Universal fine structure of nematic hedgehogs

We study in a Landau-de Gennes approach the biaxial structure of a nematic point defect with topological charge M = + 1. We aim to illuminate the role of the confining boundaries in determining the fine structure of the defect. We show that there are different regimes associated with different values of the ratio between the typical size R of the region in space occupied by the material and the biaxial correlation length ξ b . For R /ξ b >20 the core structure is already qualitatively universal, that is, independent of the confining geometry, while also for R /ξ b >200 any quantitative difference is unlikely to be detected.