Effect of boundaries on periodic patterns

  • Lorenz Kramer
  • P. C. Hohenberg
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 210)


Linear Stability Analysis Periodic Pattern Infinite System Oscillatory Instability Real Negative Root 
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  1. 1.
    This model was introduced by Swift and Hohenberg (Phys.Rev. A15, 319 (1977)) in the context of Rayleigh-Bénard convection,and its wavelength selection properties were first studied by Pomeau and Manneville (J.Phys.Lett. 40, L-609 (1979); Phys.Lett. 75A, 296 (1980)).Google Scholar
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    P.C. Hohenberg, L. Kramer and H. Riecke (to be published).Google Scholar
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    We omit all finite-e corrections.Google Scholar
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    Y. Pomeau and S. Zaleski, C.R. Acad.Sci. Paris, 290B, 505 (1980); J. Phys.(Paris) 42, 515 (1981).Google Scholar
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    M. Potier Ferry, in “Collapse: The Buckling of Structures in Theory and Practice”, J.M.T. Thomson and G.W. Hunt, ed., (Cambridge University Press, 1983).Google Scholar
  10. 10.
    The results are formulated for boundary conditions implemented on the large-x end of the system. If this is reversed the signs of aid have to be reversed.Google Scholar
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Lorenz Kramer
    • 1
  • P. C. Hohenberg
    • 2
  1. 1.Physikalisches Institut der Universität BayreuthBayreuthWest Germany
  2. 2.Bell LaboratoriesMurray HillUSA

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