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Optimal Control of Active Nematics.

Michael M Norton1, Piyush Grover2, Michael F Hagan3

  • 1Center for Neural Engineering, Department of Engineering Science and Materials, Pennsylvania State University, University Park, Pennsylvania 16801, USA and Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA.

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Summary
This summary is machine-generated.

This study introduces a framework to control active nematic systems using optimal control theory. Researchers can now precisely manipulate active nematics, guiding experimental efforts in active matter research.

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Area of Science:

  • Soft Matter Physics
  • Active Matter Systems
  • Hydrodynamics

Background:

  • Active nematic systems exhibit complex dynamics with multiple stable states.
  • Controlling these states is crucial for understanding and utilizing active matter.
  • Previous methods lacked a systematic approach for precise manipulation.

Purpose of the Study:

  • To develop the first systematic framework for sculpting active nematic systems.
  • To utilize optimal control theory to design spatiotemporal control inputs.
  • To precisely manipulate the dynamics of active nematics confined to a disk.

Main Methods:

  • Employed a hydrodynamic model of active nematics.
  • Utilized optimal control theory to identify control fields (applied vorticity and activity strength).
  • Optimized a penalty functional balancing control effort, spatial gradients, and trajectory deviations.

Main Results:

  • Demonstrated the ability to switch between clockwise and counterclockwise circulating states.
  • Identified nontrivial control inputs for restructuring active nematic dynamics.
  • Achieved economical, smooth, and rapid control of system behavior.

Conclusions:

  • Optimal control theory provides a powerful tool for manipulating active nematics.
  • The developed framework offers a guide for experimental control of active matter.
  • This research paves the way for predictable engineering of active nematic behaviors.