The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality

Handle URI:
http://hdl.handle.net/10754/599929
Title:
The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality
Authors:
Majumdar, Apala
Abstract:
We study small energy solutions within the Landau-de Gennes theory for nematic liquid crystals, subject to Dirichlet boundary conditions. We consider two-dimensional and three-dimensional domains separately. In the two-dimensional case, we establish the equivalence of the Landau-de Gennes and Ginzburg-Landau theory. In the three-dimensional case, we give a new definition of the defect set based on the normalized energy. In the threedimensional uniaxial case, we demonstrate the equivalence between the defect set and the isotropic set and prove the C 1,α-convergence of uniaxial small energy solutions to a limiting harmonic map, away from the defect set, for some 0 < a < 1, in the vanishing core limit. Generalizations for biaxial small energy solutions are also discussed, which include physically relevant estimates for the solution and its scalar order parameters. This work is motivated by the study of defects in liquid crystalline systems and their applications.
Citation:
Majumdar A (2011) The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality. CPAA 11: 1303–1337. Available: http://dx.doi.org/10.3934/cpaa.2012.11.1303.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Communications on Pure and Applied Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Dec-2011
DOI:
10.3934/cpaa.2012.11.1303
Type:
Article
ISSN:
1534-0392
Sponsors:
A. Majumdar is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), to the Oxford Centre for Collaborative Applied Mathematics and an EPSRC Career Acceleration Fellowship EP/J001686/1.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMajumdar, Apalaen
dc.date.accessioned2016-02-28T06:32:39Zen
dc.date.available2016-02-28T06:32:39Zen
dc.date.issued2011-12en
dc.identifier.citationMajumdar A (2011) The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality. CPAA 11: 1303–1337. Available: http://dx.doi.org/10.3934/cpaa.2012.11.1303.en
dc.identifier.issn1534-0392en
dc.identifier.doi10.3934/cpaa.2012.11.1303en
dc.identifier.urihttp://hdl.handle.net/10754/599929en
dc.description.abstractWe study small energy solutions within the Landau-de Gennes theory for nematic liquid crystals, subject to Dirichlet boundary conditions. We consider two-dimensional and three-dimensional domains separately. In the two-dimensional case, we establish the equivalence of the Landau-de Gennes and Ginzburg-Landau theory. In the three-dimensional case, we give a new definition of the defect set based on the normalized energy. In the threedimensional uniaxial case, we demonstrate the equivalence between the defect set and the isotropic set and prove the C 1,α-convergence of uniaxial small energy solutions to a limiting harmonic map, away from the defect set, for some 0 < a < 1, in the vanishing core limit. Generalizations for biaxial small energy solutions are also discussed, which include physically relevant estimates for the solution and its scalar order parameters. This work is motivated by the study of defects in liquid crystalline systems and their applications.en
dc.description.sponsorshipA. Majumdar is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), to the Oxford Centre for Collaborative Applied Mathematics and an EPSRC Career Acceleration Fellowship EP/J001686/1.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectGinzburg-Landauen
dc.subjectLandau-de gennesen
dc.subjectSingular seten
dc.titleThe Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxialityen
dc.typeArticleen
dc.identifier.journalCommunications on Pure and Applied Analysisen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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