On the effective conductivity of flat random two-phase models

Details On the effective conductivity of flat random two-phase models On the effective conductivity of flat random two-phase models

2004-03-09

arxiv.org/abs/cond-mat/0403256v1

Europhys.Lett. 64 (2003) 482 - 488

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 2 figures, Latex2e

Scientific paper

An approximate equation for the effective conductivity sigma_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_eff in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that sigma_eff even of 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.

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