Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle: Numerical analysis using adaptive grids

We study numerically the director and orientational order parameter configu rations in a nematic liquid crystal around a two-dimensional spherical part icle on the basis of the tensor order parameter formalism. To properly acco unt for the large length scale difference between the particle and the acco mpanying orientational defect, we devise an adaptive grid scheme in which t he lattice spacing is automatically and locally adjusted. in response to th e spatial gradient of the orientational order parameter. This adaptive grid scheme is useful in studying dynamical as well as static orientational str uctures. We present a simulation result which shows how a hedgehog defect o f topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of topological charge -1/2, located symmetrically around the particle.