Selecting improved feedback observables for defect control in active nematics

Identify scalar field observables, beyond the Landau–de Gennes free energy density f(r,t), that more effectively encode the orientation of −1/2 defects in active nematics and thereby serve as superior spatiotemporally local feedback signals for learning activity protocols α(r,t) that guide defects along target trajectories.

Background

The paper demonstrates a local learning rule for non-conservative active nematic dynamics that updates the activity field α(r,t) using differences in the free energy density f(r,t) between the target and trial trajectories. While this imperfect feedback enables control over −1/2 defect trajectories, the authors note that the free energy density may not optimally capture defect orientation, which is crucial for directional control.

They therefore suggest that other scalar observables could provide more informative feedback for learning. Determining such observables would refine the proposed method and potentially improve convergence, robustness, and biological realism of the control strategies.