Planar isotropic two-phase systems in perpendicular magnetic field: effective conductivity

Three explicit approximate expressions for the effective conductivity σˆe of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting σˆe of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions and allow to describe σˆe of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.