Laplacian Growth and Diffusion Limited Aggregation: different universality classes
arXiv:cond-mat/0103126 · doi:10.1103/PhysRevLett.87.134501
Abstract
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.
4 pages, 4 figures
Cited by in corpus (15)
- 2D growth processes: SLE and Loewner chains
- Growth activity during fingering in a porous Hele Shaw cell
- Random Matrices in 2D, Laplacian Growth and Operator Theory
- Theory of Diffusion Controlled Growth
- Iterated Conformal Dynamics and Laplacian Growth
- Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III
- Random walks, diffusion limited aggregation in a wedge, and average conformal maps
- Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles
- Anisotropic Diffusion Limited Aggregation
- Statistical Physics of Fracture Surfaces Morphology
- Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
- Transition in the Fractal Properties from Diffusion Limited Aggregation to Laplacian Growth via their Generalization
- Theory of Diffusion Controlled Growth
- New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
- Diffusion Limited Aggregation with Power-Law Pinning