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The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation

In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q

The author thanks S.J. Chapman and T. Witelski for stimulating discussions. M. Aguareles has been supported in part by grants from the Spanish Government (MTM2011-27739-C04-03), from the Catalan Government (2009SGR345) and also by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The author would also like to thank the center OCIAM of the University of Oxford where part of this research was carried out

Elsevier

Manager: Ministerio de Ciencia e Innovación (Espanya)
Generalitat de Catalunya. Agència de Gestió d’Ajuts Universitaris i de Recerca
Author: Aguareles Carrero, Maria
Abstract: In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q
The author thanks S.J. Chapman and T. Witelski for stimulating discussions. M. Aguareles has been supported in part by grants from the Spanish Government (MTM2011-27739-C04-03), from the Catalan Government (2009SGR345) and also by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The author would also like to thank the center OCIAM of the University of Oxford where part of this research was carried out
Document access: http://hdl.handle.net/2072/296462
Language: eng
Publisher: Elsevier
Rights: Tots els drets reservats
Subject: Equacions diferencials no lineals
Equacions diferencials parcials
Differential equations, Partial
Differential equations, Nonlinear
Title: The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
Type: info:eu-repo/semantics/article
Repository: Recercat

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