geq 3 $, we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zero, then the form itself is an extremal quasiconvex quadratic form, i.e. it loses its quasiconvexity whenever a convex quadratic form is subtracted from it. In the special case d=3, we slightly weaken the condition, namely we prove, that if the determinant of the acoustic tensor of the quadratic form is an extremal polynomial that is not a perfect square, then the form itself is an extremal quadratic form. In the case d=3 we also prove, that if the determinant of the acoustic tensor of the form is identically zero, then the form is either an extremal or polyconvex. Also, if the determinant of the acoustic tensor of the form is a perfect square, then the form is either extremal, polycovex, or is a sum of a rank-one form and an extremal, whose acoustic tensor determinant is identically zero. Here we use the notion of extremality introduced by Milton in [???]", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "26", subject = "Algebraic Geometry (math.AG); Analysis of PDEs (math.AP)", } @Article{Mattei:2015:BRV, author = "Ornella Mattei and Graeme W. Milton", title = "Bounds for the response of viscoelastic composites under antiplane loadings in the time domain", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "30", month = dec, year = "2015", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "To be published as a chapter of the book \booktitle{Extending the Theory of Composites to Other Areas of Science}, edited by G. W. Milton, and as a part of the PhD thesis \booktitle{On bounding the response of linear viscoelastic composites in the time domain: The variational approach and the analytic method} by O. Mattei, Universit{\`a} degli Studi di Brescia.", URL = "https://arxiv.org/abs/1602.03383", abstract = "To derive bounds on the strain and stress response of a two-component composite material with viscoelastic phases, we revisit the so-called analytic method (Bergman 1978), which allows one to approximate the complex effective tensor, function of the ratio of the component shear moduli, as the sum of poles weighted by positive semidefinite residue matrices. The novelty of this investigation lies in the application of such a method, previously applied (Milton 1980; Bergman 1980) to problems involving cyclic loadings in the frequency domain, to derive bounds in the time domain for the antiplane viscoelasticity case. The position of the poles and the residues matrices are the variational parameters of the problem: the aim is to determine such parameters in order to have the minimum (or maximum) response at any given moment in time. All the information about the composite is translated for each fixed pole configuration into constraints on the residues, the so-called sum rules. The linearity of the constraints, along with the observation that the response at a fixed time is linear in the residues, enables one to use the theory of linear programming to reduce the problem to one involving relatively few non-zero residues. Finally, bounds on the response are obtained by numerically optimizing over the pole positions. In the examples studied, the results turn out to be very accurate estimates: if sufficient information about the composite is available, the bounds can be quite tight over the entire range of time, allowing one to predict the transient behavior of the composite. Furthermore, the bounds incorporating the volume fractions (and possibly transverse isotropy) can be extremely tight at certain specific times.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "33", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2015:ASC, author = "Graeme W. Milton", title = "The algebra of subspace collections and their association with rational functions of several variables", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = "????", year = "2015", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Sun Nov 29 15:57:31 MST 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1504.08061", acknowledgement = ack-nhfb, journal-URL = "http://arxiv.org", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2015:ASI, author = "Graeme W. Milton", title = "Addendum to `{Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity' [MR3078206]}", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "471", number = "2176", pages = "20140886", day = "4", month = mar, year = "2015", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2014.0886", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "49J45 (49N15)", MRnumber = "3325210", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "See \cite{Milton:2013:SIG}.", URL = "http://rspa.royalsocietypublishing.org/content/471/2176/20140886.abstract", abstract = "The paper ``Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity'' published in Proc. R. Soc. A 2013, 469, 20130075 (doi:10.1098/rspa.2013.0075) is clarified. Notably, much more general boundary conditions are given under which sharp lower bounds on the integrals of certain quadratic functions of the fields can be obtained. More precisely, if the quadratic form is Q*-convex then any solution of the Euler--Lagrange equations will necessarily minimize the integral. As a consequence, strict Q*-convexity is found to be an appropriate condition to ensure uniqueness of the solutions of a wide class of linear Euler--Lagrange equations in a given domain $ \Omega $ with appropriate boundary conditions.", fjournal = "Proceedings A", fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "8", remark = "Bizarrely, this addendum has no assigned page numbers!", } @Article{Milton:2015:NET, author = "Graeme W. Milton", title = "New examples of three-dimensional dilational materials", journal = j-PHYS-STATUS-SOLIDI-B-BASIC-RES, volume = "252", number = "7", pages = "1426--1430", month = jul, year = "2015", CODEN = "PSSBBD", DOI = "https://doi.org/10.1002/pssb.201552297", ISSN = "0370-1972 (print), 1521-3951 (electronic)", ISSN-L = "0370-1972", bibdate = "Sun Nov 15 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/pssb.201552297/abstract", acknowledgement = ack-gwm, fjournal = "Physica Status Solidi. B, Basic Research", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3951/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2015:SAS, author = "Graeme W. Milton", title = "Superfunctions and the algebra of subspace collections and their association with rational functions of several complex variables", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "30", month = apr, year = "2015", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1504.08061", abstract = "A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of subspace collections. Operations on subspace collections are found to correspond to various operations on rational functions, such as addition, multiplication and substitution. It is established that every rational matrix valued function which is homogeneous of degree 1 can be generated from an appropriate, but not necessarily unique, subspace collection: the mapping from subspace collections to rational functions is onto, but not one to one. For some applications superfunctions may be more important than functions, as they incorporate more information about the physical problem, yet can be manipulated in much the same way as functions. Previously subspace collections had been introduced when there was an inner product on the vector (or Hilbert) space, and appropriate subspaces were mutually orthogonal. In that setting certain normalization and reduction operations on subspace collections led to a continued fraction expansion of the associated function, which allowed one to bound the function in terms of a set of weight matrices and normalization matrices that are derived from series expansions. Here we also initiate the theory of normalization and reduction operations, appropriate when there is no inner product on the space.