Growth Probability Distribution in Kinetic Aggregation Processes

Abstract

A growth process is characterized by the growth-site probability distribution $\frac{{{p}_{i}}}{i\ensuremath{\epsilon}\ensuremath{\Gamma}}$, where ${p}_{i}$ is the probability that site $i$ on the surface of the cluster becomes part of the aggregate. Equations for the ${p}_{i}'\mathrm{s}$ are solved numerically for diffusion-limited aggregation and the dielectric breakdown models by the standard Green's-function technique, and moments of the distribution are calculated indicating that a hierarchy of independent exponents is required to describe the critical behavior. The absence of a linear relation among the exponents is indicative of a nonconventional scaling for the growth probability distribution.