Influence of confining surface Gaussian curvature on the winding character of nematic disclination lines

In liquid crystals on curved surfaces, topological point-defects are attracted to Gaussian curvature of like sign. We have recently shown that this coupling extends to the surface endpoints of curvilinear disclinations of 3D nematic liquid crystals, in the context of a hybrid-aligned system with one double-undulated, homeotropic boundary and one flat boundary with degenerate planar anchoring. This system exhibits a large space of multistable configurations of disclination lines, whose properties we explore here. In this work, we use Landau-de Gennes numerical modeling to investigate how Gaussian curvature at the boundary surface influences the winding characters of disclination lines in the bulk. These winding characters are observed to vary rapidly along the defect contours. We calculate the rotation vector describing the defect's local winding geometry, and we use these calculations alongside energetic arguments to understand the heterogeneity of the multistable disclination landscape.