TRANSIENT DIFFUSION AND CONDUCTION IN HETEROGENEOUS MEDIA - BEYOND THE CLASSICAL EFFECTIVE-MEDIUM APPROXIMATION

In this paper steady-state and transient diffusion and conduction in h eterogeneous media, such as composite solids, are studied. The heterog eneities are of percolation type in the sense that a randomly-selected fraction of the system does not allow transport to take place. We pre sent several new extensions of the classical effective-medium approxim ation (EMA) for diffusion and conduction in regular network models of heterogeneous media, including an EMA for topologically-random network s, such as the Voronoi network, for which we introduce a novel stochas tic Green function, and a cluster (higher order) EMA for transient dif fusion and other dynamical properties of heterogeneous media. In all c ases the predictions are compared with the results of Monte Carlo simu lations.