Profiles of point defects in two dimensions in Landau-de Gennes theory

We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau-de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b small, we prove that this critical point is the unique global minimiser of the Landau-de Gennes energy. We investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.