Evolution from A +2 Defect to +1/2 Defects in a Cylindrical Geometry

In this work the dynamics of liquid crystal ordering in a cylindrical geometry are considered. We study a system with liquid crystalline properties that exhibits translational symmetry along the cylinder axis and, therefore, the problem is effectively two-dimensional. The orientation of liquid crystals is described by a tensorial order parameter and the dynamics are governed by a balance between the dissipation and the rate of change of free energy, which includes the elastic, thermotropic and surface energy terms. The evolution of the þ2 defect differentiating first into two þ1 disclinations and subsequently into four þ1=2 defects is analysed. Different boundary conditions, namely strong and weak or no anchoring, have been considered and the critical value for the anchoring strength, at which þ1=2 defects are very close to escaping through the boundary but still remain there at equilibrium, has been identified.