Uniaxial versus biaxial character of nematic equilibria in three dimensions

作者：Henao Duvan; Majumdar Apala^*; Pisante Adriano

来源：Calculus of Variations and Partial Differential Equations, 2017, 56(2): 55.

DOI：10.1007/s00526-017-1142-8

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 -> infinity 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.

• 出版日期2017-4