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Director precession and nonlinear waves in nematic liquid crystals under elliptic shear

Elliptic shear applied to a homeotropically oriented nematic above the electric bend Freedericks transition (FT) generates slow precession of the director. The character of the accompanying nonlinear waves changes from diffusive phase waves to dispersive ones exhibiting spirals and spatio-temporal chaos as the FT is approached from above. An exact solution of the flow alignment equations captures the observed precession and predicts its reversal for non-flow aligning materials. The FT transforms into a Hopf bifurcation opening the way to understand the wave phenomena.