74 research outputs found
On the effective conductivity of flat random two-phase models
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.Comment: 8 pages, 2 figures, Latex2
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