Electrohydrodynamic instabilities in nematic liquid crystals under dichotomous parametric modulation

The onset of EHD instabilities in nematic liquid crystals driven by parametric modulation is investigated starting with the one-dimensional linear model of Dubois-Violette. The superposition of a constant electric field with a dichotomous (stochastic or periodic) field as well as the superposition of two dichotomous stochastic fields (pregaussian noise) are considered in detail. The experimentally observed discontinuous behaviour of the threshold (direct transition towards chaos) above a critical strength of the driving field and the dependence of the threshold curve on the correlation time of the noise can be explained qualitatively. Experiments to complete the phase diagram are proposed.