On the effective conductivity of flat random two-phase models

S. A. Bulgadaev

doi:doi:10.1209/epl/i2003-00508-7

DOI: 10.1209/epl/i2003-00508-7
Europhys. Lett., 64 (4) , pp. 482-488 (2003)

On the effective conductivity of flat random two-phase models

S. A. Bulgadaev

Landau Institute for Theoretical Physics Chernogolovka, Moscow Region, Russia, 142432

sabul@dio.ru

(Received 6 January 2003; accepted in final form 2 September 2003)

Abstract
An approximate functional equation for the effective conductivity $\sigma_{\ab{eff}}$ 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 $\sigma_{\ab{eff}}$ in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that $\sigma_{\ab{eff}}$ 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.

PACS
73.61.-r - Electrical properties of specific thin films.
75.70.Ak - Magnetic properties of monolayers and thin films.

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