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Characterization of the Emergence of Order in an Oscillated Granular Layer

Daniel I. Goldman·Gemunu H. Gunaratne·M. D. Shattuck·Donald J. Kouri·David K. Hoffman·D. S. Zhang·Harry L. Swinney
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Abstract

The formation of textured patterns has been predicted to occur in two stages. The first is an early time, domain-forming stage with dynamics characterized by a disorder function $\barδ(β) \sim t^{-σ_{E}}$, with $σ_{E} = {1/2}β$; this decay is universal. Coarsening of domains occurs in the second stage, in which $\barδ(β) \sim t^{-σ_{L}}$, where $σ_{L}$ is a nonlinear function of $β$ whose form is system and model dependent. Our experiments on a vertically oscillated granular layer are in accord with theory, yielding $σ_{E}\approx 0.5β$, and $σ_{L}$ a nonlinear function of $β$.

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Daniel I. Goldman, Gemunu H. Gunaratne, M. D. Shattuck, Donald J. Kouri, David K. Hoffman, D. S. Zhang, Harry L. Swinney. 2000-05-08. Characterization of the Emergence of Order in an Oscillated Granular Layer. https://arxiv.org/abs/nlin/0005017

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