Abstract
A mean-field theory for the diffusion-controlled cluster formation is presented by considering the competition among the different portions of a growing cluster for the incoming diffusive particles. This competition is shown to introduce a screening length which depends inversely on the density of the cluster. The Hausdorff dimensionality of these clusters is shown to be where is the Euclidean dimensionality. This result is in excellent agreement with that of the computer simulations of Witten and Sander and of Meakin.
- Received 3 December 1982
DOI:https://doi.org/10.1103/PhysRevLett.50.839
©1983 American Physical Society