On the effective conductivity of flat random twophase models
Abstract
An approximate functional equation for the effective conductivity σ_{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 twophase randomly inhomogeneous model is constructed by a hierarchical method and its effective conductivity at arbitrary phase concentrations is found in the meanfield like approximation. These expressions satisfy all the necessary symmetries, reproduce the known formulas for σ_{eff} in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that σ_{eff} even of the twophase 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.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2003
 DOI:
 10.1209/epl/i2003005087
 Bibcode:
 2003EL.....64..482B
 Keywords:

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