The Average Shape of Transport-Limited Aggregates
Abstract
We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear integro-differential equation for the asymptotic shape (average conformal map) of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation, where the interface moves at its local expected velocity. Our equation accurately describes advection-diffusion-limited aggregation (ADLA), and, due to nonlinear averaging over fluctuations, the average ADLA cluster is similar, but not identical, to an exact solution of the mean-field dynamics. Similar results should apply to all models in our class, thus explaining the known discrepancies between average DLA clusters and viscous fingers in a channel geometry.
Keywords
Cite
@article{arxiv.cond-mat/0506420,
title = {The Average Shape of Transport-Limited Aggregates},
author = {Benny Davidovitch and Jaehyuk Choi and Martin Z. Bazant},
journal= {arXiv preprint arXiv:cond-mat/0506420},
year = {2009}
}