Optimal Control of Active Nematics

TL;DR

This paper develops a systematic optimal control framework for active nematics, enabling precise manipulation of their complex dynamics using minimal and smooth control inputs, with potential experimental applications.

Contribution

It introduces the first comprehensive optimal control approach for active nematics, utilizing hydrodynamic models and two control fields to switch system states efficiently.

Findings

Successfully switches nematic states using optimized control inputs.

Demonstrates control inputs are economical, smooth, and rapid.

Provides a framework for experimental control of active matter.

Abstract

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological $+\frac{1}{2}$ defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate non-trivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.