Comparison between square, triangular, or one dimensional lattice of distortions in smectic A and cholesteric crystals for superposed strain and magnetic field of any directions

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Abstract
We study the conditions of observations of a static periodic square grid or lattice of distortions in cholesteric of smectic A liquid crystals under a static magnetic field or fast tensile strain. We show that a square lattice is energetically favorable with respect to other lattices. With a tilted magnetic field H we expect two threshold fields: (a) a one dimensional distortion threshold field H1 and (b) a two dimensional square distortion field H2>H1. H1 and H2 are function of the angle θ of H with the normal to the layers. There exists only a one dimensional solution for θ>30°.