abstract

We consider energy minimizing configurations of a nematic liquid crystal
around a spherical colloid particle, in the context of the Landaude Gennes
model. The nematic is assumed to occupy the exterior of a ball of radius r_0,
satisfy homeotropic weak anchoring at the surface of the colloid, and approach
a uniform uniaxial state at infinity. We study the minimizers in two different
limiting regimes: for balls which are small compared to the characteristic
length scale r_0<
>L. The relationship between the radius and the anchoring strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a "Saturn ring" defect for relatively strong anchoring, corresponding to an exchange of eigenvalues of the Qtensor. In the limit of very large balls we obtain an axisymmetric minimizer of the OseenFrank energy, and a dipole configuration with exactly one point defect is obtained.