Generalized Ginzburg-Landau Equations Applied to Instabilities in Systems Coupling Convection and Solidification

  • Thomas Grauer
  • Hermann Haken
Part of the NATO ASI Series book series (NSSB, volume 174)


Crystal growth systems having a solid-liquid interface exhibit a variety of instabilities in their spatio-temporal behaviour. Theoretically they are described by nonlinear moving interface problems. We show that an equivalent formulation on fixed domains is possible, but at the expense of getting highly nonlinear boundary conditions. We present an extended version of the method of Generalized Ginzburg-Landau equations, which is appropriate for the weakly nonlinear analysis of this class of problems. Results are given for a solid-liquid two-phase system showing a convective instability of the Rayleigh-Benard type.


Rayleigh Number Direct Numerical Simulation Nonlinear Boundary Condition Time Dependent Solution Secondary Bifurcation 
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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Thomas Grauer
    • 1
  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Germany

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