title: Codimension-two points in annular electroconvection as a function of aspect ratio.
abstract: 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> or =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.
authors.affiliation: Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
authors.forename: V B
authors.initials: VB
authors.lastname: Deyirmenjian
authors.forename: Zahir A
authors.initials: ZA
authors.lastname: Daya
authors.forename: Stephen W
authors.initials: SW
authors.lastname: Morris