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 xi (b). For R/xi (b) > 20 the-core structure is already qualitatively universal, that is, independent of the confining geometry, while also for R/xi (b) > 200 any quantitative difference is unlikely to be detected.