Localized states in a model of pattern formation in a vertically vibrated layer

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Abstract

We consider a novel asymptotic limit of model equations proposed to describe the formation of localized states in a vertically vibrated layer of granular material or viscoelastic fluid. In physical terms, the asymptotic limit is motivated by experimental observations that localized states ("oscillons") arise when regions of weak excitation are nevertheless able to expel material rapidly enough to reach a balance with diffusion. Mathematically, the limit enables a novel weakly nonlinear analysis to be performed which allows the local depth of the granular layer to vary by O(1) amounts even when the pattern amplitude is small. The weakly nonlinear analysis and numerical computations provide a robust possible explanation of past experimental results.
Original languageEnglish
Pages (from-to)238-260
Number of pages23
JournalSIAM Journal on Applied Dynamical Systems
Volume9
Issue number1
DOIs
Publication statusPublished - 12 Mar 2010

Keywords

  • homoclinic snaking
  • oscillon
  • pattern formation
  • bifurcation

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