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

Handle URI:
http://hdl.handle.net/10754/599899
Title:
The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation
Authors:
Aguareles, M.
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. © 2014 Elsevier B.V. All rights reserved.
Citation:
Aguareles M (2014) The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation. Physica D: Nonlinear Phenomena 278-279: 1–12. Available: http://dx.doi.org/10.1016/j.physd.2014.03.007.
Publisher:
Elsevier BV
Journal:
Physica D: Nonlinear Phenomena
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jun-2014
DOI:
10.1016/j.physd.2014.03.007
Type:
Article
ISSN:
0167-2789
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorAguareles, M.en
dc.date.accessioned2016-02-28T06:31:59Zen
dc.date.available2016-02-28T06:31:59Zen
dc.date.issued2014-06en
dc.identifier.citationAguareles M (2014) The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation. Physica D: Nonlinear Phenomena 278-279: 1–12. Available: http://dx.doi.org/10.1016/j.physd.2014.03.007.en
dc.identifier.issn0167-2789en
dc.identifier.doi10.1016/j.physd.2014.03.007en
dc.identifier.urihttp://hdl.handle.net/10754/599899en
dc.description.abstractIn 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. © 2014 Elsevier B.V. All rights reserved.en
dc.description.sponsorshipThe 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.en
dc.publisherElsevier BVen
dc.subjectAsymptotic wavenumberen
dc.subjectComplex Ginzburg-Landauen
dc.subjectSpiral wavesen
dc.titleThe effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equationen
dc.typeArticleen
dc.identifier.journalPhysica D: Nonlinear Phenomenaen
dc.contributor.institutionUniversitat de Girona, Girona, Spainen
kaust.grant.numberKUK-C1-013-04en
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