各向异性扩散控制聚集集团的豪斯道夫维数

THE HAUSDORFF DIMENSION OF DIFFUSION-LIMITED AGGREGATION CLUSTERS WITH ANISOTROPIC DIFFUSION

本文通过解析计算,给出了各向异性扩散控制聚集集团有效外半角β=min{β_x,β_y},修正了文献[1]关于有效外半角β=max{β_x,β_y}的假设,对各向异性扩散控制聚集集团的豪斯道夫维数D随各向异性扩散几率p的变化公式也作了相应的修正,并进行了计算机模拟实验,发现修正后的公式与实验符合较好,与Jullien等人的计算机模拟结果进行了比较,在p≥1/4时两者的结果是一致的。

We obtain effective exterion half angle of the anisotropic diffusion DLA clusters β= min {βx, βy} by analytical calculation. The hypothesis of Yu Jiang about β = max{βx,βy} is modified and the formula of Hausdorff dimension D of the anisotropic diffusion DLA clusters varying with the anisotropic diffusion probability p is also modified. We also made simulation tests and find that the modified formula agrees well with experimental results. Finally, we compare our result with the numerical result of Jullien, and find a good coincidence when