Some Nonlinear Electrohydrodynamic Effects in Nematic Liquid Crystals

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Abstract
The nonlinear extension of the standard electrohydrodynamic equations for a single mode, in the nematic phase, results in a set of coupled nonlinear equations coupling the space charge density and the local curvature. As a result of the nonlinear form, it is possible to predict, ab-initio, the existence of periodicity. When one uses assumptions of a simplifying nature on the field quantities, the resulting formalism is capable of encompassing, in addition to the usual voltage threshold predictions for the linear approximation, equations which are similar in form to Landau's equation for velocity amplitudes of turbulent fluids suggesting the possibility of a direct explanation of the dynamic scattering mode. Other ramifications of the nonlinear theory of electrohydrodynamics are also discussed.