Nonisotropic effective-medium approximation for diffusion problems in random media

Abstract

We present the nonisotropic effective-medium approximation to solve diffusion problems in a two-dimensional anisotropic random media. The problem has been worked out by introducing a generalization of the well-known effective-medium approximation. A set of coupled nonlinear self-consistent equations must be solved to find the effective rates in each direction. We have considered (analytically) some particular models in short and large frequency limits. The dc conductivity is also compared against the isotropic case. The ac conductivity and Cole-Cole diagrams for the nonisotropic random bond percolation model have been analyzed in terms of the physical parameters that characterize the anisotropy and the disorder in the media. A monoparametric nonisotropic bond disordered model $(\ensuremath{\alpha}$ model) has also been worked out to show the applicability of the present approach in the context of weak or strong disorder. Such a model of disorder leads the system to show a quasi-one-dimensional behavior, proper of nonisotropic materials.