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

Hu, S.; Goldman, D. I.; Kouri, D. J.; Hoffman, D. K.; Swinney, H. L.; Gunaratne, G. H.

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

Authors

Description

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)
20 pages, 10 figures