Distribution of growth probabilities in fluid flow and diffusion-limited aggregation

Abstract

The authors examine the role of extrinsic noise in diffusion-limited aggregation (DLA) and a deterministic continuum theory derived from the work of Paterson (1984) on fluid flow in a Hele-Shaw cell. They show the distribution of growth probabilities for the deterministic model to be essentially the same as DLA and predict that the asymptotic value of the fractal dimension for off-lattice DLA may be closer to D approximately 1.65+or-0.03, as opposed to D=1.71. The results confirm that extrinsic noise is not essential to create the characteristic properties of DLA in models that are variations of DLA.