title: Standard and nonstandard nematic electrohydrodynamic convection in the presence of asymmetric ac electric fields.
abstract: 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) not equal-E(t+T2) , 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 sigma_{a}>0 and dielectric anisotorpy _{a}<0 ) and nonstandard (sigma_{a}<0) material parameters. We make full use of a three-dimensional linear model where two mutually perpendicular planar wave numbers q and p can be varied. Our results show that there is a qualitative difference between the boundary conditions used, which is also dependent on how many vertical Fourier modes were used in the model. We have obtained threshold values favoring oblique rolls in subharmonic and dielectric regimes in parameter space. For the nonstandard EHC parameter values, both conduction and subharmonic regimes disappear and only the dielectric threshold exists.
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, United Kingdom. j.low@bristol.ac.uk
authors.forename: Jonathan
authors.initials: J
authors.lastname: Low
authors.forename: S John
authors.initials: SJ
authors.lastname: Hogan