Crank texture

"Crank" texture of the director field in a nematic layer with negative dielectric anisotropy and homeotropic anchoring conditions. When the electric field is larger than the threshold of the Fréedericksz transition the lines of the director field become deformed as shown. For obvious reasons we call this deformation "crank texture".

The crank texture is characterised by the 2D vector field c. For symmetry reasons the crank field c is degenerated with respect to rotation around the symmetry axis z.

Umbilics are point +2π and -2π singularities of the crank field.