Phase transition and Ginzburg-Landau models occurring in the Physics of liquid crystals.

We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow vortex. Finally, we discovered that at the boundary of the illuminated region, the profile of the minimizers is given by the universal equation of Painlevé.