RESUMEN
We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigate these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium system is isotropic. These oscillatory states are characterized by a wagging motion of the paranematic director, and they occur if the tumbling parameter is sufficiently small. We also present full nonequilibrium phase diagrams in the plane spanned by the concentration and the shear rate.
RESUMEN
Based on a continuum theory, we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary "flow alignment," under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the ith component q(i)(t) of the order parameter tensor is supplemented by a control term involving the difference q(i)(t)-q(i)(t-τ). In this diagonal scheme, τ is the delay time. We demonstrate that the TDFC method successfully stabilizes flow alignment for suitable values of the control strength K and τ; these values are determined by solving an exact eigenvalue equation. Moreover, our results show that only small values of K are needed when the system is sheared from an isotropic equilibrium state, contrary to the case where the equilibrium state is nematic.
