Crossover in diffusion-limited aggregation

Abstract

We consider a generalization of the Witten-Sander model for aggregation to allow for a finite density of diffusing particles. In a continuum treatment we show that for small aggregates we recover the previous behavior that the density of the aggregate decreases inversely with the radius, but larger aggregates cross over to having constant density. Our results are in qualitative agreement with numerical simulations of the discrete model.