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

S. Hu·D. I. Goldman·D. J. Kouri·D. K. Hoffman·H. L. Swinney·G. H. Gunaratne
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Abstract

The 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)

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S. Hu, D. I. Goldman, D. J. Kouri, D. K. Hoffman, H. L. Swinney, G. H. Gunaratne. 2004-01-16. Stages of Relaxation of Patterns and the Role of Stochasticity on the Final Stage. https://arxiv.org/abs/nlin/0401022

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