Steady state solutions in a model of a cholesteric liquid crystal sample

Detalhes bibliográficos
Autor(a) principal: Costa, Fernando Pestana da
Data de Publicação: 2020
Outros Autores: Pinto, João Teixeira, Grinfeld, Michael, Mottram, Nigel, Xayxanadasy, Kedtysack
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/10102
Resumo: Motivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269–287, 2009), (da Costa et al. in Eur J Appl Math 28:243–260, 2017), (McKay in J Eng Math 87:19–28, 2014), (Millar and McKay in Mol Cryst Liq Cryst 435:277/[937]–286/[946], 2005)], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter. Employing phase space analysis techniques, time maps, and asymptotic methods to estimate integrals, together with appropriate numerical evidence, we obtain the corresponding novel bifurcation diagram and discuss its implications for liquid crystal display technology. Numerical simulations of the corresponding dynamic problem also provide suggestive evidence about stability of some solution branches, pointing to a promising avenue of further analytical, numerical, and experimental studies.
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spelling Steady state solutions in a model of a cholesteric liquid crystal sampleNon-homogeneous two-points boundary value problemsBifurcationsAsymptotic evaluation of integralsCholesteric liquid-crystal cellsFréedericksz transitionNonlinear pendulumMotivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269–287, 2009), (da Costa et al. in Eur J Appl Math 28:243–260, 2017), (McKay in J Eng Math 87:19–28, 2014), (Millar and McKay in Mol Cryst Liq Cryst 435:277/[937]–286/[946], 2005)], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter. Employing phase space analysis techniques, time maps, and asymptotic methods to estimate integrals, together with appropriate numerical evidence, we obtain the corresponding novel bifurcation diagram and discuss its implications for liquid crystal display technology. Numerical simulations of the corresponding dynamic problem also provide suggestive evidence about stability of some solution branches, pointing to a promising avenue of further analytical, numerical, and experimental studies.FP da Costa and JT Pinto: FCT/Portugal project CAMGSD UID/MAT/04459/2020. FP da Costa: University of Strathclyde David Anderson Research Professorship. FP da Costa: Erasmus Mundus Mobility with Asia grant EMMA ID 2601.UID/MAT/04459/2020Springer-VerlagRepositório AbertoCosta, Fernando Pestana daPinto, João TeixeiraGrinfeld, MichaelMottram, NigelXayxanadasy, Kedtysack2021-10-29T00:30:17Z2020-10-282020-10-28T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/10102engCosta, Fernando Pestana da; Pinto, João Teixeira; Grinfeld, Michael; Mottram, Nigel; Xayxanadasy, Kedtysack; Steady state solutions in a model of a cholesteric liquid crystal sample. "Afrika Matematika" [Em linha]. ISSN 1012-9405. Vol.32, (Published online: 28 October 2020), pp. 28.1012-940510.1007/s13370-020-00851-9info: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:RCAAP2023-11-26T01:47:21Zoai:repositorioaberto.uab.pt:10400.2/10102Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:49:46.203543Repositório 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 Steady state solutions in a model of a cholesteric liquid crystal sample
title Steady state solutions in a model of a cholesteric liquid crystal sample
spellingShingle Steady state solutions in a model of a cholesteric liquid crystal sample
Costa, Fernando Pestana da
Non-homogeneous two-points boundary value problems
Bifurcations
Asymptotic evaluation of integrals
Cholesteric liquid-crystal cells
Fréedericksz transition
Nonlinear pendulum
title_short Steady state solutions in a model of a cholesteric liquid crystal sample
title_full Steady state solutions in a model of a cholesteric liquid crystal sample
title_fullStr Steady state solutions in a model of a cholesteric liquid crystal sample
title_full_unstemmed Steady state solutions in a model of a cholesteric liquid crystal sample
title_sort Steady state solutions in a model of a cholesteric liquid crystal sample
author Costa, Fernando Pestana da
author_facet Costa, Fernando Pestana da
Pinto, João Teixeira
Grinfeld, Michael
Mottram, Nigel
Xayxanadasy, Kedtysack
author_role author
author2 Pinto, João Teixeira
Grinfeld, Michael
Mottram, Nigel
Xayxanadasy, Kedtysack
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Costa, Fernando Pestana da
Pinto, João Teixeira
Grinfeld, Michael
Mottram, Nigel
Xayxanadasy, Kedtysack
dc.subject.por.fl_str_mv Non-homogeneous two-points boundary value problems
Bifurcations
Asymptotic evaluation of integrals
Cholesteric liquid-crystal cells
Fréedericksz transition
Nonlinear pendulum
topic Non-homogeneous two-points boundary value problems
Bifurcations
Asymptotic evaluation of integrals
Cholesteric liquid-crystal cells
Fréedericksz transition
Nonlinear pendulum
description Motivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269–287, 2009), (da Costa et al. in Eur J Appl Math 28:243–260, 2017), (McKay in J Eng Math 87:19–28, 2014), (Millar and McKay in Mol Cryst Liq Cryst 435:277/[937]–286/[946], 2005)], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter. Employing phase space analysis techniques, time maps, and asymptotic methods to estimate integrals, together with appropriate numerical evidence, we obtain the corresponding novel bifurcation diagram and discuss its implications for liquid crystal display technology. Numerical simulations of the corresponding dynamic problem also provide suggestive evidence about stability of some solution branches, pointing to a promising avenue of further analytical, numerical, and experimental studies.
publishDate 2020
dc.date.none.fl_str_mv 2020-10-28
2020-10-28T00:00:00Z
2021-10-29T00:30:17Z
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/10400.2/10102
url http://hdl.handle.net/10400.2/10102
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Costa, Fernando Pestana da; Pinto, João Teixeira; Grinfeld, Michael; Mottram, Nigel; Xayxanadasy, Kedtysack; Steady state solutions in a model of a cholesteric liquid crystal sample. "Afrika Matematika" [Em linha]. ISSN 1012-9405. Vol.32, (Published online: 28 October 2020), pp. 28.
1012-9405
10.1007/s13370-020-00851-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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