Dynamics of Defects and Onset of Spatial Chaos in One-Dimensional Systems

  • A. A. Nepomnyashchy
Part of the Research Reports in Physics book series (RESREPORTS)


It is known that dissipative structures are often spatially disordered. An example is the Rayleigh-Benard convection in the horizontal fluid layer for which the complicated textures, including the domains with twisted rolls separated by domain walls, dislocations, disclinations and other types of defects are typical /1/. In this paper we consider some simple systems governed by the one-dimensional equations which enable to describe analytically the dynamics of the defects and the onset of spatial chaos.


Domain Wall Rayleigh Number Amplitude Equation Horizontal Fluid Layer Spatial Chaos 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cellular structure in instabilities. Lect. Notes in Phys., 210, Springer, Berlin e.a., 1984.Google Scholar
  2. 2.
    S. Aubry. The twist map, the extended Frenkel-Kontorova model and the devil’s staircase. Physica D, 1983, v.7, No.1–3, 240–258.CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    S.E. Burkov, V.L. Pokrovsky, G. Uimin. Soliton structures in a discrete chain. J. Phys. A., 1982, v.15, No.11, L 645–L 648.CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    M.H. Jensen, P. Bak. Mean-field theory of the three-dimensional anisotropic Ising model as a four-dimensional mapping. Phys. Rev. B, 1983, V.27, No.11, 6853–6868.CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    P.I. Belobrov, A.G. Tret’yakov, G.M. Zaslavsky. Methods of nonlinear dynamics and equilibrium structures of magnetoelastic chains. J.Stat. Phys., 1985, v.38, No.1–2, 383–404.ADSGoogle Scholar
  6. 6.
    A.J. Lichtenberg, M.A. Lieberman. Regular and stochastic motion. Springer, Berlin e.a., 1983.MATHGoogle Scholar
  7. 7.
    D.W. McLaughlin, A.C. Scott. In: Solitons in Action. Academic Press, New York e.a., 1978.MATHGoogle Scholar
  8. 8.
    V.I. Karpman, N.A. Ryabova, V.V. Solov’ev. Fluxon interactions in long Josephson junctions. Zhurnal Eksperimentalnyi i Teoreticheskoy Fiziki, 1981, v.81, pt.4(10), 1327–1336 (in Russian).Google Scholar
  9. 9.
    P. Coullet, C. Elphick, D. Repaux. Nature of spatial chaos. Phys. Rev. Lett., 1987, v.58, No.5, 431–434.CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    L.P. Vozovoi, A.A. Nepomnyashchy. Convection in the horizontal fluid layer by the spatial modulation of the bound temperature. In: Fluid Dynamics, No.7, Perm, 1974, 105–118 (in Russian).Google Scholar
  11. 11.
    L.P. Vozovoi, A.A. Nepomnyashchy. On the stability of spatially periodic convective flows in the vertical layer with wavy boundaries. Prikladnaya Matematika i Mekhanika, 1979, v.43, No.6, 998–1007 (in Russian).ADSGoogle Scholar
  12. 12.
    Yu.G. Vasilenko, E.A. Kuznetsov, V.S. L’vov e.a. On the onset of Taylor vortices in Couette flow. Zhurnal Prikladnoy Mekhaniki i Tekhnicheskoy Fiziki, 1980, No.2, 58–64 (in Russian).Google Scholar
  13. 13.
    P. Coullet. Commensurate-incommensurate transition in nonequilibrium systems. Phys. Rev. Lett., 1986, v.56, No.7, 724–727.CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    A.A. Nepomnyashchy. On the secondary convective motions in flat vertical layer. Izv. Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, 1975, No.4, 3–11 (in Russian).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • A. A. Nepomnyashchy
    • 1
  1. 1.The Institute of Mechanics of Continuous MediaUSSR Academy of Sciences, Ural CenterPermUSSR

Personalised recommendations