Theory of Diffusion Controlled Growth

Abstract

We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. 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 discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new Screening Transition in the DBM at large eta.

12 pages, 9 figures; expanded version of cond-mat/0205660

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Cited by in corpus (4)

• 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
• Structural and computational depth of diffusion limited aggregation