High-Dimensional Diffusive Growth
Soft Condensed Matter
2009-10-31 v2
Abstract
We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits a phase transition between ballistic and diffusion-controlled growth, with non-trivial corrections to cluster size at the critical point. Even in the ballistic regime, cluster scaling is controlled by extremal statistics due to the branching structure of the Cayley tree; it is the extremal nature of the fluctuations that enables us to solve the model.
Cite
@article{arxiv.cond-mat/0010400,
title = {High-Dimensional Diffusive Growth},
author = {M. B. Hastings and Thomas C. Halsey},
journal= {arXiv preprint arXiv:cond-mat/0010400},
year = {2009}
}
Comments
5 pages, 3 figures; reference added