Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring

Abstract

We study minimizers of the Landau-de Gennes energy in ${\mathbb{R}}^3\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We derive a lower bound for the energy in terms of the boundary condition and show in the extreme cases of strong and weak magnetic field strength that the longitudinal director field is energy minimizing, indicating the presence of two half-point defects, so called boojums, at two opposite points of the sphere. Using a recovery sequence, we show that the energy bound is optimal in these extreme cases.

33 pages, 5 figures, to appear in Journal of Nonlinear Science

References in corpus (4)

• Nematic liquid crystal boojums with handles on colloidal handlebodies
• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• Transformation between elastic dipoles, quadrupoles, octupoles and hexadecapoles driven by surfactant self-assembly in nematic emulsion
• The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis