Characterization of the Emergence of Order in an Oscillated Granular Layer

Details Characterization of the Emergence of Order in an Oscillated Granular Layer Characterization of the Emergence of Order in an Oscillated Granular Layer

2000-05-08

arxiv.org/abs/nlin/0005017v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 3 figures

Scientific paper

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 $\bar\delta (\beta) \sim t^{-\sigma_{E}}$, with $\sigma_{E} = {1/2}\beta$; this decay is universal. Coarsening of domains occurs in the second stage, in which $\bar\delta (\beta) \sim t^{-\sigma_{L}}$, where $\sigma_{L}$ is a nonlinear function of $\beta$ whose form is system and model dependent. Our experiments on a vertically oscillated granular layer are in accord with theory, yielding $\sigma_{E}\approx 0.5\beta$, and $\sigma_{L}$ a nonlinear function of $\beta$.

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