From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

Abstract

We propose a new class of cluster growth models where growth sites have a finite lifetime τ, which contains as special cases the Eden model (τ = ∞) and the kinetic growth walk (τ = 1). For finite but large τ values the growth process can be characterized by a crossover timet _X; for times belowt _X an Eden-type cluster is formed, while for times abovet _X the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with τ. We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).