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## Milton, Graeme Walter

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 Author ID: milton.graeme-walter Published as: Milton, G. W.; Milton, Graeme; Milton, Graeme W.; Milton, Graeme Walter External Links: MGP · Wikidata · GND
 Documents Indexed: 105 Publications since 1982, including 3 Books
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#### Co-Authors

 20 single-authored 11 Briane, Marc 11 Kang, Hyeonbae 6 Harutyunyan, Davit 6 Onofrei, Daniel 5 Lee, Hyundae 4 Ammari, Habib M. 4 Guevara Vasquez, Fernando 4 Movchan, Alexander B. 4 Seppecher, Pierre 3 Benveniste, Yakov 3 Ciraolo, Giulio 3 Grabovsky, Yury 3 Kohn, Robert Vita 3 Nesi, Vincenzo 3 Phan-Thien, Nhan 3 Serkov, Sergey K. 3 Thaler, Andrew E. 2 Berryman, James G. 2 Bouchitté, Guy 2 Camar-Eddine, Mohamed 2 Clark, Karen E. 2 Gibiansky, Leonid V. 2 Golden, Kenneth M. 2 Kim, Eunjoo 2 Mattei, Ornella 2 Nicorovici, Nicolae-Alexandru P. 2 Willis, John Raymond 1 Alali, Bacim 1 Avellaneda, Marco 1 Bardsley, Patrick 1 Boyle, Jonathan W. 1 Briggs, Nathan 1 Capdeboscq, Yves 1 Cassier, Maxence 1 Cherkaev, Andrej V. 1 Craster, Richard V. 1 Francfort, Gilles A. 1 Funchess, Gregory 1 Grimmett, Geoffrey R. 1 Helsing, Johan 1 James, Richard D. 1 Kim, Kyoungsun 1 Koch, Zoe 1 Kochmann, Dennis M. 1 Li, Xiaofei 1 Lim, Mikyoung 1 Lukkassen, Dag 1 Lurie, Konstantin A. 1 Manceau, David 1 McPhedran, Ross C. 1 Meklachi, Taoufik 1 Podolskiy, Viktor A. 1 Primrose, Michael S. 1 Sage, Daniel S. 1 Sen, Pabitra N. 1 Smereka, Peter 1 Sølna, Knut 1 Treibergs, Andrejs E. 1 Vinogradov, V. N. 1 Vinogradov, Viatcheslav 1 Wang, Jenn-Nan 1 Zhao, Michael 1 Zribi, Habib
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#### Serials

 14 Journal of the Mechanics and Physics of Solids 10 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 9 SIAM Journal on Applied Mathematics 7 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 6 Archive for Rational Mechanics and Analysis 6 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Physics 4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Communications in Mathematical Physics 2 Inverse Problems 2 Quarterly of Applied Mathematics 2 Journal of Elasticity 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Multiscale Modeling & Simulation 2 Mathematics and Mechanics of Complex Systems 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Wave Motion 1 International Journal for Numerical Methods in Engineering 1 Asymptotic Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Methods and Applications of Analysis 1 Documenta Mathematica 1 European Journal of Mechanics. A. Solids 1 Physical Review Letters 1 SIAM Journal on Applied Dynamical Systems 1 Communications in Mathematical Sciences 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 The IMA Volumes in Mathematics and its Applications 1 Cambridge Monographs on Applied and Computational Mathematics 1 Networks and Heterogeneous Media 1 Analysis and Mathematical Physics 1 Research in the Mathematical Sciences 1 Proceedings A. Royal Society of London
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#### Fields

 67 Mechanics of deformable solids (74-XX) 38 Partial differential equations (35-XX) 24 Optics, electromagnetic theory (78-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Functions of a complex variable (30-XX) 3 Numerical analysis (65-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Sequences, series, summability (40-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)

#### Citations contained in zbMATH Open

95 Publications have been cited 1,477 times in 868 Documents Cited by Year
The theory of composites. Zbl 0993.74002
Milton, Graeme W.
2002
On the cloaking effects associated with anomalous localized resonance. Zbl 1149.00310
Milton, Graeme W.; Nicorovici, Nicolae-Alexandru P.
2006
Modelling the properties of composites by laminates. Zbl 0631.73011
Milton, G. W.
1986
Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking due to anomalous localized resonance. Zbl 1282.78004
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2013
Variational bounds on the effective moduli of anisotropic composites. Zbl 0672.73012
Milton, Graeme W.; Kohn, Robert V.
1988
On characterizing the set of possible effective tensors of composites: The variational method and the translation method. Zbl 0751.73041
Milton, Graeme W.
1990
On modifications of Newton’s second law and linear continuum elastodynamics. Zbl 1347.74080
Milton, Graeme W.; Willis, John R.
2007
New bounds on effective elastic moduli of two-component materials. Zbl 0497.73016
Milton, G. W.; Phan-Thien, N.
