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

2009Journal article Open access
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dc.contributor.authorCosta, Fernando Pestana da
dc.contributor.authorGartland Jr, Eugene C.
dc.contributor.authorGrinfeld, Michael
dc.contributor.authorPinto, João Teixeira
dc.date.accessioned2010-05-14T11:50:59Z
dc.date.available2010-05-14T11:50:59Z
dc.date.issued2009
dc.description.abstractMotivated 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.pt
dc.description.versionpeerreviewed
dc.identifier.citationCOSTA, 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. 269–287pt
dc.identifier.issn0956-7925 (Print)
dc.identifier.issn1469-4425 (Online)
dc.identifier.urihttp://hdl.handle.net/10400.2/1467
dc.language.isoengpt
dc.publisherCambridge University Presspt
dc.relation.publisherversionDOI:10.1017/S0956792509007827pt
dc.relation.publisherversionpeerreviewed
dc.subjectPendulum equationpt
dc.subjectLiquid crystalspt
dc.subjectNon-homogeneous Dirichlet boundary value problems
dc.subjectBifurcation theory
dc.subjectTime maps
dc.subjectPhase plane analysis
dc.subjectTwist-Fréedericksz transition
dc.subjectLiquid crystals
dc.titleBifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditionspt
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage287pt
oaire.citation.startPage269pt
oaire.citation.titleEuropean Journal of Applied Mathematicspt
person.familyNameCosta
person.familyNameGrinfeld
person.familyNameTeixeira Pinto
person.givenNameFernando Pestana da
person.givenNameMichael
person.givenNameJoão
person.identifier.ciencia-id1610-6502-E6C5
person.identifier.orcid0000-0002-9072-797X
person.identifier.orcid0000-0002-3897-8819
person.identifier.orcid0000-0003-0190-2113
person.identifier.ridK-5942-2013
person.identifier.scopus-author-id14827970300
person.identifier.scopus-author-id7402584922
rcaap.rightsopenAccesspt
rcaap.typearticlept
relation.isAuthorOfPublication72748d24-0598-4f36-804e-87eebd0d06af
relation.isAuthorOfPublication6057da1f-64bf-439d-8b2c-0f2282e1ef91
relation.isAuthorOfPublication378f92b2-9a55-4997-b135-4e099cd76d84
relation.isAuthorOfPublication.latestForDiscovery72748d24-0598-4f36-804e-87eebd0d06af

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