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Modulated Traveling Waves in Nonequilibrium Systems

  • M. Bestehorn
  • R. Friedrich
  • H. Haken
Part of the NATO ASI Series book series (NSSB, volume 225)

Abstract

Time periodic behaviour may arise in systems far from equilibrium due to an instability of a stationary state. If such systems are additionally able to produce spatial patterns a rich variety of phenomena occurs which have recently attracted experimental as well as theoretical interest. Experimental systems under consideration are the Taylor-Couette experiment with counter rotating cylinders [1], convection in binary fluid mixtures [2], as well as higher instabilities arising in the Bénard experiment [3]. Since interesting spatio-temporal behaviour occurs already close to instability the description of the system can be formulated in terms of the synergetic concepts of order parameters and their dynamics [4] because other degrees of freedom of the systems are enslaved. The present paper gives an overview over theoretical results which have been obtained by an examination of the generalized Ginzburg-Landau equation which describes the behaviour of the system close to onset in terms of a suitably defined order parameter [5]. Section II presents this generalized Ginzburg-Landau equation. Section III deals with one-dimensional traveling wave patterns and indicates a mechanism by which modulated traveling waves are generated. Section IV is devoted to two-dimensional traveling wave patterns.

Keywords

Wave Train Amplitude Equation Oscillatory Instability Convective Roll Realistic Boundary Condition 
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.

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Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • M. Bestehorn
    • 1
  • R. Friedrich
    • 1
  • H. Haken
    • 1
  1. 1.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgart 80Germany

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