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

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

2004-01-16

arxiv.org/abs/nlin/0401022v1

Nonlinear Sciences

Pattern Formation and Solitons

20 pages, 10 figures

Scientific paper

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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