Standard and nonstandard nematic electrohydrodynamic convection in the presence of asymmetric AC electric fields

In planar nematic electrohydrodynamic convection (EHC), a microscopic liquid crystal cell is driven by a homogeneous ac electric field, which, if strong enough, causes the fluid to destabilize into a regular pattern-forming state. We consider asymmetric electric fields E(t)=E(t+T)≠−E(t+T∕2), which leads to the possibility of three different types of instabilities at onset: conductive, dielectric, and subharmonic. The first two are already well known as they are easily produced when the system is driven by symmetric electric fields; the third can only occur when the electric field symmetry is broken. We present theoretical results on EHC using linear stability analysis and Floquet theory. We consider rigid and free boundary conditions, extending the model to two Fourier modes in the vertical plane, the inclusion of flexoelectricity, and using standard (nematic electric conductivity σa>0 and dielectric anisotorpy ϵa