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The Average Shape of Transport-Limited Aggregates

Benny Davidovitch·Jaehyuk Choi·Martin Z. Bazant
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Abstract

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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Benny Davidovitch, Jaehyuk Choi, Martin Z. Bazant. 2005-06-16. The Average Shape of Transport-Limited Aggregates. https://doi.org/10.1103/physrevlett.95.075504

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