Duality and Effective Conductivity of Random Two-Phase Flat Systems

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.