Contact propagation: Percolation and other scaling regimes

Abstract

We examine the scaling behavior of stirred percolation and first-passage percolation systems in which cluster contact is rate limiting with respect to propagation or transport. For the scaling regime near the static percolation threshold, we provide details of previously reported computational estimates of the ‘‘propagation exponent,’’ and we present results for several variants of the stirred percolation model and for a first-passage percolation model. Five additional scaling regimes are predicted, three of which are verified computationally. Applications to combustion, diffusion-limited aggregation, gasification of porous solids, and crack propagation in solids are discussed.