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Reviews of topical problems


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


Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Tokyo, 153, Japan

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.

Fulltext pdf (732 KB)
Fulltext is also available at DOI: 10.1070/PU1997v040n02ABEH000193
PACS: 05.45.+b, 47.52.+j
DOI: 10.1070/PU1997v040n02ABEH000193
URL: https://ufn.ru/en/articles/1997/2/c/
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)
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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

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  12. Ohnogi H, Shiwa Y Phys. Rev. E 84 (1) (2011)
  13. Xiao Qing-kun, Gao Hong-jun Appl. Math. Mech.-Engl. Ed. 31 739 (2010)
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  16. Ohnogi H, Shiwa Y Physica D: Nonlinear Phenomena 237 3046 (2008)
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  18. Kudryashov N A, Migita A V Fluid Dyn 42 463 (2007)
  19. Sakaguchi H, Tanaka D Phys. Rev. E 76 (2) (2007)
  20. Naugolnykh K A, Rybak S A Acoust. Phys. 53 417 (2007)
  21. Golovin A A, Voorhees P W, Davis S H NATO Science Series II: Mathematics, Physics And Chemistry Vol. Advances in Sensing with Security ApplicationsSELF-ASSEMBLY OF QUANTUM DOTS FROM THIN SOLID FILMS218 Chapter 04 (2006) p. 123
  22. Dunin S Z, Mikhailov D N, Nikolayevskii V N Journal Of Applied Mathematics And Mechanics 70 251 (2006)
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  24. Tanaka D Phys. Rev. E 70 (1) (2004)
  25. Glasman E A, Golovin A A, Nepomnyashchy A A SIAM J. Appl. Math. 65 230 (2004)
  26. Maruno Ken-ichi, Ankiewicz A, Akhmediev N Physica D: Nonlinear Phenomena 176 44 (2003)
  27. Golovin A A, Matkowsky B J, Nepomnyashchy A A Physica D: Nonlinear Phenomena 179 183 (2003)
  28. Ankiewicz A, Maruno Ken-ichi, Akhmediev N Physics Letters A 308 397 (2003)
  29. Tanaka D, Kuramoto Y Phys. Rev. E 68 (2) (2003)
  30. Golovin A A, Davis S H, Voorhees P W Phys. Rev. E 68 (5) (2003)
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  32. Ankiewicz A, Maruno K, Akhmediev N Nonlinear Guided Waves and Their Applications, (2002) p. NLMD33
  33. Khomeriki R, Lepri S, Ruffo S Phys. Rev. E 64 (5) (2001)
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  37. Xi Hao-wen, Toral R et al Phys. Rev. E 62 R17 (2000)
  38. Matthews P C, Cox S M Phys. Rev. E 62 R1473 (2000)
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