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arXiv · 0801.1349

Fingered growth in channel geometry: A Loewner equation approach

T. Gubiec·P. Szymczak
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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.

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BibTeXRIS

T. Gubiec, P. Szymczak. 2008-01-09. Fingered growth in channel geometry: A Loewner equation approach. https://doi.org/10.1103/physreve.77.041602

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