Diffusion limited aggregation and its response to anisotropy
Ball, Robin. (1986) Diffusion limited aggregation and its response to anisotropy. Physica A: Statistical Mechanics and its Applications, Vol.140 (No.1-2). pp. 62-69. ISSN 0378-4371Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/0378-4371(86)90205-0
The stability of diffusion limited growths with n equivalent major fingers is investigated in two dimensions using a conformal mapping. The results imply that square lattice but not hexagonal lattice bias are relevant in simple Diffusion Limited Aggregation (DLA). In general it is found that the maximum number of fingers stable with respect to finger loss by competition is given by , where D is the apparent fractal dimension of the fingers, at least when n is even.
Computer simulations of DLA with n-fold symmetric growth rules are shown for n = 5−8, 12.
Finally it is argued that (unbiased) isotropic fractal DLA should lie at the stability limit. When combined with cone angle arguments independently relating D to the effective numbers of fingers, this determines the value … for DLA in two dimensions. This corresponds to a characteristic exterior half angle at the leading tips given by .
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Physics|
|Journal or Publication Title:||Physica A: Statistical Mechanics and its Applications|
|Publisher:||Elsevier BV * North-Holland|
|Page Range:||pp. 62-69|
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