English

Theory of Diffusion Controlled Growth

Statistical Mechanics 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.cond-mat/0205660,
  title  = {Theory of Diffusion Controlled Growth},
  author = {R. C. Ball and E. Somfai},
  journal= {arXiv preprint arXiv:cond-mat/0205660},
  year   = {2007}
}

Comments

4 pages, 3 figures, submitted to PRL

R2 v1 2026-07-22T10:37:38.493Z