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M. Briane, D. Manceau, and G. W. Milton, Homogenization of the two-dimensional Hall effect, Journal of Mathematical Analysis and Applications, vol.339, issue.2, pp.339-1468, 2008.
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URL : https://hal.archives-ouvertes.fr/hal-01427898

M. Briane and G. W. Milton, Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient, Archive for Rational Mechanics and Analysis, vol.30, issue.2, pp.715-736, 2009.
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D. J. Bergman and Y. M. Strelniker, Strong-field magnetotransport of conducting composites with a columnar microstructure, Physical Review B, vol.59, issue.3, pp.59-2180, 1999.
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D. J. Bergman and Y. M. Strelniker, Duality Transformation in a Three Dimensional Conducting Medium with Two Dimensional Heterogeneity and an In-Plane Magnetic Field, Physical Review Letters, vol.80, issue.15, pp.80-3356, 1998.
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D. J. Bergman and Y. M. Strelniker, Exact relations between magnetoresistivity tensor components of conducting composites with a columnar microstructure, Phys. Rev. B, pp.61-6288, 2000.

D. J. Bergman, Y. M. Strelniker, and A. K. Sarychev, Recent advances in strong field magneto-transport in a composite medium, Physica A: Statistical Mechanics and its Applications, vol.241, issue.1-2, pp.241-278, 1997.
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M. Briane, Nonlocal effects in two-dimensional conductivity. Archive for Rational Mechanics and Analysis, pp.255-267, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00447664

M. Briane, Homogenization of High-Conductivity Periodic Problems: Application to a General Distribution of One-Directional Fibers, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.33-60, 2003.
DOI : 10.1137/S0036141001398666

M. Briane, Homogenization of non-uniformly bounded operators: Critical barrier for nonlocal effects. Archive for Rational Mechanics and Analysis, pp.73-101, 2002.

M. Briane and J. Casado-díaz, Asymptotic behaviour of equicoercive diffusion energies in dimension two, Calculus of Variations and Partial Differential Equations, vol.110, issue.4, pp.29-455, 2007.
DOI : 10.1007/s00526-006-0074-5

URL : https://hal.archives-ouvertes.fr/hal-00365131

M. Briane and J. Casado-díaz, Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization, Communications in Partial Differential Equations, vol.22, issue.6, pp.32-935, 2007.
DOI : 10.1006/jfan.1994.1093

URL : https://hal.archives-ouvertes.fr/hal-00364659

M. Briane and J. Casado-díaz, Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients, Journal of Differential Equations, vol.245, issue.8, pp.245-2038, 2008.
DOI : 10.1016/j.jde.2008.07.027

URL : https://hal.archives-ouvertes.fr/hal-00360023

M. Briane and D. Manceau, Duality results in the homogenization of twodimensional high-contrast conductivities. Networks and Heterogeneous Media, pp.3-509, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00360041

M. Briane, D. Manceau, and G. W. Milton, Homogenization of the two-dimensional Hall effect, Journal of Mathematical Analysis and Applications, vol.339, issue.2, pp.339-1468, 2008.
DOI : 10.1016/j.jmaa.2007.07.044

URL : https://hal.archives-ouvertes.fr/hal-00372692

M. Briane and G. W. Milton, Giant Hall Effect in Composites, Multiscale Modeling & Simulation, vol.7, issue.3, pp.1405-1427, 2009.
DOI : 10.1137/08073189X

URL : https://hal.archives-ouvertes.fr/hal-01427898

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M. Briane and G. W. Milton, Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient, Archive for Rational Mechanics and Analysis, vol.30, issue.2, pp.715-736, 2009.
DOI : 10.1007/s00205-008-0200-y

URL : https://hal.archives-ouvertes.fr/hal-00130591

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M. Briane and N. Tchou, Fibered microstructures for some nonlocal Dirichlet forms, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser, pp.30-681, 2001.

A. M. Dykhne, Conductivity of a two-dimensional two-phase system. Zhurnal eksperimental(noi i teoreticheskoi fiziki, Akademia Nauk SSSR, pp.59-110, 1970.

V. N. Fenchenko, E. Ya, and . Khruslov, Asymptotic of solution of differential equations with strongly oscillating matrix of coefficients which does not satisfy the condition of uniform boundedness, Dokl. AN Ukr.SSR, p.4, 1981.

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Y. Grabovsky, An application of the general theory of exact relations to fiber-reinforced conducting composites with Hall effect The Special Issue in Honor of Graeme W, Mechanics of Materials, pp.41-456, 2009.

