Periodic deformations in nematic liquid crystals

We reconsider the possibility of periodic deformations in nematic liquid crystal samples, and present a simple method to analyze their stability near the threshold. Our method consists in finding the matrix characterizing the total energy in terms of the integration constants of the linearized solutions of the variational problem. In the undeformed state all the integration constants are identically zero. Hence the analysis of the stability of the undeformed state reduces to the analysis of the sign of the determinants of the principal minors of the matrix of the quadratic form representing the total energy of the nematic sample. We discuss the role of the saddle-splay elastic constant and of the anchoring energy strength in the stability of the modulated structure. The role of the thickness of the sample, as well as of the polar and azimuthal anchoring energies, in the phenomenon is also considered.