Diffusion of clusters with randomly growing masses.

Abstract

Diffusion of fractal clusters of dimension ${\mathit{d}}_{\mathit{f}}$ in a three-dimensional space is investigated. The diffusion process is assumed to be modeled by a standard parabolic diffusion equation but with a random diffusion coefficient. The motivation for this assumption is provided by two pieces of evidence: (1) the cluster diffusion coefficients depend on the clusters' masses, sizes, and shapes; (2) the masses of clusters change stochastically in time due to random attachment or detachment of particles. Two models of the growing process are considered: (a) a Poisson process; (b) a simple birth-and-death process with linear rules. The mean square displacement of the cluster mass centers is analyzed and its anomalous behavior is demonstrated as a function of the fractal cluster dimension.