Y. Grabovsky, Exact Relations for Effective Conductivity of Fiber-Reinforced Conducting Composites with the Hall Effect via a General Theory, SIAM Journal on Mathematical Analysis, vol.41, issue.3, pp.41-973, 2009.
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E. Ya and . Khruslov, Composite Media and Homogenization Theory, Progress in Nonlinear Differential Equations and Their Applications, 1991.

E. Ya, V. A. Khruslov, and . Marchenko, Homogenization of Partial Differential Equations . Homogenization of Partial Differential Equations, Progress in Mathematical Physics, 2006.

G. W. Milton, Classical Hall effect in two-dimensional composites: A characterization of the set of realizable effective conductivity tensors, Physical Review B, vol.38, issue.16, pp.38-11296, 1988.
DOI : 10.1103/PhysRevB.38.11296

G. W. Milton, The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics, 2002.
DOI : 10.1017/CBO9780511613357

S. Mortola and S. Steffé, Un problema di omogeneizzazione bidimensionale, Classe di Scienze Fisiche, Matematiche e Naturali, pp.78-77, 1985.

F. Murat and L. Tartar, H-convergence. Mimeographed notes, Séminaire d'Analyse Fonctionnelle et Numérique, 1978.

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L. Tartar and G. W. Milton, Private communication to References References [1] M. Bellieud and G. Bouchitté. Homogenization of elliptic problems in a fiber reinforced structure. Non local effects, Ann. Scuola Norm. Sup. Pisa, p.4, 1998.

A. Bensoussan, J. Lions, and G. C. Papanicolaou, Asymptotic analysis for periodic structures, 1978.

D. J. Bergman, Self-duality and the low field Hall effect in 2D and 3D metalinsulator composites. Percolation Structures and Processes, Annals of the Israel Physical Society, vol.5, pp.297-321, 1983.

D. J. Bergman, X. Li, and Y. M. Strelniker, Macroscopic conductivity tensor of a three-dimensional composite with a one- or two-dimensional microstructure, Physical Review B, vol.71, issue.3, pp.71-035120, 2005.
DOI : 10.1103/PhysRevB.71.035120

D. J. Bergman and Y. M. Strelniker, Magnetotransport in conducting composite films with a disordered columnar microstructure and an in-plane magnetic field, Physical Review B, vol.60, issue.18, pp.60-13016, 1999.
DOI : 10.1103/PhysRevB.60.13016

D. J. Bergman and Y. M. Strelniker, Strong-field magnetotransport of conducting composites with a columnar microstructure, Physical Review B, vol.59, issue.3, pp.59-2180, 1999.
DOI : 10.1103/PhysRevB.59.2180

D. J. Bergman and Y. M. Strelniker, Duality Transformation in a Three Dimensional Conducting Medium with Two Dimensional Heterogeneity and an In-Plane Magnetic Field, Physical Review Letters, vol.80, issue.15, pp.80-3356, 1998.
DOI : 10.1103/PhysRevLett.80.3356

D. J. Bergman and Y. M. Strelniker, Exact relations between magnetoresistivity tensor components of conducting composites with a columnar microstructure, Phys. Rev. B, pp.61-6288, 2000.

D. J. Bergman, Y. M. Strelniker, and A. K. Sarychev, Recent advances in strong field magneto-transport in a composite medium, Physica A: Statistical Mechanics and its Applications, vol.241, issue.1-2, pp.241-278, 1997.
DOI : 10.1016/S0378-4371(97)00095-2

M. Briane, Nonlocal effects in two-dimensional conductivity. Archive for Rational Mechanics and Analysis, pp.255-267, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00447664

M. Briane, Homogenization of High-Conductivity Periodic Problems: Application to a General Distribution of One-Directional Fibers, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.33-60, 2003.
DOI : 10.1137/S0036141001398666

M. Briane, Homogenization of non-uniformly bounded operators: Critical barrier for nonlocal effects. Archive for Rational Mechanics and Analysis, pp.73-101, 2002.

M. Briane and J. Casado-díaz, Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization, Communications in Partial Differential Equations, vol.22, issue.6, pp.32-935, 2007.
DOI : 10.1006/jfan.1994.1093

URL : https://hal.archives-ouvertes.fr/hal-00364659

M. Briane and D. Manceau, Duality results in the homogenization of twodimensional high-contrast conductivities. Networks and Heterogeneous Media, pp.3-509, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00360041

M. Briane, D. Manceau, and G. W. Milton, Homogenization of the two-dimensional Hall effect, Journal of Mathematical Analysis and Applications, vol.339, issue.2, pp.339-1468, 2008.
DOI : 10.1016/j.jmaa.2007.07.044

URL : https://hal.archives-ouvertes.fr/hal-00372692

M. Briane and G. W. Milton, Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient, Archive for Rational Mechanics and Analysis, vol.30, issue.2, pp.715-736, 2009.
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