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Landau-de Gennes Model of Liquid Crystals and Critical Wave Number

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Abstract

We study some variational problems of the Landau-de Gennes functional under Neumann or Dirichlet boundary conditions, which describes phase transitions of liquid crystals. We investigate the effect of the parameters, especially the chirality and the wave number, on the behavior of the minimizers. In order to describe bifurcation of a smectic phase from a nematic phase we introduce the critical wave number Q c3 and give various estimates. We examine the behavior of minimizers with small chirality and large elastic coefficients.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, 119260, Singapore

    Xing-Bin Pan

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Xing-Bin Pan

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  1. Xing-Bin Pan
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A. Kupiainen

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Pan, XB. Landau-de Gennes Model of Liquid Crystals and Critical Wave Number. Commun. Math. Phys. 239, 343–382 (2003). https://doi.org/10.1007/s00220-003-0875-8

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  • DOI: https://doi.org/10.1007/s00220-003-0875-8

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