Universal material property in conductivity of planar random microstructures

We study scatter involved in finite-size scaling of the conductivity and resistivity tensors resulting, respectively, from uniform essential and natural boundary conditions applied to domains that are finite relative to the size of a heterogeneity. For various types of planar microstructures generated from Poisson processes (multiphase Voronoi mosaics, composites with circular or needlelike inclusions, etc.) we report a universal property: the coefficient of variation of the second invariant stays practically constant at about (Formula presented) irrespective of the domain size, the boundary conditions applied to it, the contrast, and the volume fraction of either phase.