Biaxial Disclinations Around a Spherical Colloid

Abstract

We study the Landau-de Gennes theory in the one-constant limit for nematic liquid crystals in the exterior of a spherical colloid. The non-degenerate Nobili-Durand weak anchoring condition is imposed on the colloid boundary, supplemented by a homogeneous alignment condition at spatial infinity. Under an axially symmetric ansatz with an additional reflective symmetry and the Lyuksyutov constraint, we prove that biaxial boojums at the poles and a $-\frac{1}{2}$-degree Saturn ring disclination encircling the equator of the colloid can coexist within a single energy-minimizing configuration in this specific confined geometry. Finally, we rigorously characterize the local structural profile of the director field near these disclinations.

34 pages, 1 figure. Substantially revised and expanded version of arXiv:2601.12065v1; title changed from "Boojums in Liquid Crystals Around a Colloid". Added a coexistence result for biaxial boojums and a $-\frac{1}{2}$-degree Saturn ring disclination, and revised the local structural analysis