1982
A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance. Zbl 1255.78002
Milton, Graeme W.; Nicorovici, Nicolae-Alexandru P.; McPhedran, Ross C.; Podolskiy, Viktor A.
2005
Solutions to the Pólya-Szegö conjecture and the weak Eshelby conjecture. Zbl 1134.74013
Kang, Hyeonbae; Milton, Graeme W.
2008
Bounds on the elastic and transport properties of two-component composites. Zbl 0486.73063
Milton, G. W.
1982
Anomalous localized resonance using a folded geometry in three dimensions. Zbl 1348.78006
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2013
Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by aomalous localized resonance. II. Zbl 1330.35421
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2014
Composite materials with Poisson’s ratios close to -1. Zbl 0780.73047
Milton, Graeme W.
1992
Neutral coated inclusions in conductivity and anti-plane elasticity. Zbl 1090.74558
Milton, Graeme W.; Serkov, Sergey K.
2001
Inclusion pairs satisfying Eshelby’s uniformity property. Zbl 1159.74387
Kang, Hyeonbae; Kim, Eunjoo; Milton, Graeme W.
2008
Optimal bounds on the effective bulk modulus of polycrystals. Zbl 0702.73078
Avellaneda, Marco; Milton, Graeme W.
1989
Active exterior cloaking for the 2D Laplace and Helmholtz Equations. Zbl 1254.78031
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2009
An accelerated FFT algorithm for thermoelastic and nonlinear composites. Zbl 1195.74302
2008
On bounding the effective conductivity of anisotropic composites. Zbl 0631.73012
Kohn, Robert V.; Milton, Graeme W.
1986
New bounds on the effective thermal conductivity of N-phase materials. Zbl 0503.73004
Phan-Thien, N.; Milton, G. W.
1982
Invariant properties of the stress in plane elasticity and equivalence classes of composites. Zbl 0791.73011
Cherkaev, Andrei V.; Lurie, Konstantin A.; Milton, Graeme W.
1992
New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages. Zbl 1077.74591
Benveniste, Y.; Milton, G. W.
2003
Bounding the current in nonlinear conducting composites. Zbl 0991.78019
Milton, Graeme W.; Serkov, Sergey K.
2000
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases. Zbl 1328.74075
Kochmann, Dennis M.; Milton, Graeme W.
2014
On the effective viscoelastic moduli of two-phase media. I: Rigorous bounds on the complex bulk modulus. Zbl 0816.73037
Gibiansky, L. V.; Milton, G. W.
1993
Polycrystalline configurations that maximize electrical resistivity. Zbl 0734.73068
Nesi, Vincenzo; Milton, Graeme W.
1991
Multicomponent composites, electrical networks and new types of continued fraction. I. Zbl 0624.41017
Milton, G. W.
1987
Progress on the strong Eshelby’s conjecture and extremal structures for the elastic moment tensor. Zbl 1262.74018
Ammari, Habib; Capdeboscq, Yves; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.; Zribi, Habib
2010
Change of sign of the corrector’s determinant for homogenization in three-dimensional conductivity. Zbl 1118.78009
Briane, Marc; Milton, Graeme W.; Nesi, Vincenzo
2004
Exact relations for effective tensors of composites: necessary conditions and sufficient conditions. Zbl 1041.74057
Grabovsky, Yury; Milton, Graeme W.; Sage, Daniel S.
2000
On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials. Zbl 1368.74053
Milton, Graeme; Briane, Marc; Harutyunyan, Davit
2017
Exterior cloaking with active sources in two-dimensional acoustics. Zbl 1283.76065
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2011
Proof of a conjecture on the conductivity of checkerboards. Zbl 1063.82018
Milton, Graeme W.
2001
On the effective viscoelastic moduli of two-phase media. III: Rigorous bounds on the complex shear modulus in two dimensions. Zbl 0946.74049
Gibiansky, Leonid V.; Milton, Graeme W.; Berryman, James G.
1999
Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites. Zbl 0823.73043
Clark, Karen E.; Milton, Graeme W.
1995
Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method. Zbl 1252.35281
Kang, Hyeonbae; Kim, Eunjoo; Milton, Graeme W.
2012
On the effective viscoelastic moduli of two-phase media. II: Rigorous bounds on the complex shear modulus in three dimensions. Zbl 0934.74061
Milton, G. W.; Berryman, J. G.
1997
Duality relations, correspondences and numerical results for planar elastic composites. Zbl 0969.74567
Helsing, J.; Milton, G. W.; Movchan, A. B.
1997
Sets of conductivity and elasticity tensors stable under lamination. Zbl 0797.73032
Francfort, Gilles A.; Milton, Graeme W.
1994
Multicomponent composites, electrical networks and new types of continued fraction. II. Zbl 0624.41018
Milton, G. W.
