Stability of a hedgehog nematic configuration in a small closed cylindrical cavity

This letter presents a study on the stability of molecular configurations in a small closed nematic liquid-crystal cell. A volume point defect exists at the center of the cell with the molecules anchored perpendicularly to the cavity wall. We show that the transformation of a radial hedgehog to a hyperbolic one should occur when the ratio of splay-to-bend elastic constants becomes larger than a certain value that depends on the cell geometry.