Narrow Results

We investigate energetically favorable configurations of point disclinations in nematic films having a bump geometry. Gradual expansion in the bump width Δ gives rise to a sudden shift in the stable position of the disclinations from the top to the skirt of the bump. The positional shift observed across a threshold Δ^th obeys a power law function of |Δ - Δ^th|, indicating a new class of continuous phase transition that governs the defect configuration in curved nematic films.

The ’t Hooft–Polyakov monopole solution in Yang–Mills theory is given new physical interpretation in the geometric theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids.

We use the Chern–Simons action for a $𝕊𝕆(3)$-connection for the description of point disclinations in the geometric theory of defects. The most general spherically symmetric $𝕊𝕆(3)$-connection with zero curvature is found. The corresponding orthogonal spherically symmetric $𝕊𝕆(3)$ matrix and $n$-field are computed. Two examples of point disclinations are described.