Shaowen Hu et al 2004 Nonlinearity 17 1535 doi:10.1088/0951-7715/17/4/021
Shaowen Hu1, Daniel I Goldman2,7, Donald J Kouri3, David K Hoffman4, Harry L Swinney5 and Gemunu H Gunaratne6,8
Show affiliationsRecommended by J Lega
The disorder function formalism (Gunaratne et al 1998 Phys. Rev. E 57 5146) is used to show that pattern relaxation in an experiment on a vibrating layer of brass beads occurs in three distinct stages. During stage I, all length scales associated with moments of the disorder grow at a single universal rate, given by L(t) ~ t0.5. 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), nonlinear saturation (stage II), and stochasticity (stage III).
60H15 Stochastic partial differential equations (See also 35R60)
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
Issue 4 (July 2004)
Received 14 January 2004, in final form 21 April 2004
Published 21 May 2004
Shaowen Hu et al 2004 Nonlinearity 17 1535
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