Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regime

Abstract

We consider a nematic liquid crystal occupying the exterior region in R^3 outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to a strong external field, modelled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn ring defect around the particle, rather than a dipolar director field typical of a point defect.

References in corpus (1)

• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals

Cited by in corpus (6)

• The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
• Saturn ring defect around a spherical particle immersed in nematic liquid crystal
• Singular perturbation of manifold-valued maps with anisotropic energy
• Far-Field Expansions for Harmonic Maps and the Electrostatics Analogy in Nematic Suspensions
• Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring
• Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers