First-passage-time calculation of the conductivity of continuum models of multiphase composites

We formulate a Brownian-motion simulation technique to compute exactly the effective conductivity of general continuum (off-lattice) models of n-phase heterogeneous media having phase conductivities 1,...,n, where can be finite or infinite. The appropriate first-passage-time equations at the multiphase interface are derived to reduce significantly the computation time. The method is illustrated by calculating for regular and random arrays of d-dimensional, nonoverlapping spheres (d=2 and 3) for a wide range of conductivity ratios (including perfectly insulating and superconducting particles) and volume fractions.