Unpublished Paper
Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters
(2011)
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 (n⃗ ∞) clusters. The computed dimension is D=1.713±0.003.
Disciplines
Publication Date
June 20, 2011
Comments
Pre-published version from archive ArXiv. The published version is located at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.62.R5919
Citation Information
Benny Davidovitch, Anders Levermann and Itamar Procaccia. "Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters" (2011) Available at: http://works.bepress.com/benny_davidovitch/8/