Diffusion-limited aggregation and the Saffman-Taylor problem
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TL;DR
A random-walk model is proposed to simulate Darcy-law two-dimensional flows in hydrodynamics in the limit of zero-surface tension and it is clear that the mean-field .limit of diffusion-limited aggregation is a Saffman-Taylor problem.
Abstract
A random-walk model is proposed to simulate Darcy-law two-dimensional flows in hydrodynamics in the limit of zero-surface tension. The simulation is compared with the analytic and numerical results of the latter in steady-state and dynamic cases, respectively. The instabilities of the model in a flat interface are studied in the linear region. It is clear that the mean-field limit of diffusion-limited aggregation is a Saffman-Taylor problem.