1987
High-frequency homogenization for travelling waves in periodic media. Zbl 1371.35005
Harutyunyan, Davit; Milton, Graeme W.; Craster, Richard V.
2016
Bounds on the volume fractions of two materials in a three-dimensional body from boundary measurements by the translation method. Zbl 1277.78026
Kang, Hyeonbae; Milton, Graeme W.
2013
Modelling the effective conductivity function of an arbitrary two- dimensional polycrystal using sequential laminates. Zbl 0807.46091
Clark, Karen E.; Milton, Graeme W.
1994
Representations for the conductivity functions of multicomponent composites. Zbl 0715.35075
Milton, G. W.; Golden, K.
1990
Towards characterization of all $$3 \times 3$$ extremal quasiconvex quadratic forms. Zbl 06802190
Harutyunyan, Davit; Milton, Graeme Walter
2017
Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity. Zbl 1371.49010
Milton, Graeme W.
2013
The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. I: The self-consistent scheme in matrix-based composites. Zbl 1244.74009
Benveniste, Yakov; Milton, Graeme W.
2010
Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient. Zbl 1170.74019
Briane, Marc; Milton, Graeme W.
2009
Addendum to ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’. Zbl 1371.49011
Milton, Graeme W.
2015
Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex. Zbl 1329.26024
Harutyunyan, Davit; Milton, Graeme Walter
2015
The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. II: The generalized self-consistent scheme in matrix-based composites. Zbl 1244.74010
Benveniste, Yakov; Milton, Graeme W.
2010
Minimization variational principles for acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. Zbl 1186.74044
Milton, Graeme W.; Seppecher, Pierre; Bouchitté, Guy
2009
Homogenization of the two-dimensional Hall effect. Zbl 1206.78090
Briane, M.; Manceau, D.; Milton, G. W.
2008
On conjectures of Polya-Szegö and Eshelby. Zbl 1111.35119
Kang, Hyeonbae; Milton, Graeme W.
2006
Realizable (average stress, average strain) pairs in a plate with holes. Zbl 1048.74034
Milton, G. W.; Serkov, S. K.; Movchan, A. B.
2003
Optimal $$G$$-closure bounds via stability under lamination. Zbl 0941.74012
Milton, G. W.; Nesi, V.
1999
A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media. Zbl 0833.73044
Milton, G. W.; Movchan, A. B.
1995
A brief review of the translation method for bounding effective elastic tensors of composites. Zbl 0737.73019
Milton, G. W.
1990
New third-order bounds on the effective moduli of N-phase composites. Zbl 0513.73004
Phan-Thien, N.; Milton, G. W.
1983
Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking. Zbl 1375.30046
Cassier, Maxence; Milton, Graeme W.
2017
Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase. Zbl 1368.74054
Milton, Graeme; Harutyunyan, Davit; Briane, Marc
2017
On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials. Zbl 1365.35176
Harutyunyan, Davit; Milton, Graeme Walter
2017
Bounds on the volume of an inclusion in a body from a complex conductivity measurement. Zbl 1321.35221
Thaler, Andrew E.; Milton, Graeme W.
2015
Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity. Zbl 1311.65135
Kang, Hyeonbae; Kim, Kyoungsun; Lee, Hyundae; Li, Xiaofei; Milton, Graeme W.
2014
Which electric fields are realizable in conducting materials? Zbl 1315.35021
Briane, Marc; Milton, Graeme W.; Treibergs, Andrejs
2014
Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime. Zbl 1254.31001
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2012
Complete characterization and synthesis of the response function of elastodynamic networks. Zbl 1273.74144
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2011
Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type. Zbl 1211.74180
Milton, Graeme W.; Willis, John R.
2010
Giant Hall effect in composites. Zbl 1181.35016
Briane, Marc; Milton, Graeme W.
2009
Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency. Zbl 1135.94341
Milton, Graeme W.; Seppecher, Pierre
2008
The total creep of viscoelastic composites under hydrostatic or antiplane loading. Zbl 1120.74733
2005
On hierarchical structures and reiterated homogenization. Zbl 1021.35011
Lukkassen, Dag; Milton, Graeme W.
2002
Rank one plus a null-Lagrangian is an inherited property of two-dimensional compliance tensors under homogenisation. Zbl 0917.73046
Grabovsky, Yury; Milton, Graeme W.
1998
A link between sets of tensors stable under lamination and quasiconvexity. Zbl 0821.73008
Milton, Graeme W.
1994
The field equation recursion method. Zbl 0739.73002
Milton, Graeme W.
1991
Criteria for guaranteed breakdown in two-phase inhomogeneous bodies. Zbl 1434.78018
Bardsley, Patrick; Primrose, Michael S.; Zhao, Michael; Boyle, Jonathan; Briggs, Nathan; Koch, Zoe; Milton, Graeme W.
