Mohammadi F, Saberi A A, Rouhani S
Department of Physics, Sharif University of Technology, PO Box 11155-9161, Tehran, Iran.
J Phys Condens Matter. 2009 Sep 16;21(37):375110. doi: 10.1088/0953-8984/21/37/375110. Epub 2009 Aug 21.
In this paper, we analyze the scaling behavior of a diffusion-limited aggregation (DLA) simulated by the Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns, in good agreement with one obtained from an 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 the cluster. We find that all of the length scales do not have a simple scaling with the 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 the DLA cluster has an asymptotic multiscaling behavior.
在本文中，我们分析了用黑斯廷斯 - 列维托夫方法模拟的扩散限制凝聚（DLA）的标度行为。我们通过直接分析几何图案获得团簇的分形维数，这与从解析方法得到的结果吻合良好。我们计算了两点密度关联函数，并表明在大尺寸极限下，它与所获得的分形维数一致。这些都支持了图案与DLA团簇之间的统计一致性。我们还研究了与团簇边界相关的各种长度尺度及其涨落的标度性质。我们发现并非所有长度尺度都具有相同的标度修正指数的简单标度。得到周长的分形维数与团簇的分形维数相等。从界面宽度的演化计算出生长指数为β = 0.557(2)。我们还表明DLA团簇的周长具有渐近多重标度行为。
