Fingered growth in channel geometry: A Loewner equation approach
Statistical Mechanics
2009-11-13 v1 Mathematical Physics
math.MP
Abstract
A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. In a recent paper, Carleson and Makarov used the deterministic Loewner equation to describe the evolution of such a system. We extend their approach to a channel geometry and show that the presence of the side walls has a significant influence on the evolution of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.
Cite
@article{arxiv.0801.1349,
title = {Fingered growth in channel geometry: A Loewner equation approach},
author = {T. Gubiec and P. Szymczak},
journal= {arXiv preprint arXiv:0801.1349},
year = {2009}
}