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)
BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks
PT Journal Article
TI Application of fractals in condensed-matter physics
AU Olemskoi A I
FAU Olemskoi AI
AU Flat A Ya
DP 10 Dec, 1993
TA Phys. Usp.
VI 36
IP 12
PG 1087-1128
RX 10.1070/PU1993v036n12ABEH002208
SO Phys. Usp. 1993 Dec 10;36(12):1087-1128

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

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