Random walks, diffusion limited aggregation in a wedge, and average conformal maps.
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.
Sander
Leonard M
LM
Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA. lsander@umich.edu
Somfai
Ellák
E
D016000:Cluster Analysis; D004058:Diffusion; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D011336:Probability