The Average Shape of Transport-Limited Aggregates

Details The Average Shape of Transport-Limited Aggregates The Average Shape of Transport-Limited Aggregates

2005-06-16

arxiv.org/abs/cond-mat/0506420v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevLett.95.075504

We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear integro-differential equation for the asymptotic shape (average conformal map) of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation, where the interface moves at its local expected velocity. Our equation accurately describes advection-diffusion-limited aggregation (ADLA), and, due to nonlinear averaging over fluctuations, the average ADLA cluster is similar, but not identical, to an exact solution of the mean-field dynamics. Similar results should apply to all models in our class, thus explaining the known discrepancies between average DLA clusters and viscous fingers in a channel geometry.

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