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Reviews of topical problems


Application of fractals in condensed-matter physics

 a,
a Sumy State University, ul. Rimskogo-Korsakova 2, Sumy, 244007, Ukraine

Basic information about the theory of mono- and multifractal sets is presented. Geometric and thermodynamic descriptions are developed. The geometric picture is presented on the basis of the simplest examples of the Koch and Cantor fractal sets. An ultrametric space, representing the metric of a fractal set, is introduced on the basis of Cayley's hierarchical tree. The spectral characteristics of a multifractal formation are described. Attention is focused mainly on the application of the fractal concept for a thermodynamic system with partial memory loss, turbulent fluid flow, hierarchically coordinated set of statistical ensembles, Anderson's transition, and incommensurable and quasicrystalline structures.

Fulltext pdf (2 MB)
Fulltext is also available at DOI: 10.1070/PU1993v036n12ABEH002208
PACS: 64.60.Ak, 47.53.+n, 61.43.Hv, 61.44.−n (all)
DOI: 10.1070/PU1993v036n12ABEH002208
URL: https://ufn.ru/en/articles/1993/12/a/
Citation: Olemskoi A I, Flat A Ya "Application of fractals in condensed-matter physics" Phys. Usp. 36 (12) 1087–1128 (1993)
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Оригинал: Олемской А И, Флат А Я «Использование концепции фрактала в физике конденсированной среды» УФН 163 (12) 1–50 (1993); DOI: 10.3367/UFNr.0163.199312a.0001

References (60) ↓ Cited by (108) Similar articles (20)

