Numerical scheme for Swift-Hohenberg equation with strict implementation of lyapunov functional
نویسندگان
چکیده
منابع مشابه
Implementation of the Lyapunov Functional in Dif Ference Schemes for the Swift Hohenberg Equation
Abstract Using the operator splitting method Christov Pontes developed a second order in time implicit di erence scheme for solving the Swift Hohenberg equation S H which describes pattern formation in Rayleigh Benard cells For each time step the scheme involves internal iterations which improve the stability and increase the accuracy with which the Lyapunov functional for S H is approximated D...
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The Swift-Hohenberg equation is a central nonlinear model in modern physics. Originally derived to describe the onset and evolution of roll patterns in Rayleigh-Bénard convection, it has also been applied to study a variety of complex fluids and biological materials, including neural tissues. The Swift-Hohenberg equation may be derived from a Lyapunov functional using a variational argument. He...
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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...
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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 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...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2002
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(01)00151-0