各向异性扩散DLA的标度性质

THE SCALING PROPERTIES OF DLA CLUSTERS WITH ANISOTROPIC DIFFUSION

本文利用坐标变换的方法讨论了各向异性扩散对DLA集团标度行为的影响。对二维正方形点阵,解析计算了各向异性扩散DLA集团的Hausdorff维数。结果表明,此时生长集困的Hausdorff维数D随各向异性扩散概率p连续变化,其最大值为5/3,最小值为3/2,还将这里所得到的理论结果与Jullien等人的数值结果进行了比较,发现它们符合得很好。最后,还解析讨论并计算了各向异性扩散DLA的广义维数D_q(p)。

We present a coordinate transformation approach to study the effect of anisotropic diffusion-on the growth of DLA clusters. For two-dimensional square lattice, we calculate analytically the Hausdorff dimension of the anisotropic diffusive DLA clusters, and show that the Hausdorff dimension D varies continuously with the anisotropic diffusion probability p, with Dmax = 5/3 and Dmin = 3/2. We also compare our results with the numerical results of Jullien et al., and find a very good coincidence. Finally, we discuss analytically the generalized dimensions Dq for DLA clusters with anisotropic diffusion.