Monte Carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle

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Abstract
We use a Monte Carlo algorithm to simulate the director field around a spherical inclusion in a uniform nematic liquid crystal matrix. The resulting structure crucially depends on the relative strength of the nematic bulk elasticity and the director anchoring on the particle surface. When this anchoring is weak, the director field perturbations are small and have quadrupolar symmetry. With increasing strength of anchoring two topologically nontrivial situations are possible: a dipolar configuration with a satellite point defect (hedgehog) near the particle pole, or a quadrupolar configuration with a “Saturn ring” of disclination around the particle equator.