Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

Leonard M Sander; Ellák Somfai

doi:10.1063/1.1876932

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Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

Leonard M Sander·Ellák Somfai

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Abstract

We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a nontrivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.

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Cluster Analysis Diffusion Models, Theoretical Nonlinear Dynamics Physics Probability Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S.Review

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Leonard M Sander, Ellák Somfai. 2005. Random walks, diffusion limited aggregation in a wedge, and average conformal maps.. https://doi.org/10.1063/1.1876932

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