Fig. 2.

Numerical and topological evaluation of the director field. (A) System has two corners, X and Y, where the director field can choose between two winding senses. (B–D) Director fields correspond to the relative minima of the LdG free energy for a cylindrical micropost and planar interfaces, found numerically. Isosurfaces of are shown in red, where S is the leading eigenvalue of Q. Blue ellipsoids indicate the director field. The nematic is locally melted at the sharp corners. (B) Opposite winding at the two corners precludes the possibility of a disclination in the bulk. (C) Bulk disclination with (i.e., anticlockwise) winding number requires positive winding at both corners. (D) Bulk disclination with (i.e., clockwise) winding number requires negative winding at both corners. Because the numerics show that the (meta)stable states have azimuthal symmetry and that the director has no azimuthal component, we may think of these winding numbers as pseudocharges.