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "60", subject = "Algebraic Geometry (math.AG)", } @Article{Thaler:2015:BVI, author = "Andrew E. Thaler and Graeme W. Milton", title = "Bounds on the volume of an inclusion in a body from a complex conductivity measurement", journal = j-COMMUN-MATH-SCI, volume = "13", number = "4", pages = "863--892", year = "2015", CODEN = "????", DOI = "https://doi.org/10.4310/CMS.2015.v13.n4.a2", ISSN = "1539-6746 (print), 1945-0796 (electronic)", ISSN-L = "1539-6746", MRclass = "35Q60 (31A25 31B20 35J25)", MRnumber = "3325081", MRreviewer = "Shintaro Kondo", bibdate = "Sat Apr 11 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-gwm, fjournal = "Communications in Mathematical Sciences", journal-URL = "http://ProjectEuclid.org/cms", journal-URL = "http://www.intlpress.com/site/pub/pages/journals/items/cms/content/_home/index.html", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Bardsley:2016:CGB, author = "Patrick Bardsley and Michael S. Primrose and Michael Zhao and Jonathan Boyle and Nathan Briggs and Zoe Koch and Graeme W. Milton", title = "Criteria for guaranteed breakdown in two-phase inhomogeneous bodies", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", month = apr, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1088/1361-6420/aa76c5", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1604.04881", abstract = "Lower bounds are obtained on the maximum field strength in one or both phases in a body containing two-phases. These bounds only incorporate boundary data that can be obtained from measurements at the surface of the body, and thus may be useful for determining if breakdown has necessarily occurred in one of the phases, or that some other nonlinearities have occurred. It is assumed the response of the phases is linear up to the point of electric, dielectric, or elastic breakdown, or up to the point of the onset of nonlinearities. These bounds are calculated for conductivity, with one or two sets of boundary conditions, for complex conductivity (as appropriate at fixed frequency when the wavelength is much larger than the body, i.e., for quasistatics), and for two-dimensional elasticity. Sometimes the bounds are optimal when the field is constant in one of the phases, and using the algorithm of Kang, Kim, and Milton (2012) a wide variety of inclusion shapes having this property, for appropriately chosen bodies and appropriate boundary conditions, are numerically constructed. Such inclusions are known as $ E_\Omega $-inclusions.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "30", pagecount = "17", subject = "Analysis of PDEs (math.AP)", } @InCollection{Cassier:2016:ADN, author = "Aaron Welters Maxence Cassier and Graeme W. Milton", title = "Analyticity of the {Dirichlet-to-Neumann} map for the time-harmonic {Maxwell}'s equations", crossref = "Milton:2016:ETC", chapter = "4", pages = "95--122", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Cassier:2016:BHF, author = "Maxence Cassier and Graeme W. Milton", title = "Bounds on {Herglotz} functions and fundamental limits of broadband passive quasi-static cloaking", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "27", month = oct, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1063/1.4989990", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1610.08592", abstract = "Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in (Gustafson and Sj{\"o}berg 2010) and (Bernland, Luger and Gustafson 2011). These bounds apply to a wide class of linear passive systems such as electromagnetic passive materials. Among these bounds, we describe the optimal ones and also discuss their meaning in various physical situations like in the case of a transparency window, where we exhibit sharp bounds. Then, we apply these bounds in the context of broadband passive cloaking in the quasi-static regime to negatively answer the following challenging question: is it possible to construct a passive cloaking device that cloaks an object over a whole frequency band? Our rigorous approach, although limited to quasi-statics, gives quantitative limitations on the cloaking effect over a finite frequency range by providing inequalities on the polarizabilty tensor associated with the cloaking device. We emphasize that our results hold for a cloak or object of any geometrical shape.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "36", subject = "Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Complex Variables (math.CV)", } @Article{Cassier:2016:RAFa, author = "Maxence Cassier and Aaron Welters and Graeme W. Milton", title = "A rigorous approach to the field recursion method for two-component composites with isotropic phases", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "7", month = jan, year = "2016", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "This is a copy of chapter 10 in the book \booktitle{Extending the Theory of Composites to Other Areas of Science} edited by Graeme W. Milton, 2016, Milton-Patton Publishers, ISBN-13 978-1-4835-6919-2.", URL = "https://arxiv.org/abs/1601.01378", abstract = "In this chapter of the book entitled, \booktitle{Extending the Theory of Composites to Other Areas of Science} [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field equation recursion method in the abstract theory of composites to two-component composites with isotropic phases. This method is of great interest since it has proven to be a powerful tool in developing sharp bounds for the effective tensor of a composite material. The reason is that the effective tensor $ L_* $ can be interpreted in the general framework of the abstract theory of composites as the Z-operator on a certain orthogonal Z(2) subspace collection. The base case of the recursion starts with an orthogonal Z(2) subspace collection on a Hilbert space H, the Z-problem, and the associated Y-problem. We provide some new conditions for the solvability of both the Z-problem and the associated Y-problem. We also give explicit representations of the associated Z-operator and Y-operator and study their analytical properties. An iteration method is then developed from a hierarchy of subspace collections and their associated operators which leads to a continued fraction representation of the initial effective tensor $ L_* $.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "27", subject = "Mathematical Physics (math-ph)", } @InCollection{Cassier:2016:RAFb, author = "Aaron Welters Maxence Cassier and Graeme W. Milton", title = "A rigorous approach to the field recursion method", crossref = "Milton:2016:ETC", chapter = "10", pages = "287--308", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Harutyunyan:2016:HFHa, author = "Davit Harutyunyan and Richard V. Craster and Graeme W. Milton", title = "High frequency homogenization for travelling waves in periodic media", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "11", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2016.0066", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1602.03603", abstract = "We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{\"o}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector $ B_k $ and frequency $ \omega_1 $ plus a modulated Bloch carrier wave having crystal wave vector $ B_m $ and frequency $ \omega_2 $. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless $ \omega_1 = \omega_2 $ and $ (B_- B_m) \odot \Lambda \in 2 \pi \mathbb Z^d $, where $ \Lambda = (\lambda_1 \lambda_2 \ldots {} \lambda_d) $ is the periodicity cell of the medium and for any two vectors $ a = (a_1, a_2, \ldots {}, a_d) $,$ b = (b_1, b_2, \ldots {}, b_d) \in R^d $, the product $ a \cdot b $ is defined to be the vector $ (a_1 b_1, a_2 b_2, \ldots {}, a_d b_d) $. This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "30", subject = "Analysis of PDEs (math.AP)", } @Article{Harutyunyan:2016:HFHb, author = "Davit Harutyunyan and Graeme W. Milton and Richard V. Craster", title = "High-frequency homogenization for travelling waves in periodic media", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "472", number = "2191", pages = "20160066", month = jul, year = "2016", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2016.0066", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "35B27 (35C07 35L10)", MRnumber = "3540732", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings A", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "18", } @Article{Harutyunyan:2016:IDCa, author = "Davit Harutyunyan and Graeme W. Milton and Trevor J. Dick and Justin Boyer", title = "On ideal dynamic climbing ropes", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "14", month = nov, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1177/1754337116653539", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1611.04327", abstract = "We consider the rope climber fall problem in two different settings. The simplest formulation of the problem is when the climber falls from a given altitude and is attached to one end of the rope while the other end of the rope is attached to the rock at a given height. The problem is then finding the properties of the rope for which the peak force felt by the climber during the fall is minimal. The second problem of our consideration is again minimizing the same quantity in the presence of a carabiner. We will call such ropes {\it mathematically ideal}. Given the height of the carabiner, the initial height and the mass of the climber, the length of the unstretched rope, and the distance between the belayer and the carabineer, we find the optimal (in the sense of minimized the peak force to a given elongation) dynamic rope in the framework of nonlinear elasticity. Wires of shape memory materials have some of the desired features of the tension-strain relation of a mathematically ideal dynamic rope, namely a plateau in the tension over a range of strains. With a suitable hysteresis loop, they also absorb essentially all the energy from the fall, thus making them an ideal rope in this sense too.