Cluster structure and conductivity of three-dimensional continuum systems

While the cluster statistics exponents for three-dimensional continuum systems have been shown to be the same as those of lattices, the cluster structure and the conductivity exponents of such continuum systems have not been reported before. Here we present the first determination of both the fractal dimension of clusters, D, and the conductivity exponent, t, for these systems. We further describe the porcupine-like morphology of the clusters and the conductivity behavior in continuum anisotropic systems.