Uniaxial versus biaxial character of nematic equilibria in three dimensions

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Henao, Duvan and Majumdar, Apala and Pisante, Adriano (2017) Uniaxial versus biaxial character of nematic equilibria in three dimensions. Calculus of Variations and Partial Differential Equations, 56. 55. ISSN 1432-0835 (https://doi.org/10.1007/s00526-017-1142-8)

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Abstract

We study global minimizers of the Landau–de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are specific to an asymptotic limit coined in terms of a dimensionless temperature and material-dependent parameter, t and some constraints on the material parameters, and we work in the t→∞ limit that captures features of the widely used Lyuksyutov constraint (Kralj and Virga in J Phys A 34:829–838, 2001). We prove (i) that (re-scaled) global LdG minimizers converge uniformly to a (minimizing) limiting harmonic map, away from the singular set of the limiting map; (ii) we have points of maximal biaxiality and uniaxiality near each singular point of the limiting map; (iii) estimates for the size of “strongly biaxial” regions in terms of the parameter t. We further show that global LdG minimizers in the restricted class of uniaxial Q-tensors cannot be stable critical points of the LdG energy in this limit.

ORCID iDs

Henao, Duvan, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Pisante, Adriano;
  • Item type:Article
    ID code:70857
    Dates:
    Date
    Event
    30 April 2017
    Published
    4 April 2017
    Published Online
    20 February 2017
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:12 Dec 2019 15:59
    Last modified:11 Nov 2024 12:32
    URI:https://strathprints.strath.ac.uk/id/eprint/70857
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