Effective conductivity of random two-dimensional composites with circular non-overlapping inclusions

We study the effective conductivity of equal unidirectional infinite circular cylinders randomly distributed in a uniform host (disks on the plane). The problem is reduced to a boundary value problem for the two-dimensional Laplace equation. A symbolic–numerical algorithm was proposed in the previous papers to solve the boundary value problem with arbitrary deterministic locations of disks. Application of the Monte Carlo method for the uniform non-overlapping distribution of disks yields the effective conductivity of random composites. The expected value of the effective conductivity is written exactly in the form of a power series in the concentration. This formula is valid for all concentrations.