Feedback control of flow alignment in a sheared liquid crystal

Nematic liquids under shear display a variety of dynamic states, reaching from stationary flow alignment of the nematic director over various types of periodic motion toward chaos. In the framework of a continuum theory, transitions between these states correspond to bifurcations in the parameter plane. In particular, a decrease of the (shape-dependent) coupling parameter lambda(K) at a fixed, high value of the shear rate (gamma) over dot leads to a Hopf bifurcation, where flow alignment becomes unstable against oscillatory states. Here we show that within the oscillatory regime, flow alignment can be stabilized by employing time-delayed feedback control. Specifically, we explore a diagonal control scheme where the equation of motion for the ith dynamical variable q(i)(t) is supplemented by a control term involving the difference q(i)(t) - q(i)(t - tau). We also investigate the range of control strengths and delay times tau for which the control works.