Stages of Relaxation of Patterns and the Role of Stochasticity on the Final Stage

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dc.creatorHu, S.
dc.creatorGoldman, D. I.
dc.creatorKouri, D. J.
dc.creatorHoffman, D. K.
dc.creatorSwinney, H. L.
dc.creatorGunaratne, G. H.
dc.date2004-01-16
dc.date.accessioned2026-07-07T05:35:16Z
dc.date.available2026-07-07T05:35:16Z
dc.descriptionThe disorder function formalism [Gunaratne et.al., Phys. Rev. E, {\bf 57}, 5146 (1998)]^M is used to show that pattern relaxation in an experiment on a vibrated layer of brass beads^M occurs in three distinct stages. During stage I, all lengthscales associated with ^M moments of the disorder grow at a single universal rate, given by $L(t) \sim t^{0.5}$. In stage II, pattern evolution is non-universal and includes a range of growth indices. Relaxation in the final stage is characterized by a single, non-universal index. We use analysis of patterns from the Swift-Hohenberg equation to argue that mechanisms that underlie the observed pattern evolution are linear spatio-temporal dynamics (stage I), non-linear saturation (stage II), and stochasticity (stage III)
dc.description20 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/nlin/0401022
dc.identifierhttp://arxiv.org/abs/nlin/0401022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80646
dc.subjectPattern Formation and Solitons
dc.titleStages of Relaxation of Patterns and the Role of Stochasticity on the Final Stage
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