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

Research output: Contribution to journalArticle

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

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Asymptotic Limit
Nonlinear analysis
Pattern Formation
Nonlinear Analysis
Viscoelastic Fluid
Granular Materials
Granular materials
Numerical Computation
Excitation
Vary
Fluids
Experimental Results
Term
Model
Observation

Keywords

  • homoclinic snaking
  • oscillon
  • pattern formation
  • bifurcation

Cite this

Localized states in a model of pattern formation in a vertically vibrated layer. / Dawes, Jonathan H P; Lilley, S.

In: SIAM Journal on Applied Dynamical Systems, Vol. 9, No. 1, 12.03.2010, p. 238-260.

Research output: Contribution to journalArticle

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