Laplacian Growth and Diffusion Limited Aggregation: different universality classes

Details Laplacian Growth and Diffusion Limited Aggregation: different universality classes Laplacian Growth and Diffusion Limited Aggregation: different universality classes

2001-03-06

arxiv.org/abs/cond-mat/0103126v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.87.134501

It had been conjectured that Diffusion Limited Aggregates and Laplacian Growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a 1-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian Growth patterns from below. The bound value is higher than the dimension of Diffusion Limited Aggregates, showing that the two problems belong to two different universality classes.

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