Field Theory Analysis of Laplacian Growth Models

Details Field Theory Analysis of Laplacian Growth Models Field Theory Analysis of Laplacian Growth Models

2004-10-04

arxiv.org/abs/cond-mat/0410071v1

Physics

Condensed Matter

Soft Condensed Matter

PhD thesis

Scientific paper

We consider Laplacian growth problems using a field theory approach. In particular we consider the Saffman-Taylor (ST) problem. The idealized settings of the problem, with vanishing surface tension between the bubble and the surrounding fluid, is singular due to the formation of cusps after a finite time (for generic initial conditions). A natural regularization of the cusp, is the addition of surface tension, but this complicates the mathematical description of the problem a great deal. We discuss a different method of regularization which arises from the relation of the ST problem with integrable systems and matrix models.

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