Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

Detalhes bibliográficos
Autor(a) principal: Costa, Fernando Pestana da
Data de Publicação: 2009
Outros Autores: Gartland Jr, Eugene C., Grinfeld, Michael, Pinto, João Teixeira
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/1467
Resumo: Motivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst 435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses z_2 symmetry and a symmetry- breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fréedericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.
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spelling Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditionsPendulum equationLiquid crystalsNon-homogeneous Dirichlet boundary value problemsBifurcation theoryTime mapsPhase plane analysisTwist-Fréedericksz transitionLiquid crystalsMotivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst 435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses z_2 symmetry and a symmetry- breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fréedericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.Cambridge University PressRepositório AbertoCosta, Fernando Pestana daGartland Jr, Eugene C.Grinfeld, MichaelPinto, João Teixeira2010-05-14T11:50:59Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1467engCOSTA, Fernando Pestana da [et al.] - Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions. " European Journal of Applied Mathematics" [Em linha]. ISSN 0956-7925 (Print) 1469-4425 (Online). Vol. 20 (2009), p. 269–2870956-7925 (Print)info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-07T15:59:11ZPortal AgregadorONG
dc.title.none.fl_str_mv Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
title Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
spellingShingle Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
Costa, Fernando Pestana da
Pendulum equation
Liquid crystals
Non-homogeneous Dirichlet boundary value problems
Bifurcation theory
Time maps
Phase plane analysis
Twist-Fréedericksz transition
Liquid crystals
title_short Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
title_full Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
title_fullStr Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
title_full_unstemmed Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
title_sort Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
author Costa, Fernando Pestana da
author_facet Costa, Fernando Pestana da
Gartland Jr, Eugene C.
Grinfeld, Michael
Pinto, João Teixeira
author_role author
author2 Gartland Jr, Eugene C.
Grinfeld, Michael
Pinto, João Teixeira
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Costa, Fernando Pestana da
Gartland Jr, Eugene C.
Grinfeld, Michael
Pinto, João Teixeira
dc.subject.por.fl_str_mv Pendulum equation
Liquid crystals
Non-homogeneous Dirichlet boundary value problems
Bifurcation theory
Time maps
Phase plane analysis
Twist-Fréedericksz transition
Liquid crystals
topic Pendulum equation
Liquid crystals
Non-homogeneous Dirichlet boundary value problems
Bifurcation theory
Time maps
Phase plane analysis
Twist-Fréedericksz transition
Liquid crystals
description Motivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst 435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses z_2 symmetry and a symmetry- breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fréedericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01T00:00:00Z
2010-05-14T11:50:59Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/1467
url http://hdl.handle.net/10400.2/1467
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv COSTA, Fernando Pestana da [et al.] - Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions. " European Journal of Applied Mathematics" [Em linha]. ISSN 0956-7925 (Print) 1469-4425 (Online). Vol. 20 (2009), p. 269–287
0956-7925 (Print)
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv
repository.mail.fl_str_mv
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