2017
Sensitivity of anomalous localized resonance phenomena with respect to dissipation. Zbl 1341.35156
Meklachi, Taoufik; Milton, Graeme W.; Onofrei, Daniel; Thaler, Andrew E.; Funchess, Gregory
2016
Bounds on the volume fraction of the two-phase shallow shell using one measurement. Zbl 1455.74061
Kang, Hyeonbae; Milton, Graeme W.; Wang, Jenn-Nan
2014
Effective conductivities of thin-interphase composites. Zbl 1451.74027
Alali, Bacim; Milton, Graeme W.
2013
Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements. Zbl 1244.74050
Milton, Graeme W.
2012
Non-local interactions in the homogenization closure of thermoelectric functionals. Zbl 1071.35013
Camar-Eddine, M.; Milton, G. W.
2005
Bubbly flow and its relation to conduction in composites. Zbl 0729.76595
Smereka, Peter; Milton, Graeme W.
1991
Inclusions of general shapes having constant field inside the core and nonelliptical neutral coated inclusions with anisotropic conductivity. Zbl 1447.35318
Lim, Mikyoung; Milton, Graeme W.
2020
On the forces that cable webs under tension can support and how to design cable webs to channel stresses. Zbl 1427.74078
Bouchitté, Guy; Mattei, Ornella; Milton, Graeme W.; Seppecher, Pierre
2019
A new route to finding bounds on the generalized spectrum of many physical operators. Zbl 1395.35079
Milton, Graeme W.
2018
Approximating the effective tensor as a function of the component tensors in two-dimensional composites of two anisotropic phases. Zbl 1393.35012
Milton, Graeme W.
2018
Isotropic realizability of current fields in $$\mathbb{R}^3$$. Zbl 1317.35003
Briane, M.; Milton, G. W.
2015
Exact determination of the volume of an inclusion in a body having constant shear modulus. Zbl 1308.74027
Thaler, Andrew E.; Milton, Graeme W.
2014
Electromagnetic circuits. Zbl 1259.35192
Milton, Graeme W.; Seppecher, Pierre
2010
New bounds on strong field magneto-transport in multiphase columnar composites. Zbl 1230.35013
Briane, Marc; Milton, Graeme W.
2010
An antisymmetric effective Hall matrix. Zbl 1213.35058
Briane, Marc; Milton, Graeme W.
2010
Can mixing materials make electromagnetic signals travel faster? Zbl 1017.78004
Solna, Knut; Milton, Graeme W.
2002
Exact relations for composites: Towards a complete solution. Zbl 0896.35013
Grabovsky, Yury; Milton, Graeme W.
1998
Random media and composites. Proceedings of the SIAM workshop, Leesburg, Virginia (USA), December 7-10, 1988. Zbl 0707.00028
Kohn, Robert V. (ed.); Milton, Graeme W. (ed.)
1989
Inclusions of general shapes having constant field inside the core and nonelliptical neutral coated inclusions with anisotropic conductivity. Zbl 1447.35318
Lim, Mikyoung; Milton, Graeme W.
2020
On the forces that cable webs under tension can support and how to design cable webs to channel stresses. Zbl 1427.74078
Bouchitté, Guy; Mattei, Ornella; Milton, Graeme W.; Seppecher, Pierre
2019
A new route to finding bounds on the generalized spectrum of many physical operators. Zbl 1395.35079
Milton, Graeme W.
2018
Approximating the effective tensor as a function of the component tensors in two-dimensional composites of two anisotropic phases. Zbl 1393.35012
Milton, Graeme W.
2018
On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials. Zbl 1368.74053
Milton, Graeme; Briane, Marc; Harutyunyan, Davit
2017
Towards characterization of all $$3 \times 3$$ extremal quasiconvex quadratic forms. Zbl 06802190
Harutyunyan, Davit; Milton, Graeme Walter
2017
Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking. Zbl 1375.30046
Cassier, Maxence; Milton, Graeme W.
2017
Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase. Zbl 1368.74054
Milton, Graeme; Harutyunyan, Davit; Briane, Marc
2017
On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials. Zbl 1365.35176
Harutyunyan, Davit; Milton, Graeme Walter
2017
Criteria for guaranteed breakdown in two-phase inhomogeneous bodies. Zbl 1434.78018
Bardsley, Patrick; Primrose, Michael S.; Zhao, Michael; Boyle, Jonathan; Briggs, Nathan; Koch, Zoe; Milton, Graeme W.
2017
High-frequency homogenization for travelling waves in periodic media. Zbl 1371.35005
Harutyunyan, Davit; Milton, Graeme W.; Craster, Richard V.
2016
Sensitivity of anomalous localized resonance phenomena with respect to dissipation. Zbl 1341.35156
Meklachi, Taoufik; Milton, Graeme W.; Onofrei, Daniel; Thaler, Andrew E.; Funchess, Gregory
2016
Addendum to ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’. Zbl 1371.49011
Milton, Graeme W.
