منابع مشابه
Modulation Equation for Stochastic Swift-Hohenberg Equation
The purpose of this paper is to study the influence of large or unbounded domains on a stochastic PDE near a change of stability, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider the stochastic Swift-Hohenberg equation and derive rigorously the Ginzburg-Landau equation as a modulation equation for the amplitudes of...
متن کاملDefect formation in the Swift-Hohenberg equation.
We study numerically and analytically the dynamics of defect formation during a finite-time quench of the two-dimensional Swift-Hohenberg (SH) model of Rayleigh-Bénard convection. We find that the Kibble-Zurek picture of defect formation can be applied to describe the density of defects produced during the quench. Our study reveals the relevance of two factors: the effect of local variations of...
متن کاملSwift-Hohenberg equation with broken reflection symmetry.
The bistable Swift-Hohenberg equation possesses a variety of time-independent spatially localized solutions organized in the so-called snakes-and-ladders structure. This structure is a consequence of a phenomenon known as homoclinic snaking, and is in turn a consequence of spatial reversibility of the equation. We examine here the consequences of breaking spatial reversibility on the snakes-and...
متن کاملGrain boundaries in the Swift-Hohenberg equation
We study the existence of grain boundaries in the Swift-Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ODEs in normal form. We show persistence of the leading-order approximation using transversality induced by wavenum...
متن کاملSpots in the Swift-Hohenberg Equation
The existence of stationary localized spots for the planar and the three-dimensional Swift–Hohenberg equation is proved using geometric blow-up techniques. The spots found in this paper have a much larger amplitude than that expected from a formal scaling in the far field. One advantage of the geometric blow-up methods used here is that the anticipated amplitude scaling does not enter as an ass...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2008
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.6395