Theory of Diffusion Controlled Growth

Abstract

We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.

4 pages, 3 figures, submitted to PRL

References in corpus (5)

• Radial DLA: two fractal dimensions and deviations from self-similarity
• Scaling and Crossovers in Diffusion Limited Aggregation
• Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates
• Laplacian Growth and Diffusion Limited Aggregation: different universality classes
• Off-lattice noise reduction and the ultimate scaling of DLA in two dimensions

Cited by in corpus (6)

• Conformal mapping methods for interfacial dynamics
• Scaling exponent of the maximum growth probability in diffusion-limited aggregation
• Diffusion-limited aggregation in channel geometry
• Random walks, diffusion limited aggregation in a wedge, and average conformal maps
• Growth by Random Walker Sampling, and Scaling of the Dielectric Breakdown Model
• Theory of Diffusion Controlled Growth