Director configuration of a nematic liquid crystal around a spherical particle: Numerical analysis using adaptive mesh refinement

We investigate numerically the orientational configuration of a nematic liquid crystal around a spherical particle. The use of adaptive mesh refinement scheme proves quite useful to overcome the numerical difficulty arising from large scale difference between a particle and a topological defect. Our scheme reproduces successfully the hedgehog and the Saturn ring configurations that have been observed experimentally. To demonstrate that dynamical behaviors can also be investigated using our scheme, we present a simulation result which exhibits a transition from a hedgehog to a Saturn ring under the application of an external field.