由Hastings-Levitov方法生成的扩散限制聚集（DLA）周长的标度和多标度行为
Scaling and Multiscaling Behavior of the Perimeter of Diffusion-Limited Aggregation (DLA) Generated by the Hastings-Levitov Method
摘要：
本文分析了用Hastings-Levitov方法模拟的\emph{Diffusion Limited Aggregation}（DLA）的标度行为。我们得到的分形维数的集群的直接分析的几何图案在一个很好的协议从解析方法获得。我们计算的两点密度关联函数，我们表明，在大尺寸的限制，它同意得到的分形维数。这些支持的模式和DLA集群之间的统计协议。我们还研究了与团簇边界有关的各种长度尺度的标度性质及其涨落。我们发现，所有的长度标度并不都有一个简单的标度，标度指数的修正是相同的。周长的分形维数等于团簇的分形维数。从等于$β=0.557(2)$的界面宽度的演变计算生长指数。我们还证明了DLA团簇的周长具有渐近多标度行为。
英文摘要：
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good agreement with one obtained from analytical approach. We compute the two-point density correlation function and we show that in the large-size limit, it agrees with the obtained fractal dimension. These support the statistical agreement between the patterns and DLA clusters. We also investigate the scaling properties of various length scales and their fluctuations, related to the boundary of cluster. We find that all of the length scales do not have a simple scaling with same correction to scaling exponent. The fractal dimension of the perimeter is obtained equal to that of the cluster. The growth exponent is computed from the evolution of the interface width equal to $β=0.557(2)$. We also show that the perimeter of DLA cluster has an asymptotic multiscaling behavior.
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