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "21", subject = "Optimization and Control (math.OC)", } @Article{Harutyunyan:2016:IDCb, author = "David Harutyunyan and Graeme W. Milton and Trevor J. Dick and Justin Boyer", title = "On ideal dynamic climbing ropes", journal = "Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology", volume = "230", number = "2", pages = "??--??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1177/1754337116653539", ISSN = "1754-3371 (print), 1754-338X (electronic)", ISSN-L = "1754-3371", bibdate = "Wed Jul 6 09:28:16 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://pip.sagepub.com/content/early/2016/06/16/1754337116653539.abstract", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Check issue number and pages; not yet available on journal Web site.", } @InCollection{Mattei:2016:BTR, author = "Ornella Mattei and Graeme W. Milton", title = "Bounds for the transient response of viscoelastic composites", crossref = "Milton:2016:ETC", chapter = "6", pages = "149--178", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Meklachi:2016:SAL, author = "Taoufik Meklachi and Graeme W. Milton and Daniel Onofrei and Andrew E. Thaler and Gregory Funchess", title = "Sensitivity of anomalous localized resonance phenomena with respect to dissipation", journal = j-QUART-APPL-MATH, volume = "74", number = "2", pages = "201--234", year = "2016", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/1408", ISSN = "0033-569x (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "35Q60 (35J15 78A48)", MRnumber = "3505601", MRreviewer = "Bruno Scheurer", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Quarterly of Applied Mathematics", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milgrom:2016:RLI, author = "Mordehai Milgrom and Graeme W. Milton", title = "The response of linear inhomogeneous systems to coupled fields: Bounds and perturbation expansions", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "21", month = feb, year = "2016", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "To appear as Chapter 9 in the book \booktitle{Extending the Theory of Composites to other Areas of Science}, edited by Graeme W. Milton.", URL = "https://arxiv.org/abs/1602.06487", abstract = "We consider the response of a multicomponent body to n fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the various fields with different fluxes, such as electrical currents, electrical displacement currents, magnetic induction fields, energy fluxes, particle fluxes, etc. We obtain the form of the perturbation expansions of the fields and response tensor in powers of matrices which measure the difference between each component tensor and a homogeneous reference tensor L0. For the case of a statistically homogeneous or periodic composite the expansion coefficients can be expressed in terms of positive semidefinite normalization matrices alternating with positive semidefinite weight matrices, which at each given level sum to the identity matrix. In an appropriate basis the projection operators onto the relevant subspaces can be expressed in block tridiagonal form, where the blocks are functions of these weight and normalization matrices. This leads to continued fraction expansions for the effective tensor, and by truncating the continued fraction at successive levels one obtains a nested sequence of bounds on the effective tensor incorporating successively more weight and normalization matrices. The weight matrices and normalization matrices can be calculated from the series expansions of the fields which solve the conductivity problem alone, without any couplings to other fields, and then they can be used to obtain the solution for the fields and effective tensor in coupled field problems in composites.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "33", subject = "Materials Science (cond-mat.mtrl-sci)", } @InCollection{Milgrom:2016:RSC, author = "Mordehai Milgrom and Graeme W. Milton", title = "The response of systems with coupled fields", crossref = "Milton:2016:ETC", chapter = "9", pages = "255--286", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:AFM, author = "Graeme W. Milton", title = "Accelerating {FFT} methods for conducting composites", crossref = "Milton:2016:ETC", chapter = "8", pages = "235--254", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2016:AMa, author = "Graeme W. Milton", title = "Analytic Materials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "18", month = oct, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1098/rspa.2016.0613", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1610.06059", abstract = "The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer $p$. If $p$ takes its maximum value then we have a complete analytic material. Otherwise it is incomplete analytic material of rank $p$. For two-dimensional materials further progress can be made in the identification of analytic materials by using the well-known fact that a $ 90^\circ $ rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "28", subject = "Classical Physics (physics.class-ph)", } @Article{Milton:2016:AMb, author = "Graeme W. Milton", title = "Analytic materials", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "472", number = "2195", pages = "20160613:1--20160613:20", day = "16", month = nov, year = "2016", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2016.0613", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "74G05 (35C05 35Q74 74A40 74E05 74Q05)", MRnumber = "3592269", MRreviewer = "Eugenia P\'erez", bibdate = "Wed Nov 23 05:46:11 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://rspa.royalsocietypublishing.org/content/472/2195/20160613", abstract = "The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer $p$. If $p$ takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank $p$. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a $ 90^\circ $ rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.", accepted = "20 October 2016", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", received = "1 August 2016", } @InCollection{Milton:2016:CAA, author = "Graeme W. Milton", title = "Composites and the associated abstract theory", crossref = "Milton:2016:ETC", chapter = "2", pages = "47--76", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:CFL, author = "Graeme W. Milton", title = "Canonical forms for linear physics equations and key identities", crossref = "Milton:2016:ETC", chapter = "1", pages = "1--46", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:DMS, author = "Graeme W. Milton", title = "The desymmetrization method for solving the {Schr{\"o}dinger} equation", crossref = "Milton:2016:ETC", chapter = "12", pages = "319--336", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2016:FPN, author = "Graeme W. Milton and Ornella Mattei", title = "Field Patterns: A New Mathematical Object", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "18", month = nov, year = "2016", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Proc. R. Soc. A 20160819", URL = "https://arxiv.org/abs/1611.06257; https://arxiv.org/abs/1611.06257v1", abstract = "Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multicomponent potential, with as many components as the number of field patterns. Presumably if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multidimensional space that one can consider them to live, or between the different field components of the multicomponent potential if one views them that way. As a result of PT-symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "31", subject = "Optics (physics.optics); Mathematical Physics (math-ph)", } @InCollection{Milton:2016:GFS, author = "Graeme W. Milton", title = "{Green}'s functions for self-adjoint and non-self-adjoint operators", crossref = "Milton:2016:ETC", chapter = "14", pages = "355--368", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:IP, author = "Graeme W. Milton", title = "The inverse problem", crossref = "Milton:2016:ETC", chapter = "5", pages = "123--148", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:NPB, author = "Graeme W. Milton", title = "A new perspective on boundary value problems", crossref = "Milton:2016:ETC", chapter = "3", pages = "77--94", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2016:PEE, author = "Graeme W. Milton and Marc Briane and Davit Harutyunyan", title = "On the possible effective elasticity tensors of $2$-dimensional and $3$-dimensional printed materials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "10", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.2140/memocs.2017.5.41", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Math. Mech. Compl. Sys. 5 (2017) 41-94", URL = "https://arxiv.org/abs/1606.03305", abstract = "The set {$ {\rm GU}_f $} of possible effective elastic tensors of composites built from two materials with elasticity tensors $ \BC_1 > 0 $ and $ \BC_2 = 0 $ comprising the set $ U = \{ \BC_1, \BC_2 \} $ and mixed in proportions $f$ and $ 1 - f$ is partly characterized. The material with tensor $ \BC_2 = 0$ corresponds to a material which is void. (For technical reasons $ \BC_2$ is actually taken to be nonzero and we take the limit $ \BC_2 \to 0$). Specifically, recalling that {$ {\rm GU}_f$} is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases. In these cases the calculation of the minimum is reduced to a finite dimensional minimization problem that can be done numerically. Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate p-mode material, that is easily compliant to $ p \leq 5$ independent applied strains, yet supports any stress in the orthogonal space. Thus the material can easily slip in certain directions along the walls. The region outside the walls contains ``complementary Avellaneda material'' which is a hierarchical laminate which", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "39", subject = "Materials Science (cond-mat.mtrl-sci); Analysis of PDEs (math.AP)", } @InCollection{Milton:2016:PFT, author = "Graeme W. Milton", title = "{Projection Functional Theory} for finding excited states", crossref = "Milton:2016:ETC", chapter = "11", pages = "309--318", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @InCollection{Milton:2016:SAS, author = "Graeme W. Milton", title = "Superfunctions and the algebra of subspace collections", crossref = "Milton:2016:ETC", chapter = "7", pages = "179--234", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2016:TCC, author = "Graeme W. Milton and Davit Harutyunyan and Marc Briane", title = "Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "12", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.2140/memocs.2017.5.95", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Math. Mech. Compl. Sys. 5 (2017) 95--113.", URL = "https://arxiv.org/abs/1606.03722", abstract = "The set {$ {\rm GU}_f $} of possible effective elastic tensors of composites built from two materials with positive definite elasticity tensors $ \BC_1 $ and $ \BC_2 = \Gd \BC_0 $ comprising the set $ U = \{ \BC_1, \Gd \BC_0 \} $ and mixed in proportions f and 1 - f is partly characterized in the limit $ \Gd \to \infty $. The material with tensor $ \BC_2 $ corresponds to a material which (for technical reasons) is almost rigid in the limit $ \Gd \to \infty $. The paper, and the underlying microgeometries, have many aspects in common with the companion paper \booktitle{On the possible effective elasticity tensors of 2-dimensional printed materials}. The chief difference is that one has a different algebraic problem to solve: determining the subspaces of stress fields for which the thin walled structures can be rigid, rather than determining, as in the companion paper, the subspaces of strain fields for which the thin walled structure is compliant. Recalling that {$ {\rm GU}_f $} is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases. In these cases the calculation of the minimum is reduced to a finite dimensional minimization problem that can be done numerically. Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate p-mode material, that is almost rigid to $ 6 - p \leq 5 $ independent applied stresses, yet is compliant to any strain in the orthogonal space. Thus the walls, by themselves, can support stress with almost no deformation. The region outside the walls contains ``Avellaneda material'' that is a hierarchical laminate which minimizes an appropriate sum of elastic energies.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "13", subject = "Materials Science (cond-mat.mtrl-sci)", } @InCollection{Milton:2016:VPC, author = "Graeme W. Milton", title = "Variational principles and {$ Q_C^* $}-convex functions for {Schr{\"o}dinger}'s equation", crossref = "Milton:2016:ETC", chapter = "13", pages = "337--354", year = "2016", bibdate = "Thu Aug 17 18:16:17 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Bardsley:2017:CGB, author = "Patrick Bardsley and Michael S. Primrose and Michael Zhao and Jonathan Boyle and Nathan Briggs and Zoe Koch and Graeme W. Milton", title = "Criteria for guaranteed breakdown in two-phase inhomogeneous bodies", journal = j-INVERSE-PROBLEMS, volume = "33", number = "8", pages = "085006", month = aug, year = "2017", CODEN = "INPEEY", DOI = "https://doi.org/10.1088/1361-6420/aa76c5", ISSN = "0266-5611 (print), 1361-6420 (electronic)", ISSN-L = "0266-5611", MRclass = "78A48", MRnumber = "3668806", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data", journal-URL = "http://iopscience.iop.org/0266-5611/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "31", } @Article{Cassier:2017:BHF, author = "Maxence Cassier and Graeme W. Milton", title = "Bounds on {Herglotz} functions and fundamental limits of broadband passive quasistatic cloaking", journal = j-J-MATH-PHYS, volume = "58", number = "7", pages = "071504", month = jul, year = "2017", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.4989990", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "81V19", MRnumber = "3671165", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "27", } @Article{Harutyunyan:2017:RBE, author = "Davit Harutyunyan and Graeme Walter Milton", title = "On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials", journal = j-ARCH-RAT-MECH-ANAL, volume = "223", number = "1", pages = "199--212", month = jan, year = "2017", CODEN = "AVRMAW", DOI = "https://doi.org/10.1007/s00205-016-1034-7", ISSN = "0003-9527 (print), 1432-0673 (electronic)", ISSN-L = "0003-9527", MRclass = "74B05", MRnumber = "3590372", MRreviewer = "Haigang Li", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Archive for Rational Mechanics and Analysis", journal-URL = "http://link.springer.com/journal/205", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Harutyunyan:2017:TCA, author = "Davit Harutyunyan and Graeme Walter Milton", title = "Towards characterization of all $ 3 \times 3 $ extremal quasiconvex quadratic forms", journal = j-COMM-PURE-APPL-MATH, volume = "70", number = "11", pages = "2164--2190", month = nov, year = "2017", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.21699", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "74H55 (49Q12)", MRnumber = "3707491", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Mattei:2017:FPB, author = "Ornella Mattei and Graeme W. Milton", title = "Field patterns without blow up", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "27", month = apr, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1088/1367-2630/aa847d", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1705.00539", abstract = "Field patterns, first proposed by the authors in [Milton, Mattei. Proc R Soc A. 2017], are orderly patterns of characteristic lines that arise in specific space-time microstructures whose geometry in one spatial dimension plus time is somehow commensurate to the slope of the characteristic lines. In particular, in [Milton, Mattei. Proc R Soc A. 2017] the authors propose two examples of space-time geometries in which field patterns occur: they are two-phase microstructures in which rectangular space-time inclusions of one material are embedded in another material. After a sufficient large period of time, the field patterns in both microstructures have local periodicity both in time and space, due to the PT-symmetry of the chosen space-time geometries. This allows one to focus only on solving the problem on a discrete network and to define a suitable transfer matrix that, given the solution at a certain time, provides the solution after one time period. Many of the eigenvalues of this transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. However, there are also modes that blow up exponentially with time coupled with modes that decrease exponentially with time. The question as to whether there are space-time microstructures such that the transfer matrix only has eigenvalues on the unit circle finds answer in this paper where we see that certain space-time checkerboards have the property that all the modes are propagating modes, within a certain range of the material parameters. Interestingly, when there is no blow-up, the waves generated by an instantaneous disturbance at a point look like shocks with a wake of oscillatory waves. This sets an arrow of time in the sense that it would be extremely difficult to produce the initial conditions necessary to create the corresponding time-reversed waves.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "20", subject = "Classical Physics (physics.class-ph); Mathematical Physics (math-ph); Optics (physics.optics)", } @Article{Mattei:2017:FPNa, author = "Ornella Mattei and Graeme W. Milton", title = "Field patterns: a new type of wave with infinitely degenerate band structure", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "6", month = jul, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1209/0295-5075/120/54003", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1707.05756", abstract = "Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional- spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) [G. W. Milton and O. Mattei, Proc. R. Soc. A 473, 20160819 (2017), O. Mattei and G. W. Milton, arXiv:1705.00539 (2017)]. Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. By applying Bloch--Floquet theory we find that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions, a basis for which are generalized functions each concentrated on a field pattern, paramaterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "8", subject = "Classical Physics (physics.class-ph)", } @Article{Mattei:2017:FPNb, author = "Ornella Mattei and Graeme W. Milton", title = "Field patterns: A new type of wave with infinitely degenerate band structure", journal = j-EUROPHYS-LETT, volume = "120", number = "5", pages = "54003:1--54003:6", year = "2017", CODEN = "EULEEJ", DOI = "https://doi.org/10.1209/0295-5075/120/54003", ISSN = "0295-5075 (print), 1286-4854 (electronic)", ISSN-L = "0295-5075", bibdate = "Thu Apr 12 10:40:56 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://stacks.iop.org/0295-5075/120/i=5/a=54003", abstract = "Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional-spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) (Milton G. W. and Mattei O., Proc. R. Soc. A, 473 (2017) 20160819; Mattei O. and Milton G. W., New J. Phys., 19 (2017) 093022). Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. In this letter, by applying Bloch--Floquet theory, we show that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions. Each generalized function is concentrated on a specific field pattern, each parameterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.", acknowledgement = ack-nhfb, fjournal = "Europhysics Letters", journal-URL = "http://iopscience.iop.org/0295-5075", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "6", } @Article{Milton:2017:AET, author = "Graeme W. Milton", title = "Approximating the effective tensor as a function of the component tensors in two-dimensional composites of two anisotropic phases", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "7", month = may, year = "2017", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1705.02633", abstract = "A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation formula is derived for the effective matrix valued conductivity as a function of the two matrix valued conductivity tensors of the phases. This approximation should converge to the exact effective conductivity function as the number of basis fields tends to infinity. Using the approximations for the relevant operators one can also directly obtain approximations, with the same geometry, for the effective tensors of coupled field problems, including elasticity, piezoelectricity, and thermoelectricity. To avoid technical complications we assume that the phase geometry is symmetric under reflection about one of the centerlines of the unit cell.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "56", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2017:BCP, author = "Graeme W. Milton", title = "Bounds on complex polarizabilities and a new perspective on scattering by a lossy inclusion", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "22", month = apr, year = "2017", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Published in Phys. Rev. B 96, 104206 (2017)", URL = "https://arxiv.org/abs/1704.06832", abstract = "Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex dielectric constant of a two-phase medium. We also describe how analogous bounds on the orientationally averaged bulk and shear polarizabilities at a given frequency can be obtained from bounds on the effective complex bulk and shear moduli of a two-phase medium obtained by Milton, Gibiansky and Berryman, using the quasistatic variational principles of Cherkaev and Gibiansky. We also show how the polarizability problem and the acoustic scattering problem can both be reformulated in an abstract setting as ``Y -problems''. In the acoustic scattering context, to avoid explicit introduction of the Sommerfeld radiation condition, we introduce auxilliary fields at infinity and an appropriate ``constitutive law'' there, which forces the Sommerfeld radiation condition to hold. As a consequence we obtain minimization variational principles for acoustic scattering that can be used to obtain bounds on the complex backwards scattering amplitude. Some explicit elementary bounds are given.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "27", subject = "Mathematical Physics (math-ph)", } @Article{Milton:2017:ERG, author = "Graeme W. Milton and Daniel Onofrei", title = "Exact relations for {Green}'s functions in linear {PDE} and boundary field equalities: a generalization of conservation laws", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "10", month = dec, year = "2017", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1712.03597", abstract = "Many physics problems have $ J(x) = L(x)E(x) + h(x) $, source $ h(x) $, fields $E$, $J$ satisfying differential constraints, symbolized by $ E \in E$, $ J \in J$ where $E$, $J$ are orthogonal spaces. If L(x) takes values in certain nonlinear manifolds $M$, and coercivity, boundedness hold, then the Green's function satisfies exact identities. We also link Green's functions of different problems. The analysis, based on the theory of exact relations for composites, does not assume microscale variations in $ L(x)$, and allows for other equations, such as for waves in lossy media. For bodies $ \Omega $, in which $ L(x) \in M$, the Dirichlet-to-Neumann map satisfies boundary field equalities. These generalize the notion of conservation laws: the constraints on the fields inside $ \Omega $ give identities satisfied by the boundary fields, and provide extra constraints on the interior fields. A consequence is this: if a matrix valued field $ Q(x)$ with $ \nabla \cdot Q = 0$ takes values in a set B (independent of x) that lies on a nonlinear manifold, we find conditions on the manifold, and on B, that with appropriate conditions on the boundary fluxes $ q(x) = n(x) \cdot Q(x)$ (where $ n(x)$ is the outwards normal to $ \partial \Omega $) force $ Q(x)$ within $ \Omega $ to take values in a subspace $D$. This forces $ q(x)$ to take values in $ n(x) \cdot D$. We find there are additional divergence free fields inside $ \Omega $ that in turn generate additional boundary field equalities. There exist partial Null-Lagrangians, functionals $ F(w, \nabla w)$ of a vector potential $w$ and its gradient, that act as null-Lagrangians when $ \nabla w$ is constrained for $ x \in \Omega $ to take values in certain sets $A$, of appropriate non-linear manifolds, and when w satisfies appropriate boundary conditions. The extension to certain non-linear minimization problems is also sketched.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "34", subject = "Analysis of PDEs (math.AP)", } @Article{Milton:2017:FPN, author = "Graeme W. Milton and Ornella Mattei", title = "Field patterns: a new mathematical object", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "473", number = "2198", pages = "20160819", month = feb, year = "2017", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2016.0819", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", MRclass = "83C10", MRnumber = "3621490", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings A", journal-URL = "http://rspa.royalsocietypublishing.org/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "26", } @Article{Milton:2017:NOP, author = "Graeme W. Milton and Mohamed Camar-Eddine", title = "Near optimal pentamodes as a tool for guiding stress while minimizing compliance in {3$D$}-printed materials: a complete solution to the weak {$G$}-closure problem for {3$D$}-printed materials", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "6", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1016/j.jmps.2018.02.003", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1712.02292", abstract = "For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fraction $f$, and with the composite being subject to an average stress, $ \sigma^0$, Gibiansky, Cherkaev, and Allaire provided a sharp lower bound $ W^f(\sigma^0)$ on the minimum compliance energy $ \sigma^0 \colon \epsilon^0$, in which $ \epsilon^0$ is the average strain. Here we show these bounds also provide sharp bounds on the possible $ (\sigma^0, \epsilon^0)$-pairs that can coexist in such composites, and thus solve the weak G-closure problem for 3d-printed materials. The materials we use to achieve the extremal $ (\sigma^0, \epsilon^0)$-pairs are denoted as near optimal pentamodes. We also consider two-phase composites containing this isotropic elasticity material and a rigid phase with the elastic material occupying a prescribed volume fraction $f$, and with the composite being subject to an average strain, $ \epsilon^0$. For such composites, Allaire and Kohn provided a sharp lower bound $ \tilde {W} f(\epsilon^0)$ on the minimum elastic energy $ \sigma^0 \colon \epsilon^0$. We show that these bounds also provide sharp bounds on the possible $ (\sigma^0, \epsilon^0)$-pairs that can coexist in such composites of the elastic and rigid phases, and thus solve the weak $G$-closure problem in this case too. The materials we use to achieve these extremal $ (\sigma^0, \epsilon^0)$-pairs are denoted as near optimal unimodes.