Biaxial torus around nematic point defects

We study the biaxial structure of both line and point defects in a nematic liquid crystal confined within a capillary tube whose lateral boundary enfo rces homeotropic anchoring, According to Landau-de Gennes theory the local order in the material is described by a second-order tensor Q, which encomp asses both uniaxial and biaxial states. Our study is both analytical and nu merical. We show that the core of a line defect with topological charge M=1 is uniaxial in the axial direction. At the lateral boundary, the uniaxial ordering along the radial direction is reached in two qualitatively differe nt ways, depending on the sign of the order parameter on the axis. The poin t defects with charge M=+/-1 exhibit a uniaxial ring in the plane orthogona l to the cylinder axis. This ring is in turn surrounded by a torus on which the degree of biaxiality attains its maximum. The typical lengths that cha racterize the structure of these defects depend both on the cylinder radius and the biaxial correlation length. It seems that the core of the point de fect does not depend on the far nematic director field in the bulk limit. [ S1063-651X(99)07408-5].