Critical behavior of conductivity in two-phase, highly inhomogeneous composites

摘要

We study the critical behavior of the effective conductivity of a two-phase, highly inhomogeneous medium with a finite ratio of phase conductivities. We find the critical exponents above and below the percolation threshold and at the percolation threshold itself, and establish the criteria for the applicability of a percolation-like description. We also determine the requirements for linearization of the medium as a whole at the percolation threshold. Finally, we investigate the homogenization of the system near critical fields.