Reviews of topical problems

Application of fractals in condensed-matter physics

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.

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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
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. V.V. Zosimov, L.M. Lyamshev “Fractals in wave processes38 347–384 (1995)
  2. V.V. Uchaikin “Self-similar anomalous diffusion and Levy-stable laws46 821–849 (2003)
  3. A.I. Olemskoi, I.A. Sklyar “Evolution of the defect structure of a solid during plastic deformation35 (6) 455–480 (1992)
  4. L.M. Zelenyi, A.V. Milovanov “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics47 749–788 (2004)
  5. M.I. Rabinovich, M.M. Sushchik “The regular and chaotic dynamics of structures in fluid flows33 (1) 1–35 (1990)
  6. V.P. Budaev, S.P. Savin, L.M. Zelenyi “Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features54 875–918 (2011)
  7. A.I. Olemskoi “Theory of stochastic systems with singular multiplicative noise41 269–301 (1998)
  8. A.I. Olemskoi, I.V. Koplyk “The theory of spatiotemporal evolution of nonequilibrium thermodynamic systems38 1061–1097 (1995)
  9. I.M. Sokolov “Dimensionalities and other geometric critical exponents in percolation theory29 924–945 (1986)
  10. A.V. Batunin “Fractal analysis and Feigenbaum universality in hadron physics38 609–622 (1995)
  11. E.P. Emets, A.E. Novoselova, P.P. Poluektov “In situ determination of the fractal dimensions of aerosol particles37 881–887 (1994)
  12. N.M. Astaf’eva “Wavelet analysis: basic theory and some applications39 1085–1108 (1996)
  13. E.F. Mikhailov, S.S. Vlasenko “The generation of fractal structures in gaseous phase38 253–271 (1995)
  14. V.I. Alkhimov “Excluded volume effect in statistics of self-avoiding walks37 527–561 (1994)
  15. G.V. Kozlov “Structure and properties of particulate-filled polymer nanocomposites58 33–60 (2015)
  16. B.M. Smirnov “Fractal clusters29 481–505 (1986)
  17. V.S. Dotsenko “Physics of the spin-glass state36 (6) 455–485 (1993)
  18. V.S. Dotsenko “Critical phenomena and quenched disorder38 457–496 (1995)
  19. I.R. Stakhovsky “Scale invariance of shallow seismicity and the prognostic signs of earthquakes60 472–489 (2017)
  20. V.I. Alkhimov “The self-avoiding walk problem34 (9) 804–816 (1991)

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