Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond

Handle URI:
http://hdl.handle.net/10754/598693
Title:
Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond
Authors:
Majumdar, Apala; Zarnescu, Arghir
Abstract:
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W1,2, to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions. © Springer-Verlag (2009).
Citation:
Majumdar A, Zarnescu A (2009) Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond. Archive for Rational Mechanics and Analysis 196: 227–280. Available: http://dx.doi.org/10.1007/s00205-009-0249-2.
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
7-Jul-2009
DOI:
10.1007/s00205-009-0249-2
Type:
Article
ISSN:
0003-9527; 1432-0673
Sponsors:
A. Majumdar was supported by a Royal Commission for the Exhibition of 1851 Research Fellowship till October 2008. She is now 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. A. Zarnescu is supported by the EPSRC Grant EP/E010288/1-Equilibrium Liquid Crystal Configurations: Energetics, Singularities and Applications. We thank John M. Ball and Christ of Melcher for stimulating discussions.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMajumdar, Apalaen
dc.contributor.authorZarnescu, Arghiren
dc.date.accessioned2016-02-25T13:34:33Zen
dc.date.available2016-02-25T13:34:33Zen
dc.date.issued2009-07-07en
dc.identifier.citationMajumdar A, Zarnescu A (2009) Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond. Archive for Rational Mechanics and Analysis 196: 227–280. Available: http://dx.doi.org/10.1007/s00205-009-0249-2.en
dc.identifier.issn0003-9527en
dc.identifier.issn1432-0673en
dc.identifier.doi10.1007/s00205-009-0249-2en
dc.identifier.urihttp://hdl.handle.net/10754/598693en
dc.description.abstractWe study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W1,2, to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions. © Springer-Verlag (2009).en
dc.description.sponsorshipA. Majumdar was supported by a Royal Commission for the Exhibition of 1851 Research Fellowship till October 2008. She is now 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. A. Zarnescu is supported by the EPSRC Grant EP/E010288/1-Equilibrium Liquid Crystal Configurations: Energetics, Singularities and Applications. We thank John M. Ball and Christ of Melcher for stimulating discussions.en
dc.publisherSpringer Natureen
dc.titleLandau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyonden
dc.typeArticleen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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