TY - JOUR
T1 - Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation
AU - Matsushita, Mitsugu
AU - Honda, Katsuya
AU - Toyoki, Hiroyasu
AU - Hayakawa, Yoshinori
AU - Kondo, Hiroshi
PY - 1986/8
Y1 - 1986/8
N2 - Diffusion-limited aggregation (DLA) model is generalized to incorporate the dielectric breakdown model proposed by Niemeyer et al., and the new simulation method is proposed. While a growing cluster is still in the diffusion (Laplace) field, the local growth probability at a perimeter site Pps of the cluster is now given by pg(Pps) ∼|∇φ(Pps)|η, where Φ(P) is the probability of finding at a point P a random walker launched far away from the cluster. Ordinary DLA corresponds to η=1. Based on the theory of DLA proposed by Honda et al., the fractal dimension df for this generalized DLA is derived as [formula omitted], where ds is the dimension of space in which aggregation processes take place and dw is the fractal dimension of random walker trajectory. Both ds and dw are allowed to take any number larger than or equal to one. This formula is also applicable to Eden model (η=0) correctly, which means that the generalized DLA model naturally bridges a gap between ordinary DLA and Eden models.
AB - Diffusion-limited aggregation (DLA) model is generalized to incorporate the dielectric breakdown model proposed by Niemeyer et al., and the new simulation method is proposed. While a growing cluster is still in the diffusion (Laplace) field, the local growth probability at a perimeter site Pps of the cluster is now given by pg(Pps) ∼|∇φ(Pps)|η, where Φ(P) is the probability of finding at a point P a random walker launched far away from the cluster. Ordinary DLA corresponds to η=1. Based on the theory of DLA proposed by Honda et al., the fractal dimension df for this generalized DLA is derived as [formula omitted], where ds is the dimension of space in which aggregation processes take place and dw is the fractal dimension of random walker trajectory. Both ds and dw are allowed to take any number larger than or equal to one. This formula is also applicable to Eden model (η=0) correctly, which means that the generalized DLA model naturally bridges a gap between ordinary DLA and Eden models.
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U2 - 10.1143/JPSJ.55.2618
DO - 10.1143/JPSJ.55.2618
M3 - Article
AN - SCOPUS:0000435257
VL - 55
SP - 2618
EP - 2626
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 8
ER -