Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid Particle

We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball Br0, and satisfy homeotropic weak anchoring at the surface of the colloid and approach a uniform uniaxial state as |x|→∞$${|x|\to\infty}$$. We study the minimizers in two different limiting regimes: for balls which are small …