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Fractal Concepts for Disordered Systems: The Interplay of Physics and Geometry

  • H. Eugene Stanley

Abstract

One purpose of these three talks is to address the question of how fractal concepts provide a natural framework within which to discuss a range of phenomena occurring in disordered systems. A second purpose is to exemplify the degree to which the language of fractals motivates one to translate physical phenomena into geometric terms, thereby rendering complex problems more tractable.

Keywords

Fractal Dimension Random Walk Critical Exponent Minimum Path Percolation Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aharony A and Stauffer D 1984 Phys Rev Lett 52 2368CrossRefGoogle Scholar
  2. Alexander S and Orbach R 1982 J de Physique 43 L625CrossRefGoogle Scholar
  3. Barma M 1985 J Phys A 18 L277MathSciNetCrossRefGoogle Scholar
  4. Buckingham MJ and Fairbank WM 1961 In Prog Low Temp Phys Vol 3 (ed CJ Gorter) North-Holland, Amsterdam, p80Google Scholar
  5. Coniglio A 1981 Phys Rev Lett 46 250Google Scholar
  6. Coniglio A and Stanley HE 1984 Phys Rev Lett 52 1068Google Scholar
  7. Daccord G, Nittmann J and Stanley HE 1985a in On Growth and Form [Proc 1985 Cargése Nato ASI) Eds HE Stanley and N Ostrowsky ( Martinus Nijhoff, Amsterdam )Google Scholar
  8. Daccord G, Nittmann J and Stanley HE 1985b Proc Les Houches Conference on Finely Divided Metter Eds M Daoud and N Boccara ( Springer Verlag, Heidelberg )Google Scholar
  9. de Gennes PG 1976 La Recherche 7 919Google Scholar
  10. Grassberger P 1985 J Phys A 18 L215Google Scholar
  11. Havlin S and Ben-Avraham D 1983 J Phys A 16 L483Google Scholar
  12. Havlin S and Nossal R 1984 J Phys A 17 L427Google Scholar
  13. Herrmann HJ, Hong DC and Stanley HE 1984 J Phys A 17 L261 Herrmann HJ and Stanley HE 1985 to be submittedGoogle Scholar
  14. Meakin P 1985 in On Growth and Form [Proc 1985 Cargèse Nato ASI] Eds HE Stanley and N Ostrowsky ( Martinus Nijhoff, Amsterdam )Google Scholar
  15. Meakin P, Majid I, Havlin S and Stanley HE 1984 J Phys A 17 L975Google Scholar
  16. Meakin P and Stanley HE 1983 Phys Rev Lett 51 1457Google Scholar
  17. Meakin P and Stanley HE 1984 J Phys A 17 L173Google Scholar
  18. Nakanishi H and Stanley HE 1980 Phys Rev B 22 2466Google Scholar
  19. Nakanishi H and Stanley HE 1981 J Phys A 14 693Google Scholar
  20. Nittmann J, Daccord G and Stanley HE 1985 Nature 314 141 Pandey RB and Stauffer D 1983 Phys Rev Lett 51 527Google Scholar
  21. Pike R and Stanley HE 1981 J Phys A 14 L169Google Scholar
  22. Ritzenberg AL and Cohen RJ 1984 Phys Rev B 30 4038Google Scholar
  23. Sapoval B, Rosso M and Gouyet JF 1985 J Physique Lett 46 L149Google Scholar
  24. Stanley HE 1977 J Phys A 10 L211Google Scholar
  25. Stanley HE 1981 in Int Conf on Disordered Systems and Localization Eds C Castellani, C DiCastro and L Peliti ( Springer Verlag, Heidelberg )Google Scholar
  26. Stanley HE 1982a in Proc NATO Advanced Study Institute on Structural Elements in Statistical Mechanics and Particle Physics Eds K Fredenhagen and J Honerkamp ( Plenum Press, New York )Google Scholar
  27. Stanley HE 1982b in Physics as Natural Philosophy: Festschrift in Honor of Laszlo Tisza Eds A Shimony and H Feshbach ( MIT Press, Cambridge )Google Scholar
  28. Stanley HE 1982c Prog Physics (Beijing) 30 95Google Scholar
  29. Stanley HE 1983 J Phys Soc Japan Suppl 52 151Google Scholar
  30. Stanley HE 1984a in Kinetics of Aggregation and Gelation Eds F Family and D Landau ( North Holland, Amsterdam )Google Scholar
  31. Stanley HE 1984b J Stat Phys 36 843Google Scholar
  32. Stanley HE 1985 in Ency on Polymer Science ( Wiley, New York )MATHGoogle Scholar
  33. Stanley HE, Birgeneau RJ, Reynolds PJ and Nicoll JF 1976 J Phys C 9 L553Google Scholar
  34. Stanley HE and Coniglio A 1983 in Percolation Structures and Processes Eds G Deutscher, R Zallen and J Adler ( Adam Hilger, Bristol )Google Scholar
  35. Stanley HE and Coniglio A 1984 Phys Rev B 29 522MathSciNetCrossRefGoogle Scholar
  36. Stanley HE, Reynolds PJ, Redner S and Family F 1982 in Real-Space Renormalization Eds TW Burkhardt and JMJ van Leeuwen ( Springer Verlag, Heidelberg )Google Scholar
  37. Witten TA and Sander LM 1981 Phys Rev Lett 47 1499Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • H. Eugene Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA

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