Modelling porous structures by repeated Sierpinski carpets

Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law 〈 r...

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Bibliographic Details
Published in:Physica A 2001-03, Vol.292 (1), p.1-8
Main Authors: Tarafdar, Sujata, Franz, Astrid, Schulzky, Christian, Hoffmann, Karl Heinz
Format: Article
Language:English
Subjects:
Anomalous diffusion
Fractals
Random walk
Sierpinski carpets
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Summary:Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law 〈 r 2〉∼ t 2/ d w , where 〈 r 2〉 is the mean square distance covered in time t and d w >2 is the random walk dimension. The question is: How is the macroscopic diffusivity related to the characteristics of the small scale fractal structure, which is hidden in the large-scale homogeneous material? In particular, do structures with same d w necessarily lead to the same diffusion coefficient at the same iteration stage? The present paper tries to shed some light on these questions.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(00)00573-2