Duality and Effective Conductivity of Random Two-Phase Flat Systems
Abstract
The possible functional forms of the effective conductivity sigma_e of the randomly inhomogeneous two-phase systems at arbitrary values of concentrations are discussed. Two explicit approximate expressions for effective conductivity are found using a duality relation, a series expansion of sigma_e in the inhomogeneity parameter z and some additional conjectures about functional form of sigma_e. They differ from the effective medium approximation, satisfy all necessary requirements and reproduce the known formulas for sigma_e in weakly inhomogeneous case. This can signify also that sigma_e of the two-phase randomly inhomogeneous systems may be a nonuniversal function, depending on some details of the structure of the random inhomogeneities.
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Cite
@article{arxiv.cond-mat/0403272,
title = {Duality and Effective Conductivity of Random Two-Phase Flat Systems},
author = {S. A. Bulgadaev},
journal= {arXiv preprint arXiv:cond-mat/0403272},
year = {2007}
}
Comments
9 pages, 1 figure, Latex2e