Dynamic pattern formation in Swift-Hohenberg equations
نویسندگان
چکیده
منابع مشابه
Defect 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...
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We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our models to allow exact stripe solutions. In the generalized models, stripes become unstable to the skew-varicose, oscillatory skew-varicose, and cross-roll i...
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Spiral-defect chaos (SDC) in Rayleigh-Bénard convection is a well-established spatio-temporal complex pattern, which competes with stationary rolls near the onset of convection. The characteristic properties of SDC are accurately described on the basis of the standard three-dimensional Boussinesq equations. As a much simpler and attractive two-dimensional model for SDC generalized Swift-Hohenbe...
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In this paper we study the dynamic bifurcation of the SwiftHohenberg equation on a periodic cell Ω = [−L,L]. It is shown that the equations bifurcates from the trivial solution to an attractor Aλ when the control parameter λ crosses the critical value. In the odd periodic case, Aλ is homeomorphic to S 1 and consists of eight singular points and their connecting orbits. In the periodic case, Aλ ...
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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...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2011
ISSN: 0033-569X,1552-4485
DOI: 10.1090/s0033-569x-2011-01260-1