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "20", subject = "Analysis of PDEs (math.AP)", } @Article{Milton:2017:PEE, author = "Graeme W. Milton and Marc Briane and Davit Harutyunyan", title = "On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials", journal = j-MATH-MECH-COMPLEX-SYST, volume = "5", number = "1", pages = "41--94", year = "2017", DOI = "https://doi.org/10.2140/memocs.2017.5.41", ISSN = "2325-3444 (print), 2326-7186 (electronic)", ISSN-L = "2325-3444", MRclass = "74Q20 (35Q74 74B10)", MRnumber = "3677943", MRreviewer = "Carmen Calvo-Jurado", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics and Mechanics of Complex Systems", journal-URL = "https://msp.org/memocs/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2017:SFI, author = "Graeme W. Milton", title = "The set of forces that ideal trusses, or wire webs, under tension can support", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "30", month = apr, year = "2017", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1705.00381", abstract = "The problem of determining those multiplets of forces, or sets of force multiplets, acting at a set of points, such that there exists a truss structure, or wire web, that can support these force multiplets with all the elements of the truss or wire web being under tension, is considered. The two-dimensional problem where the points are at the vertices of a convex polygon is essentially solved: each multiplet of forces must be such that the net anticlockwise torque around any vertex of the forces summed over any number of consecutive points clockwise past the vertex must be non-negative; and one can find a truss structure that supports under tension, and only supports, those force multiplets in a convex polyhedron of force multiplets that is generated by a finite number of force multiplets each satisfying the torque condition. Progress is also made on the problem where only a subset of the points are at the vertices of a convex polygon, and the other points are inside. In particular, in the case where only one point is inside, an explicit procedure is described for constructing a suitable truss, if one exists. An alternative recipe to that provided by Guevara Vasquez, Milton, and Onofrei (2011), based on earlier work of Camar Eddine and Seppecher (2003), is given for constructing a truss structure, with elements under either compression or tension, that supports an arbitrary collection of balanced forces at the vertices of a convex polygon. Finally some constraints are given on the forces that a three-dimension truss, or wire web, under tension must satisfy.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "28", subject = "Mathematical Physics (math-ph); Classical Physics (physics.class-ph)", } @Article{Milton:2017:TCC, author = "Graeme W. Milton and Davit Harutyunyan and Marc Briane", title = "Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase", journal = j-MATH-MECH-COMPLEX-SYST, volume = "5", number = "1", pages = "95--113", year = "2017", DOI = "https://doi.org/10.2140/memocs.2017.5.95", ISSN = "2325-3444 (print), 2326-7186 (electronic)", ISSN-L = "2325-3444", MRclass = "74Q20 (35Q74)", MRnumber = "3677944", bibdate = "Fri Feb 9 06:34:00 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics and Mechanics of Complex Systems", journal-URL = "https://msp.org/memocs/", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Moulinec:2017:CIM, author = "Herv{\'e} Moulinec and Pierre Suquet and Graeme W. Milton", title = "Convergence of iterative methods based on {Neumann} series for composite materials: theory and practice", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "16", month = nov, year = "2017", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1711.05880", abstract = "Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier space, and the constitutive law in real space. The methods correspond to series expansions of appropriate operators and to series expansions for the effective tensor as a function of the component moduli. It is shown that the singularity structure of this function can shed much light on the convergence properties of the iterative Fast Fourier Transform methods. We look at a model example of a square array of conducting square inclusions for which there is an exact formula for the effective conductivity (Obnosov). Theoretically some of the methods converge when the inclusions have zero or even negative conductivity. However, the numerics do not always confirm this extended range of convergence and show that accuracy is lost after relatively few iterations. There is little point in iterating beyond this. Accuracy improves when the grid size is reduced, showing that the discrepancy is linked to the discretization. Finally, it is shown that none of the three iterative schemes investigated over-performs the others for all possible microstructures and all contrasts.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "41", subject = "Numerical Analysis (math.NA)", } @Article{Milton:2018:NOP, author = "Graeme W. Milton and Mohamed Camar-Eddine", title = "Near optimal pentamodes as a tool for guiding stress while minimizing compliance in {3$D$}-printed materials: a complete solution to the weak {$G$}-closure problem for {3$D$}-printed materials", journal = j-J-MECH-PHYS-SOLIDS, volume = "114", pages = "194--208", year = "2018", CODEN = "JMPSA8", DOI = "https://doi.org/10.1016/j.jmps.2018.02.003", ISSN = "0022-5096 (print), 1873-4782 (electronic)", ISSN-L = "0022-5096", MRnumber = "3783452", bibdate = "Mon Apr 9 16:56:14 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Mechanics and Physics of Solids", journal-URL = "http://www.sciencedirect.com/science/journal/00225096", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", } @Article{Milton:2018:NRF, author = "Graeme W. Milton", title = "A new route to finding bounds on the spectrum of many physical operators", journal = "arXiv.org", volume = "??", number = "??", pages = "??--??", day = "10", month = mar, year = "2018", CODEN = "????", ISSN = "2331-8422", ISSN-L = "2331-8422", bibdate = "Thu Apr 12 10:25:06 MDT 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://arxiv.org/abs/1803.03726", abstract = "Here we obtain bounds on the spectrum of that operator whose inverse, when it exists, gives the Green's function. We consider the wide of physical problems that can be cast in a form where a constitutive equation $ J(x) = L(x)E(x) - h(x) $ with a source term $ h(x) $ holds for all $x$ in some domain $ \Omega $, and relates fields $E$ and $J$ that satisfy appropriate differential constraints, symbolized by $ E \in E_\Omega $ and $ J \in J_\Omega $ where $ E_\Omega $ and $ J_\Omega $ are orthogonal spaces that span the space $ H_\Omega $ of square-integrable fields in which $h$ lies. Boundedness and coercivity conditions on the moduli $ L(x)$ ensure there exists a unique $E$ for any given $h$, i.e., $ E = G_\Omega h$ which then establishes the existence of the Green's function $ G_\Omega $. We show that the coercivity condition is guaranteed to hold if weaker conditions, involving generalized quasiconvex functions, are satisfied. The advantage is that these weaker conditions are easier to verify, and for multiphase materials they can be independent of the geometry of the phases. For $ L(x)$ depending linearly on a vector of parameters $ z = (z_1, z_2, \ldots {}, z_n)$, we obtain constraints on $z$ that ensure the Green's function exists, and hence which provide bounds on the spectrum.", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", pagecount = "30", subject = "Mathematical Physics (math-ph)", }

%%% ==================================================================== %%% Publications about Graeme W. Milton and his works:

