Abstract
We consider a model originally introduced to study layer-undulated structures in bent-core molecule liquid crystals. We first prove existence of minimizers, thenanalyze a simplified version used to study how in columnar phases the width of the column affects the type of switching, which occurs under an applied electric field. We show via $\Gamma$-convergence that as the width of the column tends to infinity, rotation around the tilt cone is favored, provided the coefficient of the coupling term, between the polar parameter, the nematic parameter, and the layer normal is large.
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