Random walks are used to obtain the diffusion constant for continuum percolation models of composite materials in two and three dimensions. An Einstein relation is then used to find the conductivity. The same calculation gives the dielectric constant for the composite. First-passage-time methods and special boundary conditions are used for systems where both materials have finite conductivity, where one component is a superconductor, and where one component does not conduct. The percolation models consist of randomly placed overlapping spheres in three dimensions or disks in two dimensions. Our results are consistent with known results where applicable and are far better than effective medium theories. Estimates for anomalous diffusion exponents at percolation were also found.

• Received 27 November 1989

DOI:https://doi.org/10.1103/PhysRevA.41.3052