Threshold field for a nematic liquid crystal confined between two coaxial cylinders

We consider a nematic liquid crystal constrained by two coaxial cylinders under the action of low-frequency axial or radial electric fields. Assuming an initially hybrid configuration, we find the equilibrium texture of the nematic subjected to weak anchoring boundary conditions on both cylindrical surfaces. We analyze the distinct textures of the nematic as a function of the strength of the interaction of the nematic with the sidewalls, the radii ratio of the cylinders, and the applied electric field. Also, for each radii ratio and strength of the nematic-surface interaction, we determine the critical field for which a complete alignment of the nematic liquid crystal occurs.