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.
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Literature Cited
Adam M, Delsanti M, Durand D, Hild G and Munch JP, 1981 Pure and Appl Chem 53 1489
Adler J, Aharony A and Stauffer D, 1985 J Phys A 18 L129
Aharony A and Stauffer D, 1984 Phys Rev Lett 52 2368
Alexander S, 1983 Ann Israel Phys Soc 5 149
Ben-Avraham D and Havlin S, 1982 J Phys A 15 L691
Bunde A, Herrmann HJ, Margolina A and Stanley HE, 1985a Phys Rev Lett 55 653
Bunde A, Herrmann HJ and Stanley HE, 1985b J Phys A 18 L523
Bunde A, Coniglio A, Hong DC and Stanley HE, 1985c J Phys A 18 L137
Coniglio A and Stanley HE, 1984 Phys Rev Lett 52 1068
DeArcangelis L, Redner S and Coniglio A 1985 Phys Rev. B 31 4725
Donsker MD and Varadhan SRS, 1975 Comm Pure Appl Math 28 1, 279, 525
Family F and Vicsek T, 1985 J Phys A 18 L75
Fisher ME, Ma SK and Nickel B, 1972 Phys Rev Lett 29 917
Gefen Y, Aharony A and Alexander S, 1983 Phys Rev Lett 50 77
de Gennes PG, 1976 La Recherche 7 919
de Gennes PG, 1980 J Phys (Paris) Colloq 41 C3 - C17
Halsey TC, Meakin P and Procaccia I ,1985 Phys Rev Lett (submitted)
Havlin S, 1984 Phys Rev Lett 53 1705
Havlin S, Djordjevic Z, Majid I, Stanley HE and Weiss GH, 1984 Phys Rev Lett 53 178
Hemmer S and Hemmer PC, 1984 J Chem Phys 81 584
Herrmann HJ and Stanley HE 1985 Z Phys B 36 (1 Sept)
Hong DC, Stanley HE, Coniglio A and Bunde A, 1985 Phys Rev B 32 xxx
Jullien R and Botet R, 1985 Phys Rev Lett 54 2055
Kertèsz J, 1983 J Phys A 16 L471
Kremer K and Lyklema JW, 1984 J Phys A 17 L691
Kunz H and Souillard B, 1978 J Stat Phys 19 77
Leyvraz F, 1985 J Phys A 18 xxx
Leyvraz F, Adler J, Aharony A, Bunde A, Coniglio A, Hong DC, Stanley HE and Stauffer D, 1985 J Phys A Lett 18 xxx
Leyvraz F and Stanley HE 1983 Phys Rev Lett 51 2048
Majid I, Jan N, Coniglio A and Stanley HE, 1984 Phys Rev Lett 52 1257
Margolina A, Nakanishi H, Stauffer D and Stanley HE, 1984 J Phys A 17 1683
Meakin P and Sander LM, 1985 Phys Rev Lett 54 2053
Meakin P, Stanley HE, Coniglio A and Witten TA, 1985 Phys Rev A 32 (1 Oct)
Peliti L 1984 J de Physique 45 L125
Plischke M and Racz Z, 1984 Phys Rev Lett 53 415
Rammal R and Toulouse G, 1983 J de Physique 44 L13
Sahimi M, 1985 J Phys A 18 1543
Sapoval B, Rosso M and Gouyet JF, 1985 J Physique Lett 46 L149
Stanley HE, Kang K,Redner S and Blumberg RL, 1983 Phys Rev Lett 51 1223
Stanley HE, Majid I, Margolina A and Bunde A, 1984 Phys Rev Lett 53 1706
Turkevich LA and Scher H, 1985 Phys Rev Let 55 xxx
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© 1991 Springer Science+Business Media New York
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Stanley, H.E., Bunde, A., Coniglio, A., Hong, D.C., Meakin, P., Witten, T.A. (1991). Fractal Properties of “Disordered Surfaces” and The Termite Problem. In: Pynn, R., Skjeltorp, A. (eds) Scaling Phenomena in Disordered Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1402-9_26
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