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 th...

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Autor: Aguareles Carrero, Maria
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/11225
Acesso em linha:http://hdl.handle.net/10256/11225
Access Level:acceso embargado
Palavra-chave:Equacions diferencials no lineals
Equacions diferencials parcials
Differential equations, Partial
Differential equations, Nonlinear
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spelling The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equationAguareles Carrero, MariaEquacions diferencials no linealsEquacions diferencials parcialsDifferential equations, PartialDifferential equations, NonlinearIn 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 qThe 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 outElsevierMinisterio de Ciencia e Innovación (Espanya)Generalitat de Catalunya. Agència de Gestió d'Ajuts Universitaris i de Recercainfoinfo2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10256/11225http://hdl.handle.net/10256/11225© Physica. D, Nonlinear phenomena, 2014, vol. 278-279, p. 1-12Articles publicats (D-IMA)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2014.03.007info:eu-repo/semantics/altIdentifier/issn/0167-2789info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03AGAUR/2009-2013/2014 SGR-345Tots els drets reservatsinfo:eu-repo/semantics/embargoedAccessoai:recercat.cat:10256/112252026-05-29T05:05:01Z
dc.title.none.fl_str_mv The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
title The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
spellingShingle The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
Aguareles Carrero, Maria
Equacions diferencials no lineals
Equacions diferencials parcials
Differential equations, Partial
Differential equations, Nonlinear
title_short The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
title_full The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
title_fullStr The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
title_full_unstemmed The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
title_sort The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg-Landau equation
dc.creator.none.fl_str_mv Aguareles Carrero, Maria
author Aguareles Carrero, Maria
author_facet Aguareles Carrero, Maria
author_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (Espanya)
Generalitat de Catalunya. Agència de Gestió d'Ajuts Universitaris i de Recerca
dc.subject.none.fl_str_mv Equacions diferencials no lineals
Equacions diferencials parcials
Differential equations, Partial
Differential equations, Nonlinear
topic Equacions diferencials no lineals
Equacions diferencials parcials
Differential equations, Partial
Differential equations, Nonlinear
description 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
publishDate 2014
dc.date.none.fl_str_mv 2014
info
info
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10256/11225
http://hdl.handle.net/10256/11225
url http://hdl.handle.net/10256/11225
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2014.03.007
info:eu-repo/semantics/altIdentifier/issn/0167-2789
info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03
AGAUR/2009-2013/2014 SGR-345
dc.rights.none.fl_str_mv Tots els drets reservats
info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv Tots els drets reservats
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv © Physica. D, Nonlinear phenomena, 2014, vol. 278-279, p. 1-12
Articles publicats (D-IMA)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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