Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation
Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation
复制标题
扩散限制聚集的概括和分形维数
DOI：
10.1143/jpsj.55.2618
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发表时间：
1986
影响因子：
1.7
通讯作者：
H. Kondo
中科院分区：
文献类型：
--
作者：
M. Matsushita;K. Honda;H. Toyoki;Y. Hayakawa;H. Kondo
将扩散限制聚集（DLA）模型推广到Niemeyer等人提出的介质击穿模型，提出了新的模拟方法。当一个生长的团簇仍然处于扩散（拉普拉斯）场中时，在团簇的周边位置P ps的局部生长概率现在由pg（P ps）给出|φ（P ps）|n，其中φ（P）是在点P找到一个远离群集发射的随机步行者的概率。普通DLA对应于η=1。在本田等人提出的DLA理论的基础上，导出了这种广义DLA的分形维数df ={ds 2 +η（dw-1）} / {ds +η（dw-1）}，其中ds是聚集过程发生的空间维数，dw是随机步行者轨迹的分形维数. d s和d w都可以取大于或等于1的任意数。该公式同样适用于Eden模型（η=0），这意味着广义DLA模型自然地弥补了与广义DLA模型之间的差距。
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 P ps of the cluster is now given by p g ( P ps )∼ | ∇φ( P ps ) | n , 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 d f for this generalized DLA is derived as d f ={ d s 2 +η( d w -1)} / { d s +η( d w -1)}, where d s is the dimension of space in which aggregation processes take place and d w is the fractal dimension of random walker trajectory. Both d s and d w 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 betw...