Short-wavelength instability and transition to chaos in distributed systems with additional symmetry

A review is presented of the theory of pattern formation in extended, dissipative, highly nonequilibrium systems. Emphasis is placed on systems which, in addition to spatial translations and rotations, have additional continuous symmetry group(s). It is shown that the additional symmetry destabilizes dramatically the ground state of the system thus causing it to make a direct transition from a spatially uniform to a turbulent state in an analogous fashion to the second-order phase transition in quasi-equilibrium systems. Apart from the theoretical analysis, a discussion of experimental data is given.

PACS: 05.45.+b, 47.52.+j
DOI: 10.1070/PU1997v040n02ABEH000193
URL: https://ufn.ru/en/articles/1997/2/c/
Web of Science

A1997WT28000003
Citation: Tribel’skii M I "Short-wavelength instability and transition to chaos in distributed systems with additional symmetry" Phys. Usp. 40 159–180 (1997)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Трибельский М И «Коротковолновая неустойчивость и переход к хаосу в распределенных системах с дополнительной симметрией» УФН 167 167–190 (1997); DOI: 10.3367/UFNr.0167.199702c.0167

References (74) Cited by (40) Similar articles (20) ↓

V.S. Anishchenko, T.E. Vadivasova et al “Statistical properties of dynamical chaos” Phys. Usp. 48 151–166 (2005)
B.S. Kerner, V.V. Osipov “Autosolitons” Sov. Phys. Usp. 32 101–138 (1989)
A. Loskutov “Fascination of chaos” Phys. Usp. 53 1257–1280 (2010)
A.F. Volkov, Sh.M. Kogan “Physical phenomena in semiconductors with negative differential conductivity” Sov. Phys. Usp. 11 881–903 (1969)
B.I. Ivlev, N.B. Kopnin “Theory of current states in narrow superconducting channels” Sov. Phys. Usp. 27 206–227 (1984)
V.I. Klyatskin, D. Gurarie “Coherent phenomena in stochastic dynamical systems” Phys. Usp. 42 165 (1999)
V.P. Skripov, A.V. Skripov “Spinodal decomposition (phase transitions via unstable states)” Sov. Phys. Usp. 22 389–410 (1979)
B.S. Kerner, V.V. Osipov “Self-organization in active distributed media: scenarios for the spontaneous formation and evolution of dissipative structures” Sov. Phys. Usp. 33 (9) 679–719 (1990)
V.S. Anishchenko, A.B. Neiman et al “Stochastic resonance: noise-enhanced order” Phys. Usp. 42 7–36 (1999)
V.V. Zosimov, L.M. Lyamshev “Fractals in wave processes” Phys. Usp. 38 347–384 (1995)
A.I. Olemskoi, I.V. Koplyk “The theory of spatiotemporal evolution of nonequilibrium thermodynamic systems” Phys. Usp. 38 1061–1097 (1995)
K.N. Alekseev, G.P. Berman et al “Dynamical chaos in magnetic systems” Sov. Phys. Usp. 35 (7) 572–590 (1992)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)
N.A. Veretenov, N.N. Rosanov, S.V. Fedorov “Laser solitons: topological and quantum phenomena” Phys. Usp. 65 131–162 (2022)
A.G. Merzhanov, Rumanov É N “Nonlinear effects in macroscopic kinetics” Sov. Phys. Usp. 30 293–316 (1987)
F.M. Kuni, A.K. Shchekin, A.P. Grinin “Theory of heterogeneous nucleation for vapor undergoing a gradual metastable state formation” Phys. Usp. 44 331–370 (2001)
M.I. Rabinovich, M.M. Sushchik “The regular and chaotic dynamics of structures in fluid flows” Sov. Phys. Usp. 33 (1) 1–35 (1990)
V.I. Tatarskii “Criteria for the degree of chaos” Sov. Phys. Usp. 32 450–451 (1989)
K.G. Selivanov “Counting vacua in supersymmetric Yang-Mills theory” Phys. Usp. 45 675–686 (2002)
M.I. Kaganov, A.V. Chubukov “Interacting magnons” Sov. Phys. Usp. 30 1015–1040 (1987)

The list is formed automatically.