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Theory of Diffusion Controlled Growth

R. C. Ball·E. Somfai
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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.

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BibTeXRIS

R. C. Ball, E. Somfai. 2002-05-31. Theory of Diffusion Controlled Growth. https://doi.org/10.1103/physrevlett.89.135503

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