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 ${\mathrm{\sigma }}_{\mathit{e}}$ of general continuum (off-lattice) models of n-phase heterogeneous media having phase conductivities ${\mathrm{\sigma }}_1$,...,${\mathrm{\sigma }}_{\mathit{n}}$, where ${\mathrm{\sigma }}_{\mathit{i}}$ 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 ${\mathrm{\sigma }}_{\mathit{e}}$ 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.