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    The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals

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    Type
    Article
    Authors
    MAJUMDAR, APALA
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2011-09-06
    Online Publication Date
    2011-09-06
    Print Publication Date
    2012-02
    Permanent link to this record
    http://hdl.handle.net/10754/599949
    
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    Abstract
    We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau-de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg-Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg-Landau limit for the Landau-de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau-de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities. © Copyright Cambridge University Press 2011.
    Citation
    MAJUMDAR A (2011) The radial-hedgehog solution in Landau–de Gennes’ theory for nematic liquid crystals. European Journal of Applied Mathematics 23: 61–97. Available: http://dx.doi.org/10.1017/S0956792511000295.
    Sponsors
    This publication is based on work 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. The author gratefully acknowledges stimulating discussions with Chong Luo, Valeriy Slastikov and Epifanio Virga. We thank Luc Nguyen and Arghir Zarnescu for helpful comments and suggestions on an earlier version.
    Publisher
    Cambridge University Press (CUP)
    Journal
    European Journal of Applied Mathematics
    DOI
    10.1017/S0956792511000295
    ae974a485f413a2113503eed53cd6c53
    10.1017/S0956792511000295
    Scopus Count
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