Duality and Effective Conductivity of Random Two-Phase Flat Systems

The possible functional forms of the effective conductivity σ_e of 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 σ_e in the inhomogeneity parameter z, and some additional conjectures about the functional form of σ_e. They differ from the effective medium approximation, satisfy all necessary requirements, and reproduce the known formulas for σ_e in the weakly inhomogeneous case. This can also signify that σ_e of the two-phase randomly inhomogeneous systems may be a nonuniversal function, depending on some details of the structure of the random inhomogeneities.