Interface growth in two dimensions: A Loewner-equation approach

Details Interface growth in two dimensions: A Loewner-equation approach Interface growth in two dimensions: A Loewner-equation approach

2010-08-11

arxiv.org/abs/1008.1992v1

Physics

Condensed Matter

Statistical Mechanics

To appear in Physical Review E

Scientific paper

The problem of Laplacian growth in two dimensions is considered within the Loewner-equation framework. Initially the problem of fingered growth recently discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77, 041602 (2008)] is revisited and a new exact solution for a three-finger configuration is reported. Then a general class of growth models for an interface growing in the upper-half plane is introduced and the corresponding Loewner equation for the problem is derived. Several examples are given including interfaces with one or more tips as well as multiple growing interfaces. A generalization of our interface growth model in terms of ``Loewner domains,'' where the growth rule is specified by a time evolving measure, is briefly discussed.

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