Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation

概要

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Diffusion-limited aggregation (DLA) model is generalized to incorporate the dielec-tric breakdown model proposed by Niemeyer et at. , and the new simulation method isproposed. While a growing cluster is still in the diffusion (Laplace) field, the localgrowth probability at a perimeter site P,. of the cluster is now given by p.(P,.)- l rC(7'..) l ', where cp(P) is the probability of finding at a point P a random walkerlaunched far away from the cluster. Ordinary DLA corresponds to 77=1. Based onthe theory of DLA proposed by Honda et al., the fractal dimension d, for thisgeneralized DLA is derived as d,=gd:A-r7(d. -1)}/{d.-l-7(V. -1)}, where d. is thedimension of space in which aggregation processes take place and d. is the fractaldimension of random walker trajectory. Both d. and d. are allowed to take anynumber larger than or equal to one. This formula is also applicable to Eden model(77=0) correctly, which means that the generalized DLA model naturally bridges agap between ordinary DLA and Eden models.
社団法人日本物理学会の論文
1986-08-15