2015
Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex. Zbl 1329.26024
Harutyunyan, Davit; Milton, Graeme Walter
2015
Bounds on the volume of an inclusion in a body from a complex conductivity measurement. Zbl 1321.35221
Thaler, Andrew E.; Milton, Graeme W.
2015
Isotropic realizability of current fields in $$\mathbb{R}^3$$. Zbl 1317.35003
Briane, M.; Milton, G. W.
2015
Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by aomalous localized resonance. II. Zbl 1330.35421
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2014
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases. Zbl 1328.74075
Kochmann, Dennis M.; Milton, Graeme W.
2014
Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity. Zbl 1311.65135
Kang, Hyeonbae; Kim, Kyoungsun; Lee, Hyundae; Li, Xiaofei; Milton, Graeme W.
2014
Which electric fields are realizable in conducting materials? Zbl 1315.35021
Briane, Marc; Milton, Graeme W.; Treibergs, Andrejs
2014
Bounds on the volume fraction of the two-phase shallow shell using one measurement. Zbl 1455.74061
Kang, Hyeonbae; Milton, Graeme W.; Wang, Jenn-Nan
2014
Exact determination of the volume of an inclusion in a body having constant shear modulus. Zbl 1308.74027
Thaler, Andrew E.; Milton, Graeme W.
2014
Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking due to anomalous localized resonance. Zbl 1282.78004
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2013
Anomalous localized resonance using a folded geometry in three dimensions. Zbl 1348.78006
Ammari, Habib; Ciraolo, Giulio; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.
2013
Bounds on the volume fractions of two materials in a three-dimensional body from boundary measurements by the translation method. Zbl 1277.78026
Kang, Hyeonbae; Milton, Graeme W.
2013
Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity. Zbl 1371.49010
Milton, Graeme W.
2013
Effective conductivities of thin-interphase composites. Zbl 1451.74027
Alali, Bacim; Milton, Graeme W.
2013
Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method. Zbl 1252.35281
Kang, Hyeonbae; Kim, Eunjoo; Milton, Graeme W.
2012
Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime. Zbl 1254.31001
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2012
Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements. Zbl 1244.74050
Milton, Graeme W.
2012
Exterior cloaking with active sources in two-dimensional acoustics. Zbl 1283.76065
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2011
Complete characterization and synthesis of the response function of elastodynamic networks. Zbl 1273.74144
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2011
Progress on the strong Eshelby’s conjecture and extremal structures for the elastic moment tensor. Zbl 1262.74018
Ammari, Habib; Capdeboscq, Yves; Kang, Hyeonbae; Lee, Hyundae; Milton, Graeme W.; Zribi, Habib
2010
The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. I: The self-consistent scheme in matrix-based composites. Zbl 1244.74009
Benveniste, Yakov; Milton, Graeme W.
2010
The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. II: The generalized self-consistent scheme in matrix-based composites. Zbl 1244.74010
Benveniste, Yakov; Milton, Graeme W.
2010
Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type. Zbl 1211.74180
Milton, Graeme W.; Willis, John R.
2010
Electromagnetic circuits. Zbl 1259.35192
Milton, Graeme W.; Seppecher, Pierre
2010
New bounds on strong field magneto-transport in multiphase columnar composites. Zbl 1230.35013
Briane, Marc; Milton, Graeme W.
2010
An antisymmetric effective Hall matrix. Zbl 1213.35058
Briane, Marc; Milton, Graeme W.
2010
Active exterior cloaking for the 2D Laplace and Helmholtz Equations. Zbl 1254.78031
Guevara Vasquez, Fernando; Milton, Graeme W.; Onofrei, Daniel
2009
Homogenization of the three-dimensional Hall effect and change of sign of the Hall coefficient. Zbl 1170.74019
Briane, Marc; Milton, Graeme W.
2009
Minimization variational principles for acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. Zbl 1186.74044
Milton, Graeme W.; Seppecher, Pierre; Bouchitté, Guy
2009
Giant Hall effect in composites. Zbl 1181.35016
Briane, Marc; Milton, Graeme W.
2009
Solutions to the Pólya-Szegö conjecture and the weak Eshelby conjecture. Zbl 1134.74013
Kang, Hyeonbae; Milton, Graeme W.
2008
Inclusion pairs satisfying Eshelby’s uniformity property. Zbl 1159.74387
Kang, Hyeonbae; Kim, Eunjoo; Milton, Graeme W.
2008
An accelerated FFT algorithm for thermoelastic and nonlinear composites. Zbl 1195.74302
2008
Homogenization of the two-dimensional Hall effect. Zbl 1206.78090
Briane, M.; Manceau, D.; Milton, G. W.
2008
Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency. Zbl 1135.94341
Milton, Graeme W.; Seppecher, Pierre
2008
On modifications of Newton’s second law and linear continuum elastodynamics. Zbl 1347.74080
Milton, Graeme W.; Willis, John R.
