Extended weakly nonlinear theory of planar nematic convection

We study theoretically convection phenomena in a laterally extended planar nematic layer driven by an ac-electric held (electroconvection in the condu ction regime) or by a thermal gradient (thermoconvection). We use an order- parameter approach and demonstrate that the sequence of bifurcations found experimentally or in the numerical computations can be recovered, provided a homogeneous twist mode of the director is considered as a new active mode . Thus we elucidate the bifurcation to the new "abnormal rolls" [E. Plaut e t al., Phys. Rev. Lett. 79, 2367 (1997)]. The coupling between spatial modu lations of the twist mode and the mean flow is shown to give an important m echanism for the long-wavelength zig-zag instability. The twist mode is als o responsible for the widely observed bimodal instability of rolls. Finally , a Hopf bifurcation in the resulting bimodal structures is found, which co nsists of director oscillations coupled with a periodic switching between t he two roll amplitudes. A systematic investigation of the microscopic mecha nisms controlling all these bifurcations is presented. This establishes a c lose analogy between electroconvection and thermoconvection. Moreover, a "d irector-wave-vector frustration" is found to explain most of the bifurcatio ns. [S1063-651X(99)01102-2].