有限分枝Sierpinski地毯的阻力缩放和随机行走尺寸

SIGSAM Bull. Pub Date : 2000-09-01 DOI:10.1145/377604.377608

C. Schulzky, A. Franz, K. Hoffmann

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引用次数: 23

摘要

提出了一种计算有限分枝Sierpinski地毯随机行走维数的新算法。分形结构被解释为一个电阻网络，其电阻缩放指数是用Mathematica计算的。爱因斯坦关系的分形形式，将扩散与导电性联系起来，用来给出随机游走维度的数值。

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Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets

We present a new algorithm to calculate the random walk dimensionof finitely ramified Sierpinski carpets. The fractal structure isinterpreted as a resistor network for which the resistance scalingexponent is calculated using Mathematica. A fractal form of theEinstein relation, which connects diffusion with conductivity, isused to give a numerical value for the random walk dimension.

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SIGSAM Bull.

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