Homogenization of the two-dimensional Hall effect

Marc Briane (1) , David Manceau (2) , Graeme W. Milton (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre
3 Department of Mathematics - University of Utah

In this paper, we study the two-dimensional Hall effect in a highly heterogeneous conducting material in the low magnetic field limit. Extending Bergman's approach in the framework of H-convergence we obtain the effective Hall coefficient which only depends on the corrector of the material resistivity in the absence of a magnetic field. A positivity property satisfied by the effective Hall coefficient is then deduced from the homogenization process. An explicit formula for the effective Hall coefficient is derived for anisotropic interchangeable two-phase composites.

Mots clés: Homogenization; Hall effect; dimension two; two-phase composite

Domaines: Equations aux dérivées partielles [math.AP]

Marc Briane, David Manceau, Graeme W. Milton. Homogenization of the two-dimensional Hall effect. Journal of Mathematical Analysis and Applications, 2008, 339 (2), pp.1468 - 1484. ⟨10.1016/j.jmaa.2007.07.044⟩. ⟨hal-00372692v2⟩