On the effective conductivity of flat random two-phase models
Abstract
An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly inhomogeneous model is constructed by a hierarchical method and its effective conductivity at arbitrary phase concentrations is found in the mean-field-like approximation. These expressions satisfy all the necessary symmetries, reproduce the known formulas for sigma_eff in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that sigma_eff even of two-phase randomly inhomogeneous system may be a nonuniversal function and can depend on some details of the structure of the inhomogeneous regions. The percolation limit is briefly discussed.
Cite
@article{arxiv.cond-mat/0403256,
title = {On the effective conductivity of flat random two-phase models},
author = {S. A. Bulgadaev},
journal= {arXiv preprint arXiv:cond-mat/0403256},
year = {2007}
}
Comments
8 pages, 2 figures, Latex2e