PMID: 11308922Apr 20, 2001Paper

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
B Kol, A Aharony

Abstract

Cylindrical lattice diffusion-limited aggregation, 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.

References

May 1, 1988·Physical Review A: General Physics·T Nagatani
Jul 1, 1989·Physical Review A: General Physics·S Tolman, P Meakin
Nov 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H KaufmanL Woog
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B DavidovitchI Procaccia
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B Kol, A Aharony

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Citations

Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sheng-You HuangZhun-Zhi Jin
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ellák SomfaiLeonard M Sander

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