@Article{Berryman:2009:FDT, author = "James G. Berryman", title = "Frequency dependent thermal expansion in binary viscoelastic composites", journal = j-MECH-MATER, volume = "41", number = "4", pages = "463--480", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.013", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000106", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Berryman:2009:ISI, author = "James G. Berryman and Elena Cherkaev and Igor Sevostianov", title = "Introduction to the Special Issue in Honor of {Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science}", journal = j-MECH-MATER, volume = "41", number = "4", pages = "355--355", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2008.11.005", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S016766360800166X", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Cherkaev:2009:BEP, author = "Andrej V. Cherkaev", title = "Bounds for effective properties of multimaterial two-dimensional conducting composites", journal = j-MECH-MATER, volume = "41", number = "4", pages = "411--433", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.027", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000052", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Francfort:2009:POB, author = "Gilles A. Francfort and Fran{\c{c}}ois Murat", title = "The proofs of the optimal bounds for mixtures of two anisotropic conducting materials in two dimensions", journal = j-MECH-MATER, volume = "41", number = "4", pages = "448--455", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.020", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000039", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Grabovsky:2009:AGT, author = "Yury Grabovsky", title = "An application of the general theory of exact relations to fiber-reinforced conducting composites with {Hall} effect", journal = j-MECH-MATER, volume = "41", number = "4", pages = "456--462", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.012", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000064", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Jasiuk:2009:SIE, author = "Iwona Jasiuk", title = "Stress invariance and exact relations in the mechanics of composite materials: Extensions of the {CLM} result: a review", journal = j-MECH-MATER, volume = "41", number = "4", pages = "394--404", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.001", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S016766360900009X", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Kang:2009:CPS, author = "Hyeonbae Kang", title = "Conjectures of {P{\'o}lya--Szeg{\H{o}}} and {Eshelby}, and the {Newtonian} potential problem: A review", journal = j-MECH-MATER, volume = "41", number = "4", pages = "405--410", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.019", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000131", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Lopez-Pamies:2009:MEH, author = "O. Lopez-Pamies and P. {Ponte Casta{\~n}eda}", title = "Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability", journal = j-MECH-MATER, volume = "41", number = "4", pages = "364--374", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.006", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000040", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{McPhedran:2009:PCB, author = "R. C. McPhedran and A. B. Movchan and N. V. Movchan", title = "Platonic crystals: Bloch bands, neutrality and defects", journal = j-MECH-MATER, volume = "41", number = "4", pages = "356--363", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.005", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000027", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Sevostianov:2009:ECC, author = "Igor Sevostianov and Mark Kachanov", title = "Elasticity-conductivity connections for contacting rough surfaces: An overview", journal = j-MECH-MATER, volume = "41", number = "4", pages = "375--384", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.002", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000076", acknowledgement = ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Smyshlyaev:2009:PLE, author = "Valery P. Smyshlyaev", title = "Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization", journal = j-MECH-MATER, volume = "41", number = "4", pages = "434--447", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.009", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Mon May 30 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000088", acknowledgement = ack-gwm, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Article{Willis:2009:EER, author = "John R. Willis", title = "Exact effective relations for dynamics of a laminated body", journal = j-MECH-MATER, volume = "41", number = "4", pages = "385--393", month = apr, year = "2009", CODEN = "MSMSD3", DOI = "https://doi.org/10.1016/j.mechmat.2009.01.010", ISSN = "0167-6636 (print), 1872-7743 (electronic)", ISSN-L = "0167-6636", bibdate = "Thu Nov 26 08:41:39 2015", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.sciencedirect.com/science/journal/01676636/41/4", note = "Special Issue in Honor of Graeme W. Milton, 2007 Winner of the William Prager Medal of the Society of Engineering Science.", URL = "http://www.sciencedirect.com/science/article/pii/S0167663609000118", acknowledgement = ack-gwm # " and " # ack-nhfb, fjournal = "Mechanics of Materials: an International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01676636", } @Misc{Anonymous:2016:GWM, author = "Anonymous", title = "{Graeme W. Milton}", howpublished = "Press release by the Scientific Committee of the International Research Center MEMOCS", pages = "2", day = "25", month = may, year = "2016", bibdate = "Wed Jul 06 09:52:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Announcement of the award of the 2015 International Tullio Levi-Civit{\`a} Prize.", URL = "http://memocs.univaq.it/wp-content/uploads/2016/05/MiltonLaudatio.pdf", acknowledgement = ack-nhfb, } @Misc{Anonymous:2016:NMT, author = "Anonymous", title = "New math tools for new materials", howpublished = "Press releases.", day = "21", month = nov, year = "2016", bibdate = "Wed Nov 23 05:43:50 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "https://www.eurekalert.org/pub_releases/2016-11/uou-nmt112116.php", abstract = "University of Utah mathematician Graeme Milton presents a new tool for understanding how energy waves move through complex materials, opening up possibilities to design materials that absorb or bend energy as desired. His solution for so-called ``analytic materials'' was published November 15 in Proceedings of the Royal Society A.", acknowledgement = ack-nhfb, } @Misc{Anonymous:2016:TCR, author = "Anonymous", title = "Theoretical climbing rope could brake falls: Now mathematicians need material to make it a reality", howpublished = "University of Utah Web site.", day = "6", month = jul, year = "2016", bibdate = "Wed Jul 06 09:49:05 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "Describes work published in \cite{Harutyunyan:2016:IDCb}", URL = "unews.utah.edu/theoretical-climbing-rope-could-brake-falls/Boyee", acknowledgement = ack-nhfb, keywords = "David Harutyunyan; Graeme W. Milton; Justin Boyer; Trevor J. Dick", } @Article{Miller:2017:SMF, author = "Johanna L. Miller", title = "Semiconductor metamaterial fools the {Hall} effect", journal = j-PHYS-TODAY, volume = "70", number = "2", pages = "21--23", month = feb, year = "2017", CODEN = "PHTOAD", DOI = "https://doi.org/10.1063/pt.3.3453", ISSN = "0031-9228 (print), 1945-0699 (electronic)", ISSN-L = "0031-9228", bibdate = "Mon Jul 31 17:15:13 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", note = "The journal issue cover image is based on work by Graeme Milton and colleagues.", URL = "http://physicstoday.scitation.org/na101/home/literatum/publisher/aip/journals/content/pto/2017/pto.2017.70.issue-2/pto.2017.70.issue-2/20170202/pto.2017.70.issue-2.cover.jpg", acknowledgement = ack-nhfb, fjournal = "Physics Today", journal-URL = "http://www.physicstoday.org/", remark = "This article describes work by Graeme Milton and colleagues on a 3D materials design that contradicts standard textbook discussions of the Hall effect. Such a material has now been manufactured in a laboratory, and is pictured in the article.", } @Article{Sharma:2017:BRE, author = "Pradeep Sharma", title = "Book Review: {{\booktitle{Extending the Theory of Composites to Other Areas of Science}}, edited by Graeme W. Milton}", journal = j-J-APPL-MECH, volume = "84", number = "3", pages = "036501--1", day = "25", month = jan, year = "2017", CODEN = "JAMCAV", DOI = "https://doi.org/10.1115/1.4035525", ISSN = "0021-8936 (print), 1528-9036 (electronic)", bibdate = "Mon Jun 04 09:33:11 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib", URL = "http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=2594947", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Mechanics", journal-URL = "http://appliedmechanics.asmedigitalcollection.asme.org/issues.aspx", pagecount = "1", papernumber = "JAM-16-1598", } @Article{Grabovsky:2018:BRE, author = "Yury Grabovsky", title = "Book Review: {{\booktitle{Extending the Theory of Composites to Other Areas of Science}}, edited and authored by Graeme W. Milton}", journal = j-SIAM-REVIEW, volume = "60", number = "2", pages = "475--481", month = "????", year = "2018", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/18N97456X", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Mon Jun 4 09:14:47 MDT 2018", bibsource = "http://epubs.siam.org/toc/siread/60/2; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 2018", }

%%% ==================================================================== %%% Cross-referenced entries and conference proceedings must come last. %%% They are sorted in publication order with ``bibsort --byyear''.

