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

2020-10-28Journal article Open access
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dc.contributor.authorCosta, Fernando Pestana da
dc.contributor.authorPinto, João Teixeira
dc.contributor.authorGrinfeld, Michael
dc.contributor.authorMottram, Nigel
dc.contributor.authorXayxanadasy, Kedtysack
dc.date.accessioned2020-10-30T10:05:06Z
dc.date.available2021-10-29T00:30:17Z
dc.date.issued2020-10-28
dc.description.abstractMotivated 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.pt_PT
dc.description.sponsorshipFP 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.pt_PT
dc.description.sponsorshipUID/MAT/04459/2020
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationCosta, 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.pt_PT
dc.identifier.doi10.1007/s13370-020-00851-9pt_PT
dc.identifier.issn1012-9405
dc.identifier.urihttp://hdl.handle.net/10400.2/10102
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringer-Verlagpt_PT
dc.subjectNon-homogeneous two-points boundary value problemspt_PT
dc.subjectBifurcationspt_PT
dc.subjectAsymptotic evaluation of integralspt_PT
dc.subjectCholesteric liquid-crystal cellspt_PT
dc.subjectFréedericksz transitionpt_PT
dc.subjectNonlinear pendulumpt_PT
dc.titleSteady state solutions in a model of a cholesteric liquid crystal samplept_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.titleAfrika Matematikapt_PT
oaire.citation.volume32pt_PT
person.familyNameCosta
person.familyNameTeixeira Pinto
person.familyNameGrinfeld
person.givenNameFernando Pestana da
person.givenNameJoão
person.givenNameMichael
person.identifier.ciencia-id1610-6502-E6C5
person.identifier.orcid0000-0002-9072-797X
person.identifier.orcid0000-0003-0190-2113
person.identifier.orcid0000-0002-3897-8819
person.identifier.ridK-5942-2013
person.identifier.scopus-author-id14827970300
person.identifier.scopus-author-id7402584922
rcaap.embargofctExigência da editorapt_PT
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication72748d24-0598-4f36-804e-87eebd0d06af
relation.isAuthorOfPublication378f92b2-9a55-4997-b135-4e099cd76d84
relation.isAuthorOfPublication6057da1f-64bf-439d-8b2c-0f2282e1ef91
relation.isAuthorOfPublication.latestForDiscovery72748d24-0598-4f36-804e-87eebd0d06af

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