Exact Results for Conductivity of 2D Isotropic Heterophase Systems
Abstract
The duality relation for the effective conductivity sigmae of 2D isotropic heterophase systems is used for obtaining the exact results for sigmae at arbitrary number of phases N. The exact values of sigmae correspond to the fixed points of the duality transformations. The new exact results for sigmae, generalizing the well-known exact values of sigmae 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 sigmae takes constant values. These results are checked in the framework of various approximations for different random heterophase systems.
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