Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters

Abstract

Diffusion Limited Aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding boundary of the fractal cluster. The theory is applicable from very small (2-3 particles) to asymptotically large (n \to \infty) clusters. The computed dimension is D=1.713\pm 0.003.

References in corpus (1)

• Conformal Theory of the Dimensions of Diffusion Limited Aggregates

Cited by in corpus (24)

• Growth activity during fingering in a porous Hele Shaw cell
• Influence of pore-scale disorder on viscous fingering during drainage
• Log-periodic route to fractal functions
• Laplacian Growth and Diffusion Limited Aggregation: different universality classes
• Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates
• Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
• Growth Exponents with 3.99 Walkers
• Conformal approach to cylindrical DLA
• Scaling exponent of the maximum growth probability in diffusion-limited aggregation
• Iterated Conformal Dynamics and Laplacian Growth
• Void Formation and Roughening in Slow Fracture
• Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps
• Bi-Laplacian Growth Patterns in Disordered Media
• The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events
• Statistical Physics of Fracture Surfaces Morphology
• Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
• Variable size particle probing of the DLA cluster properties
• Transition in the Fractal Properties from Diffusion Limited Aggregation to Laplacian Growth via their Generalization
• The dimension of Diffusion Limited Aggregates grown on a line
• New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
• Scaling and Multiscaling Behavior of the Perimeter of Diffusion-Limited Aggregation (DLA) Generated by the Hastings-Levitov Method
• The Harmonic Measure for critical Potts clusters
• Scaling properties of viscous fingering
• The fractal dimensions of Laplacian growth: an analytical approach based on a universal dimensionality function