Sciweavers

SIAMADS
2010

Localized States in a Model of Pattern Formation in a Vertically Vibrated Layer

13 years 6 months ago
Localized States in a Model of Pattern Formation in a Vertically Vibrated Layer
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. Key words. homoclinic snaking, pattern formation, bifurcation, oscillon AMS subject classifications. 34C37, 34E13, 35B32, 76T25 DOI. 10.1137/090762865
J. H. P. Dawes, S. Lilley
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMADS
Authors J. H. P. Dawes, S. Lilley
Comments (0)