@Preamble{
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@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/|"}
@String{inst-CORNELL = "Cornell University"}
@String{inst-CORNELL:adr = "Ithaca, New York."}
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@String{j-EUROPHYS-LETT = "Europhysics Letters"}
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in Engineering"}
@String{j-INVERSE-PROBLEMS = "Inverse Problems"}
@String{j-J-APPL-MECH = "Journal of Applied Mechanics"}
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Applications"}
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Solids"}
@String{j-J-PHYS-D = "Journal of Physics D: Applied Physics"}
@String{j-J-REINF-PLAST-COMPOS = "Journal of Reinforced Plastics and
Composites"}
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= Modelisation math{\'e}matique et
analyse num{\'e}rique: $M^2AN$"}
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Edinburgh"}
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Physical Sciences"}
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Mathematical and physical sciences"}
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Engineering Sciences"}
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@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"}
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@String{j-WAVE-MOTION = "Wave Motion"}
@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"}
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@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"}
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@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."}
@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,
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@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{\'e}rez",
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",
MRreviewer = "Alexander G. Kolpakov",
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",
MRreviewer = "Heng Wang",
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",
MRreviewer = "Martin Fuchs",
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",
MRreviewer = "Leonard Constantin Kreutz",
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{Kern:2018:THE,
author = "Christian Kern and Graeme W. Milton and Muamer Kadic
and Martin Wegener",
title = "Theory of the {Hall} effect in three-dimensional
metamaterials",
journal = j-NEW-J-PHYS,
volume = "20",
number = "8",
pages = "083034",
month = aug,
year = "2018",
CODEN = "NJOPFM",
DOI = "https://doi.org/10.1088/1367-2630/aad92b",
ISSN = "1367-2630",
bibdate = "Fri Oct 25 07:31:51 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "New Journal of Physics",
journal-URL = "http://iopscience.iop.org/1367-2630",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Milton:2018: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 = j-SIAM-J-MATH-ANA,
volume = "50",
number = "3",
pages = "3327--3364",
month = "????",
year = "2018",
CODEN = "SJMAAH",
DOI = "https://doi.org/10.1137/17M1130356",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "35J57 (35A35 35B10 35Q74 74Qxx 78A15)",
MRnumber = "3817761",
MRreviewer = "Jari Taskinen",
bibdate = "Wed Oct 9 18:57:19 MDT 2019",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/50/3;
http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmathana2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
onlinedate = "January 2018",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Milton:2018:ALR,
author = "Graeme W. Milton and Ross C. McPhedran",
title = "Anomalous localized resonance and associated
cloaking",
journal = j-SIAM-NEWS,
volume = "51",
number = "6",
pages = "6, 8",
year = "2018",
ISSN = "1557-9573",
MRclass = "74M05 (78A45)",
MRnumber = "3821771",
bibdate = "Fri Oct 25 07:37:56 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@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",
MRclass = "74A05 (74P05)",
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:NRFa,
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)",
}
@Article{Milton:2018:NRFb,
author = "Graeme W. Milton",
title = "A new route to finding bounds on the generalized
spectrum of many physical operators",
journal = j-J-MATH-PHYS,
volume = "59",
number = "6",
pages = "061508, 23",
year = "2018",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.5032204",
ISSN = "0022-2488",
ISSN-L = "0022-2488",
MRclass = "47A10 (81Q10 81Q12)",
MRnumber = "3819079",
bibdate = "Fri Oct 25 07:39:24 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Milton:2018:SC,
author = "G. W. Milton",
title = "Stiff competition",
journal = j-NATURE,
volume = "564",
number = "7734",
pages = "E1--E1",
month = dec,
year = "2018",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/s41586-018-0724-8",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Fri Oct 25 07:20:18 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Moulinec:2018: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 = j-INT-J-NUMER-METHODS-ENG,
volume = "114",
number = "10",
pages = "1103--1130",
year = "2018",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.5777",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
MRclass = "74E30 (65R20 65T50)",
MRnumber = "3803534",
bibdate = "Fri Oct 25 07:40:15 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
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{Kadic:2019:M,
author = "Muamer Kadic and Graeme W. Milton and Martin van Hecke
and Martin Wegener",
title = "{$3$D} metamaterials",
journal = j-NATURE-REV-PHYS,
volume = "1",
number = "3",
pages = "198--210",
month = jan,
year = "2019",
DOI = "https://doi.org/10.1038/s42254-018-0018-y",
ISSN = "2522-5820",
bibdate = "Fri Oct 25 07:21:32 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature Reviews Physics",
journal-URL = "https://www.nature.com/natrevphys/archive",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Milton:2019: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 = j-RES-MATH-SCI,
volume = "6",
number = "2",
pages = "Paper No. 19, 36",
year = "2019",
DOI = "https://doi.org/10.1007/s40687-019-0179-z",
ISSN = "2522-0144 (print), 2197-9847 (electronic)",
MRclass = "35J08 (35A30 35J25 35R30 65N21)",
MRnumber = "3911801",
bibdate = "Fri Oct 25 07:41:12 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "Research in the Mathematical Sciences",
journal-URL = "https://www.springer.com/journal/40687",
keywords = "Boundary field equalities; Exact relations; Green s
functions; Inhomogeneous media; Inverse problems",
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@Article{Lim:2020:IGS,
author = "Mikyoung Lim and Graeme W. Milton",
title = "Inclusions of General Shapes Having Constant Field
Inside the Core and Nonelliptical Neutral Coated
Inclusions With Anisotropic Conductivity",
journal = j-SIAM-J-APPL-MATH,
volume = "80",
number = "3",
pages = "1420--1440",
month = "????",
year = "2020",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/19M1246225",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Fri Mar 12 09:25:34 MST 2021",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/smjmap/80/3;
http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath2020.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
onlinedate = "January 2020",
}
@Article{Milton:2020:PED,
author = "Graeme W. Milton",
title = "A possible explanation of dark matter and dark energy
involving a vector torsion field",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--14",
day = "25",
month = mar,
year = "2020",
bibdate = "Mon Apr 13 11:29:12 2020",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
URL = "https://arxiv.org/abs/2003.11587",
abstract = "A simple gravitational model with torsion is studied,
and it is suggested that it could explain the dark
matter and dark energy in the universe. It can be
reinterpreted as a model using the Einstein
gravitational equations where space--time has regions
filled with a perfect fluid with negative energy
(pressure) and positive mass density, other regions
containing an anisotropic substance that in the rest
frame (where the momentum is zero) has negative mass
density and a uniaxial stress tensor, and possibly
other ``luminal'' regions where there is no rest frame.
It is suggested that the torsion vector field is
inhomogeneous throughout space--time, and possibly
turbulent.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Graeme Milton/0000-0002-4000-3375",
}
@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",
}
@Article{Bouchitte:2019:FCW,
author = "Guy Bouchitt{\'e} and Ornella Mattei and Graeme W.
Milton and Pierre Seppecher",
title = "On the forces that cable webs under tension can
support and how to design cable webs to channel
stresses",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
volume = "475",
number = "2223",
pages = "20180781",
day = "6",
month = mar,
year = "2019",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.2018.0781",
ISSN = "1364-5021 (print), 1471-2946 (electronic)",
ISSN-L = "1364-5021",
MRclass = "74K05 (74A10)",
MRnumber = "3942026",
bibdate = "Fri Oct 18 15:58:52 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/milton-graeme-w.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society A: Mathematical,
Physical, and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@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",
}
