Global dynamics in a liquid crystal flow

The results of an experimental study of cellular flow in a small aspect ratio nematic liquid crystal cell are presented. The purpose was to investigate the role that dynamical systems theory can play in describing the behaviour of a complex fluid system on a microscopic scale. Initial investigations are concerned with primary flows consisting of either six or eight convection cells. These developed smoothly from the undisturbed nematic with variation in the control parameter and possessed maximum symmetry consistent with the flow domain. As the external forcing was increased spontaneous symmetry-breaking occurred, giving rise to a multiplicity of solutions. Two different oscillatory flows could also be realised, and it is shown that each was the result of a Hopf bifurcation affected by noise internal to the system. The study is then extended to consider codimension-2 points in the solution set. A Takens-Bogdanov point is identified, and this was the organising centre for global dynamics in a surrounding region of parameter space. Behaviour in accordance with a degenerate Hopf bifurcation of codimension-2 is also described. Here, the degenerate bifurcation point was the origin of two lines of Hopf bifurcations, one supercritical and one subcritical, and a line of periodic folds. Finally, a detailed study of global dynamics in the liquid crystal cell is presented. Pattern dynamics in accordance with an imperfect gluing bifurcation are described, and the effect of inevitable physical imperfections is shown to give rise to complex periodic and aperiodic solutions. A systematic investigation of chaotic dynamics is also given, and the behaviour is related to a system governed by ordinary differential equations that was studied by Sil'nikov. (author)Available from British Library Document Supply Centre-DSC:D203904 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo