Fractals in wave processes

V.V. Zosimov^a, L.M. Lyamshev^b
^aResearch Institute of Applied Acoustics, Dubna, Moscow Region, Russian Federation
^bN.N. Andreev Acoustics Institute, Russian Academy of Sciences, ul. Shvernika 4, Moscow, 117036, Russian Federation

A review of fundamental results on fractal structure manifestation in wave processes is presented. Elastic properties and dispersion of fractal materials are discussed; their distribution density, and the shape of wave functions of their localised elastic oscillations, fractons. Examples of their application for the explanation of amorphic properties of solids are presented. Patterns of wave scattering and emission by fractal structures are examined. Principal methods of random signal analysis employed to reveal different fractal structures associated with these signals are described. Data on fractal properties of wave fields are discussed.

PACS: 47.35.+i, 47.52.+j, 47.53.+n, 61.43.Hv (all)
DOI: 10.1070/PU1995v038n04ABEH000080
URL: https://ufn.ru/en/articles/1995/4/a/
Web of Science

A1995RH54700001
Citation: Zosimov V V, Lyamshev L M "Fractals in wave processes" Phys. Usp. 38 347–384 (1995)

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Оригинал: Зосимов В В, Лямшев Л М «Фракталы в волновых процессах» УФН 165 361–402 (1995); DOI: 10.3367/UFNr.0165.199504a.0361

References (165) Cited by (67) Similar articles (20) ↓

M.I. Rabinovich, M.M. Sushchik “The regular and chaotic dynamics of structures in fluid flows” Sov. Phys. Usp. 33 (1) 1–35 (1990)
A.I. Olemskoi, A.Ya. Flat “Application of fractals in condensed-matter physics” Phys. Usp. 36 (12) 1087–1128 (1993)
B.M. Smirnov “Fractal clusters” Sov. Phys. Usp. 29 481–505 (1986)
E.P. Emets, A.E. Novoselova, P.P. Poluektov “In situ determination of the fractal dimensions of aerosol particles” Phys. Usp. 37 881–887 (1994)
B.M. Smirnov “Observational properties of ball lightning” Sov. Phys. Usp. 35 (8) 650–670 (1992)
E.F. Mikhailov, S.S. Vlasenko “The generation of fractal structures in gaseous phase” Phys. Usp. 38 253–271 (1995)
I.M. Sokolov “Dimensionalities and other geometric critical exponents in percolation theory” Sov. Phys. Usp. 29 924–945 (1986)
B.M. Smirnov “Processes involving clusters and small particles in a buffer gas” Phys. Usp. 54 691–721 (2011)
B.M. Smirnov “Metal nanostructures: from clusters to nanocatalysis and sensors” Phys. Usp. 60 1236–1267 (2017)
A. Loskutov “Fascination of chaos” Phys. Usp. 53 1257–1280 (2010)
V.V. Uchaikin “Self-similar anomalous diffusion and Levy-stable laws” Phys. Usp. 46 821–849 (2003)
S.S. Abdullaev, G.M. Zaslavskii “Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media” Sov. Phys. Usp. 34 (8) 645–664 (1991)
S.N. Gurbatov, A.I. Saichev, I.G. Yakushkin “Nonlinear waves and one-dimensional turbulence in nondispersive media” Sov. Phys. Usp. 26 857–876 (1983)
I.R. Stakhovsky “Scale invariance of shallow seismicity and the prognostic signs of earthquakes” Phys. Usp. 60 472–489 (2017)
G.R. Ivanitskii, A.A. Deev, E.P. Khizhnyak “Long-term dynamic structural memory in water: can it exist?” Phys. Usp. 57 37–65 (2014)
G.V. Kozlov, V.U. Novikov “A cluster model for the polymer amorphous state” Phys. Usp. 44 681–724 (2001)
V.S. Anishchenko, A.B. Neiman et al “Stochastic resonance: noise-enhanced order” Phys. Usp. 42 7–36 (1999)
A.I. Olemskoi, I.A. Sklyar “Evolution of the defect structure of a solid during plastic deformation” Sov. Phys. Usp. 35 (6) 455–480 (1992)
A.V. Batunin “Fractal analysis and Feigenbaum universality in hadron physics” Phys. Usp. 38 609–622 (1995)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)

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