Europhys. Lett., 64 (4) , pp. 482-488 (2003)
On the effective conductivity of flat random two-phase modelsS. A. Bulgadaev
Landau Institute for Theoretical Physics Chernogolovka, Moscow Region, Russia, 142432 email@example.com
(Received 6 January 2003; accepted in final form 2 September 2003)
An approximate functional equation for the effective conductivity of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly inhomogeneous model is constructed by a hierarchical method and its effective conductivity at arbitrary phase concentrations is found in the mean-field-like approximation. These expressions satisfy all the necessary symmetries, reproduce the known formulas for in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that even of the two-phase randomly inhomogeneous system may be a nonuniversal function and can depend on some details of the structure of the inhomogeneous regions. The percolation limit is briefly discussed.
73.61.-r - Electrical properties of specific thin films.
75.70.Ak - Magnetic properties of monolayers and thin films.
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