Existence of stable parabolic umbilic degeneracies in passive nematic textures

Determine whether parabolic umbilic degeneracies (the D5^± singularity class in the tomography of a nematic director field) can occur as stable features in passive nematic liquid crystals, rather than only as transient structures during dynamical transitions. If such stable configurations exist, ascertain the physical conditions under which they are realized.

Background

The paper classifies structural changes in nematic textures using singularity theory, focusing on four principal degeneracies that appear in tomographies of director fields: fold (A2), elliptic umbilic (D4^-), parabolic umbilic (D5^±), and hyperbolic umbilic (D6^+). It notes that fold, hyperbolic umbilic, and elliptic umbilic types occur in observed stable textures.

Parabolic umbilics are argued to arise transiently during defect crossings because meron tethers must connect disclinations after such crossings. However, the authors explicitly state they are not aware of observations of parabolic umbilics as stable features in passive materials, leaving open whether such stable configurations exist.