New bounds on strong field magneto-transport in multiphase columnar composites
Résumé
This paper provides new bounds on the effective properties in dimension two of multiphase composites with isotropic phases having nonsymmetric conductivities. This is relevant to classical strong field magneto-transport in heterogeneous conductors with columnar microstructure, with a magnetic field in the direction of the columns. On the one hand, a polygon-like G-closure for multiphase composites without prescribed volume fractions is derived for isotropic effective resistivities. On the other hand, the G-closure of the possible average currents associated with a given applied electric field is found for anisotropic multiphase composites with prescribed volume fractions. This extends the G-closure result obtained by Ra˘ıtum and Tartar for symmetric conductivities.