@Book{Milton:2002:TC, author = "Graeme W. Milton", booktitle = "The Theory of Composites", title = "The Theory of Composites", volume = "6", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xxviii + 719", year = "2002", DOI = "https://doi.org/10.1017/CBO9780511613357", ISBN = "0-521-78125-6", ISBN-13 = "978-0-521-78125-1", LCCN = "TA418.9.C6 M58 2001", MRclass = "74Qxx (74A40 74E30 74Pxx 78A48 82B99 82D20)", MRnumber = "1899805 (2003d:74077)", MRreviewer = "Gr{\'e}goire Allaire", bibdate = "Sat May 04 06:33:55 2002", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib", note = "Series editors: P. G. Ciarlet, A. Iserles, Robert V. Kohn, and M. H. Wright.", price = "US\$80", series = "Cambridge Monographs on Applied and Computational Mathematics", URL = "http://www.math.utah.edu/books/tcbook", acknowledgement = ack-gwm # " and " # ack-nhfb, keywords = "composite materials; differential equations, partial; homogenization (differential equations)", ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "NHFB was the chief technical editor for this book, and wrote the author/editor indexing software, the {\TeX} DVI-to-PostScript driver and the initial Web site for the book, at \path=http://www.math.utah.edu/books/tcbook/index.html=.", tableofcontents = "1. Introduction \\ 2. Some equations of interest and numerical approaches to solving them \\ 3. Duality transformations in two-dimensional media \\ 4. Translations and equivalent media \\ 5. Some microstructure-independent exact relations \\ 6. Exact relations for coupled equations \\ 7. Assemblages of spheres, ellipsoids, and other neutral inclusions \\ 8. Tricks for generating other exactly solvable microgeometries \\ 9. Laminate materials \\ 10. Approximations and asymptotic formulas \\ 11. Wave propagation in the quasistatic limit \\ 12. Reformulating the problem of finding effective tensors \\ 13. Variational principles and inequalities \\ 14. Series expansions for the fields and effective tensors \\ 15. Correlation functions and how they enter series expansions \\ 16. Other perturbation solutions \\ 17. General theory of exact relations and links between effective tensors \\ 18 Analytic properties \\ 19. Y -tensors \\ 20. Y -tensors and effective tensors in electrical circuits \\ 21. Bounds on the properties of composites \\ 22. Classical variational principle bounds \\ 23. Bounds from the Hashin--Shtrikman variational inequalities \\ 24. Bounds using the compensated compactness or translation method \\ 25. Choosing the translations and finding microgeometries that attain the bounds \\ 26. Bounds incorporating three-point correlation functions \\ 27. Bounds using the analytic method \\ 28. Fractional linear transformations as a tool for generating bounds \\ 29. Field equation recursion method \\ 30. Properties of the G-closure and extremal families of composites \\ 31. Bounding of effective moduli as a quasiconvexification problem", } @Proceedings{Milton:2003:PSI, editor = "Graeme W. Milton and K. M. Golden and D. Dobson and Z. V. Vardeny", booktitle = "Proceedings of the {Sixth International Conference on Electrical Transport and Optical Properties of Inhomogeneous Media: ETOPIM 6, held in Snowbird, UT, USA, 15--19 July 2002}", title = "Proceedings of the {Sixth International Conference on Electrical Transport and Optical Properties of Inhomogeneous Media: ETOPIM 6, held in Snowbird, UT, USA, 15--19 July 2002}", volume = "338(1--4)", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xiii + 374", year = "2003", ISBN = "", ISBN-13 = "", ISSN = "0921-4526 (print), 1873-2135 (electronic)", LCCN = "", bibdate = "Sat Jul 03 12:05:44 2004", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib", series = "Physica B, Condensed Matter", URL = "http://www.elseview.com/locate/physb; http://www.math.utah.edu/etopim/", acknowledgement = ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", remark = "Technical editing by Nelson H. F. Beebe and Eleen Collins. No ISBN assigned: this is a combined journal issue.", xxnote = "Book cover page has incorrect A. Z. Vardeny instead of V. Z. Vardeny.", } @Book{Milton:2016:ETC, editor = "Graeme W. Milton", booktitle = "Extending the Theory of Composites to Other Areas of Science", title = "Extending the Theory of Composites to Other Areas of Science", publisher = "Milton--Patton Publishers", address = "P.O. Box 581077, Salt Lake City, UT 85148, USA", pages = "xx + 422", year = "2016", ISBN = "1-4835-6919-5 (print), 1-4835-6920-9 (e-book)", ISBN-13 = "978-1-4835-6919-2 (print), 978-1-4835-6920-8 (e-book)", LCCN = "????", bibdate = "Wed Jul 06 09:36:32 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib", URL = "http://www.math.utah.edu/books/milton", acknowledgement = ack-gwm # " and " # ack-nhfb, ORCID-numbers = "Graeme Milton/0000-0002-4000-3375", tableofcontents = "1: Canonical forms for linear physics equations and key identities / Graeme W. Milton / 1 \\ 2: Composites and the associated abstract theory / Graeme W. Milton / 47 \\ 3: A new perspective on boundary value problems / Graeme W. Milton / 77 \\ 4: Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations / Maxence Cassier, Aaron Welters and Graeme W. Milton / 95 \\ 5: The inverse problem / Graeme W. Milton / 123 \\ 6: Bounds for the transient response of viscoelastic composites / Ornella Mattei and Graeme W. Milton / 149 \\ 7: Superfunctions and the algebra of subspace collections / Graeme W. Milton / 179 \\ 8: Accelerating FFT methods for conducting composites / Graeme W. Milton / 235 \\ 9: The response of systems with coupled fields / Mordehai Milgrom and Graeme W. Milton / 255 \\ 10: A rigorous approach to the field recursion method / Maxence Cassier, Aaron Welters and Graeme W. Milton / 287 \\ 11: Projection Functional Theory for finding excited states / Graeme W. Milton / 309 \\ 12: The desymmetrization method for solving the Schr{\"o}dinger equation / Graeme W. Milton / 319 \\ 13: Variational principles and $Q_C^*$-convex functions for Schr{\"o}dinger's equation / Graeme W. Milton / 337 \\ 14: Green's functions for self-adjoint and non-self-adjoint operators / Graeme W. Milton / 355 \\ Bibliography / / 369 \\ Author/editor index / / 401 \\ Index / / 413", }

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