Coarsened Lattice Model for Random Granular Systems

In random systems consisting of grains with size distributions the transport properties are difficult to explore by network models. However, the concentration dependence of effective conductivity and its critical properties can be considered within coarsened lattice model proposed that takes into account information from experimentally known size histograms. For certain classes of size distributions the specific local arrangements of grains can induce either symmetrical or unsymmetrical critical behaviour at two threshold concentrations. Using histogram related parameters the non-monotonic behaviour of the conductor-insulator and conductor-superconductor threshold is demonstrated.