Effective conductivity of 2D isotropic two-phase systems in magnetic field

TL;DR

This paper derives explicit approximate formulas for the effective electrical conductivity of 2D isotropic two-phase systems in magnetic fields, aligning well with experimental data and applicable to various media.

Contribution

It introduces a linear fractional transformation approach to connect conductivities with and without magnetic fields, providing a new analytical tool for inhomogeneous media.

Findings

Explicit approximate expressions for sigma_e in magnetic fields.

Qualitative agreement with experimental data.

Applicable to diverse two-phase systems, including regular, nonregular, and random media.

Abstract

Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They allow to describe sigma_{e} of various inhomogeneous media at arbitrary phase concentrations x and magnetic fields. the x-dependence plots of sigma_e at some values of inhomogeneity and magnetic field are constructed. Their behaviour is qualitatively compatible with the existing experimental data. The obtained results are applicable for different two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and admit a direct experimental checking.