Fractal Properties of “Disordered Surfaces” and The Termite Problem View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1991

AUTHORS

H. Eugene Stanley , A. Bunde , A. Coniglio , D. C. Hong , P. Meakin , T. A. Witten

ABSTRACT

In this second lecture, I shall turn to the topic of fractal surfaces, for which knowledge of only “the” fractal dimension df is not sufficient to describe the essential physics. In fact, we must distinguish between the entire external perimeter or “hull,” with its corresponding fractal dimension dh, and the unscreened portion of the external perimeter and its fractal dimension d. A very simple argument gives rise to an expression for du in terms of df and dp, the fractal dimension of the particles used to probe the surface. We shell see that the concept of the unscreened perimeter is at the heart of transport in a two-component random medium made up of superconductors and normal resistors. In particular, the exponent \(\tilde s = s/v\) for characterizing the divergence of the macroscopic conductivity at the percolation threshold pc is identically equal to du. More... »

PAGES

307-333

References to SciGraph publications

Book

TITLE

Scaling Phenomena in Disordered Systems

ISBN

978-1-4757-1404-3
978-1-4757-1402-9

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4757-1402-9_26

DOI

http://dx.doi.org/10.1007/978-1-4757-1402-9_26

DIMENSIONS

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36 schema:description In this second lecture, I shall turn to the topic of fractal surfaces, for which knowledge of only “the” fractal dimension df is not sufficient to describe the essential physics. In fact, we must distinguish between the entire external perimeter or “hull,” with its corresponding fractal dimension dh, and the unscreened portion of the external perimeter and its fractal dimension d. A very simple argument gives rise to an expression for du in terms of df and dp, the fractal dimension of the particles used to probe the surface. We shell see that the concept of the unscreened perimeter is at the heart of transport in a two-component random medium made up of superconductors and normal resistors. In particular, the exponent \(\tilde s = s/v\) for characterizing the divergence of the macroscopic conductivity at the percolation threshold pc is identically equal to du.
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