Optimal Control of Active Nematics

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.

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Cited by in corpus (21)

• Topological active matter
• Submersed Micropatterned Structures Control Active Nematic Flow, Topology and Concentration
• Design of nematic liquid crystals to control microscale dynamics
• Active matter under control: Insights from response theory
• Learning to Control Active Matter
• Optimal transport and control of active drops
• The 2024 Motile Active Matter Roadmap
• Design rules for controlling active topological defects
• Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics
• Exact coherent structures and phase space geometry of pre-turbulent 2D active nematic channel flow
• Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity
• Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
• Friction mediated phase transition in confined active nematics
• Optimal Control in Soft and Active Matter
• Mechanochemical Topological Defects in an Active Nematic
• Dynamic control of self-assembly of quasicrystalline structures through reinforcement learning
• Closed-loop control of active nematic flows
• Reinforcement Learning reveals fundamental limits on the mixing of active particles
• Stress and Alignment Response to Curved Obstacles in Growing Bacterial Monolayers
• Field-controlled interfacial transport and pinning in an active spin system
• Machine Learning Forecasting of Active Nematics