Envelope Equations Near the Onset of a Hexagonal Pattern : Complex Dynamics in Nonlinear Systems

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概要

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• We present the amplitude equation including slow spatial modulations for the hexagonal patterns observed near the onset of the Benard instability in the presence of non-Boussinesq effects. In contrast to the onset of convection in Boussinesq approximation for rigid-rigid boundary conditions, we do not find a generalized thermodynamic potential. The same conclusion is found to hold for surface tension driven Marangoni convection and for temporally modulated convection. We also point out the applicability of our approach to other systems such as the Rosenzweig instability in ferrofluids as well as to the baroclinic instability and to the buckling of plates and shells, for which an envelope equation, which is second order in time, results.

• 理論物理学刊行会の論文
• 1990-03-28

著者

• Brand Helmut

  Fb7 Physik University Essen : Center For Nonlinear Studies Ms-b 258 Los Alamos National Laboratory U

• BRAND Helmut

  FB7, Physik, University Essen

• BRAND Helmut

  FB7, Physik, University Essen : Center for Nonlinear Studies, MS-B 258 Los Alamos National Laboratory University of California

関連論文

• Envelope Equations Near the Onset of a Hexagonal Pattern : Complex Dynamics in Nonlinear Systems
• Nonlinear Phasedynamics for the Spatially Periodic States of the Taylor Instability

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