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arXiv · 1008.1965

Loewner equation for Laplacian growth: A Schwarz-Christoffel-transformation approach

M. Durán·G. L. Vasconcelos
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Abstract

The problem of Laplacian growth is considered within the Loewner-equation framework. A new method of deriving the Loewner equation for a large class of growth problems in the half-plane is presented. The method is based on the Schwarz-Christoffel transformation between the so-called `mathematical planes' at two infinitesimally separated times. Our method not only reproduces the correct Loewner evolution for the case of slit-like fingers but also can be extended to treat more general growth problems. In particular, the Loewner equation for the case of a bubble growing into the half-plane is presented.

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M. Durán, G. L. Vasconcelos. 2010-08-11. Loewner equation for Laplacian growth: A Schwarz-Christoffel-transformation approach. https://doi.org/10.1088/1742-6596%2F246%2F1%2F012023

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