  1. Mandelbrot B B Science 155 636 (1967)
  2. Mandelbrot B B The Fractal Geometry Of Nature (Freeman, New York, 1982)
  3. Feder E Fractals (Plenum Press, New York, 1988)
  4. Pietronero L and E Tosatti [Eds] Fractals In Physics (North-Holland, N.Y., 1986)
  5. Smirnov B M Physics Of Fractal Clusters [in Russian] (Nauka, Moscow, 1991)
  6. Smirnov B M Usp. Fiz. Nauk 149 177 (1986); Smirnov B M Sov. Phys. Usp. 29 481 (1986)
  7. Jullien R Comm. Mod. Phys. Part B Vol. 13 (4) 177–205 (1987)
  8. McCauley J L Phys. Rep. 189 225 (1990)
  9. Paladin G and A Vulpiani Phys. Rep. 156 147 (1987)
  10. Halsey T C, M N Jensen, L P Kadanoff, I Procaccia, and B I Shraiman Phys. Rev. A 33 1141 (1986)
  11. Levine D and P J Steinhardt Phys. Rev. B 34 596 (1986); Socolar J E and P J Steinhardt Phys. Rev. B 34 617 (1986)
  12. Structural Levels Of Plastic Strain And Fracture [in Russian] (Nauka, Novosibirsk, 1990)
  13. Synergetics And Fatigue Fracture Of Metals [in Russian] (Nauka, Moscow, 1989)
  14. Panin V E, V A Likhachev, and Yu V Grinyaev Structural Levels Of Deformation Of Solids [in Russian] (Nauka, Novosibirsk, 1985)
  15. Olemskoi A I and I A Sklyar Usp. Fiz. Nauk. 162 29 (1992); Olemskoi A I and I A Sklyar Sov. Phys. Usp. 35 455 (1992)
  16. Nigmatullin R R Teor. Matem. Fiz. 90 354 (1992)
  17. Rammal R, G Toulouse, and M A Virasoro Rev. Mod. Phys. 58 765 (1986)
  18. Binder K and A P Joung Rev. Mod. Phys. 58 801 (1986)
  19. Ginzburg S L Irreversible Phenomena In Spin Glasses [in Russian] (Nauka, Moscow, 1989)
  20. Olemskoi A I and E A Toropov Fiz. Met. Metalloved. 9 5 (1991)
  21. Olemskoi A I Fiz. Tverd. Tela 30 3384 (1988); Olemskoi A I Sov. Phys. Solid State 30 30, 1944 (1988)
  22. Olemskoi A I and I I Naumov in Ref. 13 p. 200
  23. Olemskoi A I Fiz. Met. Metalloved. 68 56 (1989)
  24. Olemskoi A I and Yu I Paskal’ Preprint No. 30 (Institute of Physics and Applied Mathematics, Tomsk Affiliate of the Siberian Branch of the USSR Academy of Sciences, Tomsk, 1988)
  25. Olemskoi A I and E A Toropov Fiz. Met. Metalloved., No. 7 32 (1991)
  26. Adelman D, C P Burmester, L T Wille, P A Sterne, and R Gronsky J. Phys.: Condensed Matter 4 L585 (1992)
  27. Kjems J and T Freltoft Scaling Phenomena In Disordered Systems (Plenum Press, New York, 1985)
  28. Porod G Small Angle X-Ray Scattering (Academic Press, New York, 1983)
  29. Samko S G, A A Kilbas, and O I Marichev Integrals And Derivatives Of Fractional Order And Their Applications [in Russian] (Nauka i tekhnika, Minsk, 1987)
  30. Forster D Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Functions (W. A. Benjamin, Reading, MA, 1975)
  31. Zubarev D N Nonequilibrium Statistical Thermodynamics [in Russian] (Nauka, Moscow, 1971)
  32. Olemskoi A I, I V Koplyk, I A Sklyar, E A Toropov, and A Ya Flat Izv. Vyssh. Uchebn. Zaved., Fiz. 1 90 (1993)
  33. Jonscher A K Dielectric Relaxation In Solids (Chelsea Dielectric Press, London, 1983)
  34. Landau L D and E M Lifshitz Statistical Physics (Pergamon Press, New York, 1977)
  35. Katsnel’son A A and A I Olemskoi Microscopic Theory Of Inhomogeneous Structures [in Russian] (Moscow State University Press, Moscow, 1987)
  36. Parisi G Phys. Rev. Lett. 50 1946 (1983)
  37. Landau L D and E M Lifshitz Fluid Mechanics (Pergamon Press, New York, 1989)
  38. Feigenbaum M J J. Stat. Phys. 19 25 (1978); Feigenbaum M J J. Stat. Phys. 21 668 (1979)
  39. Abramovitz M and I Stegan [Eds] Handbook Of Special Functions (Dover Press, New York)
  40. Haken H Synergetics (Springer-Verlag, New York, 1983); Haken H Advanced Synergetics: Instability Hierarchies Of Self-Organizing Systems And Devices (Springer-Verlag, New York, 1983)
  41. Bak P Rep. Prog. Phys. 45 587 (1981)
  42. Jensen M H and P Bak Phys. Rev. A 30 1960, 1970 (1984)
  43. Svitanovic P, M H Jensen, L P Kadanoff, and I Procaccia Phys. Rev. Lett. 55 343 (1985)
  44. Shenker S J Physica D 5 405 (1982)
  45. Anderson P W Phys. Rev. 109 1492 (1958)
  46. Disordered Systems And Localization. Lecture Notes In Physics Vol. Vol. 149 (Springer-Verlag, New York, 1981)
  47. Derrida B and E Gardner J. De Phys. Paris 45 1283 (1984)
  48. Parisi G and A Vulpiani J. Phys. A. 19 L425 (1986)
  49. Olemskoi A I Phys. Status Solidi 160 569 (1990)
  50. Lifshitz E M and L P Pitaevskii Physical Kinetics [in Russian] (Nauka, Moscow, 1979)
  51. Wilson K G and J Kogut Phys. Rep. C 12 75 (1974)
  52. Patashinskii A Z and V L Pokrovskii Fluctuation Theory Of Phase Transitions (Pergamon Press, N.Y., 1979)
  53. Aksenov V L, M Bobeth, N M Plakida, and I Schreiber J. Phys. C. 20 375 (1987)
  54. Mezard M and M A Virasoro J. De Phys. Paris 46 1293 (1985)
  55. Palmer R G Adv. Phys. 31 669 (1982)
  56. Serva M and G Paladin Phys. Rev. Lett. 70 105 (1993)
  57. Parisi G J. Phys. A 13 1101 (1980)
  58. Bell J M, N E Frankel, and S Inawashiro Phys. Rev. B 33 476, 487 (1986)
  59. Gnedenko V V Course In Probability Theory [in Russian] (Nauka, Moscow, 1988)
  60. Amit D J, H Gutfreund, and H Sompolinsky Ann. Phys. 173 30 (1987)
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