2007
On the cloaking effects associated with anomalous localized resonance. Zbl 1149.00310
Milton, Graeme W.; Nicorovici, Nicolae-Alexandru P.
2006
On conjectures of Polya-Szegö and Eshelby. Zbl 1111.35119
Kang, Hyeonbae; Milton, Graeme W.
2006
A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance. Zbl 1255.78002
Milton, Graeme W.; Nicorovici, Nicolae-Alexandru P.; McPhedran, Ross C.; Podolskiy, Viktor A.
2005
The total creep of viscoelastic composites under hydrostatic or antiplane loading. Zbl 1120.74733
2005
Non-local interactions in the homogenization closure of thermoelectric functionals. Zbl 1071.35013
Camar-Eddine, M.; Milton, G. W.
2005
Change of sign of the corrector’s determinant for homogenization in three-dimensional conductivity. Zbl 1118.78009
Briane, Marc; Milton, Graeme W.; Nesi, Vincenzo
2004
New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages. Zbl 1077.74591
Benveniste, Y.; Milton, G. W.
2003
Realizable (average stress, average strain) pairs in a plate with holes. Zbl 1048.74034
Milton, G. W.; Serkov, S. K.; Movchan, A. B.
2003
The theory of composites. Zbl 0993.74002
Milton, Graeme W.
2002
On hierarchical structures and reiterated homogenization. Zbl 1021.35011
Lukkassen, Dag; Milton, Graeme W.
2002
Can mixing materials make electromagnetic signals travel faster? Zbl 1017.78004
Solna, Knut; Milton, Graeme W.
2002
Neutral coated inclusions in conductivity and anti-plane elasticity. Zbl 1090.74558
Milton, Graeme W.; Serkov, Sergey K.
2001
Proof of a conjecture on the conductivity of checkerboards. Zbl 1063.82018
Milton, Graeme W.
2001
Bounding the current in nonlinear conducting composites. Zbl 0991.78019
Milton, Graeme W.; Serkov, Sergey K.
2000
Exact relations for effective tensors of composites: necessary conditions and sufficient conditions. Zbl 1041.74057
Grabovsky, Yury; Milton, Graeme W.; Sage, Daniel S.
2000
On the effective viscoelastic moduli of two-phase media. III: Rigorous bounds on the complex shear modulus in two dimensions. Zbl 0946.74049
Gibiansky, Leonid V.; Milton, Graeme W.; Berryman, James G.
1999
Optimal $$G$$-closure bounds via stability under lamination. Zbl 0941.74012
Milton, G. W.; Nesi, V.
1999
Rank one plus a null-Lagrangian is an inherited property of two-dimensional compliance tensors under homogenisation. Zbl 0917.73046
Grabovsky, Yury; Milton, Graeme W.
1998
Exact relations for composites: Towards a complete solution. Zbl 0896.35013
Grabovsky, Yury; Milton, Graeme W.
1998
On the effective viscoelastic moduli of two-phase media. II: Rigorous bounds on the complex shear modulus in three dimensions. Zbl 0934.74061
Milton, G. W.; Berryman, J. G.
1997
Duality relations, correspondences and numerical results for planar elastic composites. Zbl 0969.74567
Helsing, J.; Milton, G. W.; Movchan, A. B.
1997
Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites. Zbl 0823.73043
Clark, Karen E.; Milton, Graeme W.
1995
A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media. Zbl 0833.73044
Milton, G. W.; Movchan, A. B.
1995
Sets of conductivity and elasticity tensors stable under lamination. Zbl 0797.73032
Francfort, Gilles A.; Milton, Graeme W.
1994
Modelling the effective conductivity function of an arbitrary two- dimensional polycrystal using sequential laminates. Zbl 0807.46091
Clark, Karen E.; Milton, Graeme W.
1994
A link between sets of tensors stable under lamination and quasiconvexity. Zbl 0821.73008
Milton, Graeme W.
1994
On the effective viscoelastic moduli of two-phase media. I: Rigorous bounds on the complex bulk modulus. Zbl 0816.73037
Gibiansky, L. V.; Milton, G. W.
1993
Composite materials with Poisson’s ratios close to -1. Zbl 0780.73047
Milton, Graeme W.
1992
Invariant properties of the stress in plane elasticity and equivalence classes of composites. Zbl 0791.73011
Cherkaev, Andrei V.; Lurie, Konstantin A.; Milton, Graeme W.
1992
Polycrystalline configurations that maximize electrical resistivity. Zbl 0734.73068
Nesi, Vincenzo; Milton, Graeme W.
1991
The field equation recursion method. Zbl 0739.73002
Milton, Graeme W.
1991
Bubbly flow and its relation to conduction in composites. Zbl 0729.76595
Smereka, Peter; Milton, Graeme W.
