Codimension-two points in annular electroconvection as a function of aspect ratio

We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting, submicron thick liquid crystal film suspended between concentric circular electrodes and driven by an applied voltage between its inner and outer edges. We explicitly calculate the coefficient g of the leading cubic nonlinearity and systematically study its dependence on the system's geometrical and material parameters. The radius ratio alpha quantifies the film's geometry while a dimensionless number P, similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed alpha, g is a decreasing function of P, as P becomes smaller, and is nearly constant for P greater than or similar to 1. As P -> 0, g ->infinity. We find that g is a nontrivial and discontinuous function of alpha. We show that the discontinuities occur at codimension-two points that are accessed by varying alpha.