Reviews of topical problems

Minimal chaos, stochastic webs, and structures of quasicrystal symmetry

The relationship between the problem of the symmetry of a plane tiling and the properties of nonintegrable dynamic systems is reviewed. The formation of stochastic layers and a stochastic web in the motion of linear and nonlinear oscillators subjected to a perturbation is discussed in detail. Emphasis is placed on research on the symmetry properties of a stochastic web with a fractal structure of a quasicrystal type. Structures with a quasicrystal symmetry form as a result of an interaction of two types of symmetries: translational and rotational. Various characteristics of structures with a quasicrystal symmetry are discussed: the distributions of stable and unstable points, the state density, and the Fourier spectrum. Quasicrystal structures in solid state physics, hydrodynamics, botany, and ornamental art are discussed.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1988v031n10ABEH005632
PACS: 61.44.Br, 05.45.Df (all)
DOI: 10.1070/PU1988v031n10ABEH005632
Citation: Zaslavskii G M, Sagdeev R Z, Usikov D A, Chernikov A A "Minimal chaos, stochastic webs, and structures of quasicrystal symmetry" Sov. Phys. Usp. 31 887–915 (1988)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Заславский Г М, Сагдеев Р З, Усиков Д А, Черников А А «Минимальный хаос, стохастическая паутина и структуры с симметрией типа „квазикристалл“» УФН 156 193–251 (1988); DOI: 10.3367/UFNr.0156.198810a.0193

References (83) Cited by (58) Similar articles (20) ↓

  1. M.V. Kalashnik, M.V. Kurgansky, O.G. Chkhetiani “Baroclinic instability in geophysical fluid dynamics65 1039–1070 (2022)
  2. K.V. Koshel, S.V. Prants “Chaotic advection in the ocean49 1151–1178 (2006)
  3. O.G. Onishchenko, O.A. Pokhotelov et alStructure and dynamics of concentrated mesoscale vortices in planetary atmospheres63 683–697 (2020)
  4. B.M. Smirnov “Electrical cycle in the Earth’s atmosphere57 1041–1062 (2014)
  5. A.N. Vulfson, O.O. Borodin “The system of convective thermals as a generalized ensemble of Brownian particles59 109–120 (2016)
  6. F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin “Stability and vortex structures of quasi-two-dimensional shear flows33 (7) 495–520 (1990)
  7. O.G. Onishchenko, O.A. Pokhotelov, N.M. Astaf’eva “Generation of large-scale eddies and zonal winds in planetary atmospheres51 577–589 (2008)
  8. G.M. Zaslavskii, B.V. Chirikov “Stochastic instability of non-linear oscillations14 549–568 (1972)
  9. V.M. Fedorov “Problems of parameterization of the radiation block in physical and mathematical climate models and the possibility of their solution66 914–930 (2023)
  10. Yu.Kh. Vekilov, M.A. Chernikov “Quasicrystals53 537–560 (2010)
  11. L.Kh. Ingel, M.V. Kalashnik “Nontrivial features in the hydrodynamics of seawater and other stratified solutions55 356–381 (2012)
  12. A. Loskutov “Fascination of chaos53 1257–1280 (2010)
  13. S.S. Abdullaev, G.M. Zaslavskii “Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media34 (8) 645–664 (1991)
  14. A.S. Monin “Hydrodynamic instability29 843–868 (1986)
  15. V.S. Anishchenko, T.E. Vadivasova et alStatistical properties of dynamical chaos48 151–166 (2005)
  16. A.A. Chernyshov, K.V. Karelsky, A.S. Petrosyan “Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas57 421–452 (2014)
  17. B.F. Gordiets, V.Ya. Panchenko “Gas lasers with solar excitation29 703–719 (1986)
  18. Yu.L. Klimontovich “Nonlinear Brownian motion37 737–766 (1994)
  19. A.L. Virovlyansky, D.V. Makarov, S.V. Prants “Ray and wave chaos in underwater acoustic waveguides55 18–46 (2012)
  20. S.V. Bulanov, Ja.J. Wilkens et alLaser ion acceleration for hadron therapy57 1149–1179 (2014)

The list is formed automatically.

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: Editorial office contacts About the journal Terms and conditions