System-Size Selection of Instability Modes of Periodic Roll Structures in Nematic Electroconvection

We experimentally investigated the instability of periodic roll structures in electroconvection of a planar-aligned nematic liquid crystal, with particular focus on the system size along the roll axis. We systematically varied the system size and compared the transitions in the convection pattern as the applied voltage was increased. In larger systems, the pattern transitioned to defect turbulence, a form of weak turbulence. In this state, defects are generated irregularly within the periodic structure as the convection rolls become inclined. In smaller systems, we observed angle-deflective oscillation, a time-periodic oscillation of the roll inclination angle. To describe the instability of these periodic convective structures, we propose an activator-inhibitor model for the coupled dynamics of the nematic director and the roll orientation, and show that the type of Hopf-unstable mode is selected by the system size along the roll axis.