Homogenization of the magneto-resistance in dimension two
Résumé
A general formula for the effective magneto-resistance in a two-dimensional heterogeneous conductor submitted to a low magnetic field is given through H-convergence. In the periodic case, it is proved that the dissipation energy due to the effective magneto-resistance is greater than or equal to the average of the energy due to the local magneto-resistance, and that the equality holds if and only if the local Hall coefficient is constant. This agrees with an anisotropic extension of the Kohler law in the framework of the ordinary magneto-resistance. The result is illustrated by the case of a two-phase rank-one laminate.