Efficient simulation technique to compute effective properties of heterogeneous media

We present a new simulation technique to "exactly" yield effective transport properties of disordered heterogeneous media in which the transport process is governed by a steady-state diffusion equation. Hence, the algorithm, which is based upon simulating the Brownian motion of a diffusing particle, can be applied to determine the effective electrical and thermal conductivity, dielectric constant, magnetic permeability, diffusion coefficient associated with flow past fixed obstacles, and the trapping rate associated with diffusion-controlled reactions among sinks. The simulation method is shown to have a very fast execution time. The technique is illustrated by computing the trapping rate associated with diffusion-controlled reactions; it is demonstrated to have an execution time that is at least an order of magnitude faster than previous simulation methodologies.