Duality and Effective Conductivity of Random Two-Phase Flat Systems
Abstract
The possible functional forms of the effective conductivity sigmae 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 sigmae in the inhomogeneity parameter z and some additional conjectures about functional form of sigmae. They differ from the effective medium approximation, satisfy all necessary requirements and reproduce the known formulas for sigmae in weakly inhomogeneous case. This can signify also that sigmae 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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