Diffusion limited aggregation as a Markovian process: site-sticking conditions

Details Diffusion limited aggregation as a Markovian process: site-sticking conditions Diffusion limited aggregation as a Markovian process: site-sticking conditions

2000-09-20

arxiv.org/abs/cond-mat/0009297v1

Physics

Condensed Matter

Statistical Mechanics

27 Revtex pages, 16 figures

Scientific paper

10.1103/PhysRevE.63.046117

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the probabilities that the front moves from one configuration to another at each growth step, calculated exactly by solving the Laplace equation and using the proper normalization. The method is applied for a series of approximations, which include only a finite number of rows near the front. The fractal dimensionality of the aggregate is extrapolated to a value near 1.68.

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