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

2005/02/15 by S. A. Bulgadaev, F. V. Kusmartsev
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Fractional Differential Equations Solutions #Numerical methods in inverse problems #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physleta.2005.01.071

published as Physics Letters A337 (2005) 449-456 · 10 pages, Latex2e, 3 figures

openalex publication_date 2005/02/15 · arxiv created 2005/04/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Related

• Duality and Effective Conductivity of Random Two-Phase Flat Systems
• On universality of conductivity of planar random self-dual systems
• Electrical conductivity of inhomogeneous two component media in two dimensions
• On the effective conductivity of flat random two-phase models
• Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three