1991
On characterizing the set of possible effective tensors of composites: The variational method and the translation method. Zbl 0751.73041
Milton, Graeme W.
1990
Representations for the conductivity functions of multicomponent composites. Zbl 0715.35075
Milton, G. W.; Golden, K.
1990
A brief review of the translation method for bounding effective elastic tensors of composites. Zbl 0737.73019
Milton, G. W.
1990
Optimal bounds on the effective bulk modulus of polycrystals. Zbl 0702.73078
Avellaneda, Marco; Milton, Graeme W.
1989
Random media and composites. Proceedings of the SIAM workshop, Leesburg, Virginia (USA), December 7-10, 1988. Zbl 0707.00028
Kohn, Robert V. (ed.); Milton, Graeme W. (ed.)
1989
Variational bounds on the effective moduli of anisotropic composites. Zbl 0672.73012
Milton, Graeme W.; Kohn, Robert V.
1988
Multicomponent composites, electrical networks and new types of continued fraction. I. Zbl 0624.41017
Milton, G. W.
1987
Multicomponent composites, electrical networks and new types of continued fraction. II. Zbl 0624.41018
Milton, G. W.
1987
Modelling the properties of composites by laminates. Zbl 0631.73011
Milton, G. W.
1986
On bounding the effective conductivity of anisotropic composites. Zbl 0631.73012
Kohn, Robert V.; Milton, Graeme W.
1986
New third-order bounds on the effective moduli of N-phase composites. Zbl 0513.73004
Phan-Thien, N.; Milton, G. W.
1983
New bounds on effective elastic moduli of two-component materials. Zbl 0497.73016
Milton, G. W.; Phan-Thien, N.
1982
Bounds on the elastic and transport properties of two-component composites. Zbl 0486.73063
Milton, G. W.
1982
New bounds on the effective thermal conductivity of N-phase materials. Zbl 0503.73004
Phan-Thien, N.; Milton, G. W.
1982
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#### Cited by 1,118 Authors

 52 Milton, Graeme Walter 29 Kang, Hyeonbae 25 Ammari, Habib M. 21 Nguyen, Hoai-Minh 18 Schiavone, Peter 16 Briane, Marc 16 Lipton, Robert P. 16 Liu, Hongyu 15 Wang, Xu 14 Lim, Mikyoung 14 Nesi, Vincenzo 13 He, Qichang 13 Onofrei, Daniel 12 Lee, Hyundae 11 Chen, Tungyang 11 Helsing, Johan 11 Li, Hongjie 11 Ponte Castañeda, Pedro 11 Schneider, Matti 10 Yu, SangHyeon 9 Benveniste, Yakov 9 Capdeboscq, Yves 9 Pham, Duc Chinh 8 Deng, Youjun 8 Guenneau, Sébastien 8 Idiart, Martín I. 8 Kamiński, Marcin Marek 8 Sevostianov, Igor 8 Zhang, Hai 7 Ando, Kazunori 7 Gibiansky, Leonid V. 7 Guevara Vasquez, Fernando 7 Kohn, Robert Vita 7 Le Quang, Hung 7 Norris, Andrew N. 7 Triki, Faouzi 7 Visintin, Augusto 7 Willis, John Raymond 6 Andrianov, Igor V. 6 Bonnetier, Eric 6 Cherkaev, Andrej V. 6 Gao, Cun-Fa 6 Grabovsky, Yury 6 Lukkassen, Dag 6 Mityushev, Vladimir V. 6 Movchan, Alexander B. 6 Parnell, William J. 6 Rodríguez-Ramos, Reinaldo 6 Torquato, Sal 6 Vondřejc, Jaroslav 6 Zou, Wennan 5 Buryachenko, Valeriy A. 5 Cherkaev, Elena 5 Craster, Richard V. 5 Dai, Ming 5 Geers, Marc G. D. 5 Harutyunyan, Davit 5 Kim, Kyoungsun 5 Lassas, Matti 5 Liu, Liping 5 Mattei, Ornella 5 Mogilevskaya, Sofia G. 5 Monchiet, Vincent 5 Ruiz, Matias 5 Sabina, Federico J. 5 Sage, Daniel S. 5 Seppecher, Pierre 5 Suquet, Pierre-Marie 5 Uhlmann, Gunther Alberto 5 Vigdergauz, Shmuel 5 Zeman, Jan 5 Zheng, Quanshui 4 Barchiesi, Emilio 4 Bhattacharya, Kaushik 4 Böhlke, Thomas 4 Bonnet, Guy 4 Bravo-Castillero, Julián 4 Brun, Michele 4 Ciraolo, Giulio 4 Conti, Sergio 4 Crouch, Steven L. 4 Danishevskiĭ, Vladislav Valentinovich 4 Guinovart-Díaz, Raúl 4 Guzina, Bojan B. 4 Huang, Mojia 4 Kabel, Matthias 4 Kalamkarov, Alexander L. 4 Kouznetsova, Varvara G. 4 Li, Jichun 4 Miyanishi, Yoshihisa 4 Obnosov, Yurii V. 4 Peigney, Michaël 4 Penta, Raimondo 4 Perfekt, Karl-Mikael 4 Svendsen, Bob 4 Vogelius, Michael S. 3 Ahzi, Saïd 3 Alberti, Giovanni S. 3 Andrä, Heiko 3 Avazmohammadi, Reza ...and 1,018 more Authors
all top 5

