Subharmonic pattern formation in a nematic cell – A 1D flexoelectric model approach

The application of an AC electric field to a nematic liquid crystal cell produces two distinct instability pattern regimes, conductive or dielectric. Recently, asymmetric electric field waveforms have been shown to cause a period-doubling subharmonic bifurcation. We extend these calculations to include flexoelectricity in the one-dimensional case. We calculate the threshold values for the electric field strength determining the optimum oblique angle at which the roll patterns form. We find, in some areas of parameter space, the formation of oblique rolls is favoured over normal rolls. In addition we find cross-over points from normal to oblique rolls called Lifshitz points. These have been found in the subharmonic and dielectric regions of the linear stability diagram.