New stability results for patterns in a model of long-wavelength convection

Anne C. Skeldon*, Mary Silber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We consider the transition from a spatially uniform state to a steady, spatially periodic pattern in a partial differential equation describing long-wavelength convection [E. Knobloch, Pattern selection in long-wavelength convection, Physica D 41 (1990) 450-479]. This both extends existing work on the study of rolls, squares and hexagons and demonstrates how recent generic results for the stability of spatially periodic patterns may be applied in practice. We find that squares, even if stable to roll perturbations, are often unstable when a wider class of perturbations is considered. We also find scenarios where transitions from hexagons to rectangles can occur. In some cases we find that, near onset, more exotic spatially periodic planforms are preferred over the usual rolls, squares and hexagons.

Original languageEnglish (US)
Pages (from-to)117-133
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume122
Issue number1-4
DOIs
StatePublished - 1998

Keywords

  • Convection
  • Hexagons
  • Pattern formation
  • Symmetry

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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