#### Cited in 156 Serials

 107 Journal of the Mechanics and Physics of Solids 45 Archive for Rational Mechanics and Analysis 44 International Journal of Engineering Science 39 Acta Mechanica 32 Computer Methods in Applied Mechanics and Engineering 31 Mathematics and Mechanics of Solids 26 Journal of Elasticity 26 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 22 ZAMP. Zeitschrift für angewandte Mathematik und Physik 22 European Journal of Mechanics. A. Solids 19 Journal of Mathematical Physics 17 Continuum Mechanics and Thermodynamics 16 Wave Motion 15 Computational Mechanics 15 SIAM Journal on Applied Mathematics 13 International Journal for Numerical Methods in Engineering 13 Journal de Mathématiques Pures et Appliquées. Neuvième Série 13 Calculus of Variations and Partial Differential Equations 11 International Journal of Solids and Structures 11 European Journal of Applied Mathematics 11 SIAM Journal on Mathematical Analysis 10 Communications in Mathematical Physics 10 Journal of Computational Physics 10 Mathematical Methods in the Applied Sciences 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 9 Journal of Mathematical Analysis and Applications 8 Journal of Differential Equations 8 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 7 Archive of Applied Mechanics 6 Computers & Mathematics with Applications 5 Quarterly of Applied Mathematics 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Applicable Analysis 4 Journal d’Analyse Mathématique 4 Journal of Statistical Physics 4 Applications of Mathematics 4 Applied Mathematical Modelling 4 International Applied Mechanics 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Multiscale Modeling & Simulation 4 Waves in Random and Complex Media 4 Acta Mechanica Sinica 4 Networks and Heterogeneous Media 4 Advances in Mathematical Physics 3 International Journal of Modern Physics B 3 Communications on Pure and Applied Mathematics 3 Physics Letters. A 3 Journal of Computational and Applied Mathematics 3 Mechanics Research Communications 3 Advances in Applied Mathematics 3 Journal of Integral Equations and Applications 3 Engineering Analysis with Boundary Elements 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 New Journal of Physics 3 Journal of Modern Optics 3 Mathematics and Mechanics of Complex Systems 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 International Journal of Plasticity 2 Inverse Problems 2 Journal of Engineering Mathematics 2 Journal of Fluid Mechanics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Mathematics of Computation 2 Acta Mathematica Vietnamica 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Journal of Functional Analysis 2 Journal of Optimization Theory and Applications 2 Mathematische Annalen 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Physica D 2 Applied Numerical Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Communications in Partial Differential Equations 2 SIAM Journal on Scientific Computing 2 Journal of Applied Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 SIAM Journal on Applied Dynamical Systems 2 Inverse Problems in Science and Engineering 2 Inverse Problems and Imaging 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 Research in the Mathematical Sciences 2 Journal de l’École Polytechnique – Mathématiques 1 Communications in Algebra 1 Journal of Applied Mathematics and Mechanics 1 Physica A 1 Physics Reports 1 Ukrainian Mathematical Journal 1 Physics of Fluids, A 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Meccanica 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis ...and 56 more Serials
all top 5

#### Cited in 45 Fields

 580 Mechanics of deformable solids (74-XX) 237 Partial differential equations (35-XX) 143 Optics, electromagnetic theory (78-XX) 62 Numerical analysis (65-XX) 55 Calculus of variations and optimal control; optimization (49-XX) 51 Fluid mechanics (76-XX) 43 Statistical mechanics, structure of matter (82-XX) 26 Functions of a complex variable (30-XX) 23 Operator theory (47-XX) 19 Classical thermodynamics, heat transfer (80-XX) 18 Integral equations (45-XX) 13 Potential theory (31-XX) 12 Biology and other natural sciences (92-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Probability theory and stochastic processes (60-XX) 9 Functional analysis (46-XX) 8 Convex and discrete geometry (52-XX) 8 Mechanics of particles and systems (70-XX) 6 Real functions (26-XX) 6 Approximations and expansions (41-XX) 6 Quantum theory (81-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Differential geometry (53-XX) 4 Operations research, mathematical programming (90-XX) 3 Geophysics (86-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Associative rings and algebras (16-XX) 2 Topological groups, Lie groups (22-XX) 2 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 2 Sequences, series, summability (40-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Statistics (62-XX) 2 Relativity and gravitational theory (83-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX)

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