Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
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Publication Date: | 2009 |
Other Authors: | , , |
Format: | Article |
Language: | eng |
Source: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Download full: | http://hdl.handle.net/10400.2/1467 |
Summary: | 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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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:RCAAP2023-11-16T15:14:06Zoai:repositorioaberto.uab.pt:10400.2/1467Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:18.176628Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
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 |
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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 |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799134999041015808 |