Regensburg 2000 – scientific programme
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DY: Dynamik und Statistische Physik
DY 50: Hydrodynamik und Turbulenz I
DY 50.1: Talk
Friday, March 31, 2000, 09:30–09:45, H2
Pattern formation in the presence of frozen noise — •Martin Hammele and Walter Zimmermann — Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken
The interplay between spatially periodic or frozen stochastic modulations and nonlinearity is investigated for a modified Swift–Hohenberg equation and a modified Ginzburg–Landau equation. The modifications of the bifurcation by random modulations are analytically calculated. The threshold shift and the slope of the bifurcation is determined by a pertubational calculation for small values of D L2, with D the noise strength and L the system length. For arbitrary values of D L2 we introduce a selfconsistent method which is in agreement with fully numerical calculations. These analytical methods are also applied to the Ginzburg–Landau equation with spatially varying frequencies. Here the spatially distributed frequencies lead to a new frequency and, surprisingly, the threshold takes its minimum at finite wavenumber.