Anomalous diffusion on random fractal composites
Anomalous diffusion on random fractal composites
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随机分形复合材料上的反常扩散
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Tarafdar
中科院分区：
文献类型：
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作者：
D. N. Anh;P. Blaudeck;K. H. Hoffmann;Janett Prehl;S. Tarafdar
由确定性分形图的组合生成的随机分形图的优点是在某种程度上易于处理，但也更接近真实材料，因为它们是部分无序的。在目前的工作中，我们的注意力集中在两个不同的Sierpinski地毯生成器的随机组合产生的分形所表现出的显著的非线性混合行为。当具有不同反常扩散指数和相同或不同分维的图案组合在一起时，有效扩散指数一般不能表示为各组分的扩散指数的线性加权平均。对于某些成分，有效指数可以显示最大值或最小值。对这一有趣现象的解释是基于地毯生成器的详细信息，特别是关于“连接点”的数量和位置，这些连接点决定了“分形复合体”的连通性。
Stochastic fractals, generated from combinations of deterministic fractals, have the advantage of being tractable to some extent, but also being closer to real materials, since they are partially disordered. In the present work, we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different Sierpinski carpet generators. When patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together, the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents. The effective exponent may show a maximum or minimum for certain compositions. An explanation of this interesting phenomenon is offered on the basis of details of the carpet generator, particularly on the number and position of ‘connection points’, which determine the connectivity of the ‘fractal composite’.