Feedback control of flow alignment in sheared liquid crystals.

Area of Science:

• Condensed matter physics
• Soft matter physics
• Nonlinear dynamics

Background:

• Liquid crystals exhibit complex nonequilibrium behavior under shear flow.
• Uncontrolled systems can display oscillatory director dynamics, deviating from desired states like flow alignment.
• Controlling these dynamical states is crucial for understanding and manipulating soft matter systems.

Purpose of the Study:

• To investigate the manipulation of nonequilibrium behavior in sheared liquid crystals using closed-loop feedback control.
• To stabilize the stationary "flow alignment" state.
• To explore the effectiveness of time-delayed feedback control (TDFC) under different initial conditions.

Main Methods:

• Application of continuum theory to model liquid crystal hydrodynamics.
• Implementation of time-delayed feedback control (TDFC) by adding a control term to the equation of motion.
• Determination of optimal control parameters (strength K and delay time τ) by solving an exact eigenvalue equation.

Main Results:

• TDFC successfully stabilizes the flow alignment state for specific values of control strength (K) and delay time (τ).
• The method is particularly effective when shearing from an isotropic equilibrium state, requiring smaller control strengths compared to starting from a nematic state.
• The study provides a quantitative method for stabilizing desired dynamical states in sheared liquid crystals.

Conclusions:

• Closed-loop feedback control, specifically TDFC, offers a viable strategy for manipulating the nonequilibrium dynamics of sheared liquid crystals.
• The findings highlight the importance of initial conditions in controlling soft matter systems.
• This research contributes to the fundamental understanding and potential applications of active control in complex fluids.