Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

TL;DR

This paper derives explicit approximate formulas for the effective conductivity of planar isotropic two-phase systems in a magnetic field, applicable to various media and conditions, enabling experimental validation.

Contribution

It introduces a dual linear fractional transformation method to connect effective conductivity with and without magnetic field for diverse two-phase systems.

Findings

Formulas applicable to regular, nonregular, and random systems

Results valid for arbitrary phase concentrations and magnetic fields

Potential for direct experimental verification

Abstract

Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e 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 sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.