Exact Results for Conductivity of 2D Isotropic Heterophase Systems
Disordered Systems and Neural Networks
2009-11-10 v3
Abstract
The duality relation for the effective conductivity sigma_{e} of 2D isotropic heterophase systems is used for obtaining the exact results for sigma_{e} at arbitrary number of phases N. The exact values of sigma_{e} correspond to the fixed points of the duality transformations. The new exact results for sigma_{e}, generalizing the well-known exact values of sigma_{e} for N = 2,3 at equal phase concentrations, are found. It is shown that for N > 3 there exist the whole hyperplanes in the space of phase concentrations, on which sigma_{e} takes constant values. These results are checked in the framework of various approximations for different random heterophase systems.
Cite
@article{arxiv.cond-mat/0303622,
title = {Exact Results for Conductivity of 2D Isotropic Heterophase Systems},
author = {S. A. Bulgadaev},
journal= {arXiv preprint arXiv:cond-mat/0303622},
year = {2009}
}
Comments
12 pages, latex-2e, 2 figures, small corrections and reference are added