Percolation and conductivity in evolving disordered media

Percolation theory and the associated percolation networks have provided deep insights into the transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the bonds of the networks remain constant throughout the entire process. There are, however, many important problem in which the conductance of the bonds in the networks evolves over time and does not remain constant. We introduce two percolation models to study the evolution of the conductivity of such networks. These two models are related to natural and industrial processes involving clogging, precipitation, and dissolution. The effective conductivity of the models are shown to follow known power laws near the percolation threshold, despite radically different behavior both away from and even close to the individual percolation threshold. The behavior of the networks close to the percolation threshold are described by critical exponents, yielding bounds for traditional critical exponents. We show that one of the two models belongs to the traditional universality class of percolation conductivity, while the second model yields non-universal scaling exponents.