Fluctuations and Pattern Selection Near an Eckhaus Instability

Details Fluctuations and Pattern Selection Near an Eckhaus Instability Fluctuations and Pattern Selection Near an Eckhaus Instability

1993-02-19

arxiv.org/abs/cond-mat/9302028v1

Phys.Rev.Lett.70:3576-3579,1993

Physics

Condensed Matter

13 pages REVTeX + 2 postscript figures

Scientific paper

10.1103/PhysRevLett.70.3576

We study the effect of fluctuations in the vicinity of an Eckhaus instability. The classical stability limit, which is defined in the absence of fluctuations, is smeared out into a region in which fluctuations and nonlinearities dominate the decay of unstable states. The width of this region is shown to grow as $ D^{1/2} $, where $D$ is the intensity of the fluctuations. We find an effective stability boundary that depends on $D$. A numerical solution of the stochastic Swift-Hohenberg equation in one dimension is used to test this prediction and to study pattern selection when the initial unstable state lies within the fluctuation dominated region. The asymptotically selected state differs from the predictions of previous analyses. Finally, the nonlinear relaxation for $D > 0$ is shown to exhibit a scaling form.

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