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DE-SC0022280: Dynamics and Control of Active Nematics using Nonlinear Reduced-Order Models

Award Status: Active
  • Institution: The Board of Regents, University of Nebraska for the University of Nebraska-Lincoln, Lincoln, NE
  • DUNS: 555456995
  • PM: Markowitz, Michael
  • Most Recent Award Date: 09/14/2021
  • Number of Support Periods: 1
  • PI: grover, piyush
  • Current Budget Period: 08/01/2021 - 07/31/2022
  • Current Project Period: 08/01/2021 - 07/31/2024
  • Supplement Budget Period: N/A

Public Abstract

  Dynamics and control of active nematics using nonlinear reduced-order models

Piyush Grover, University of Nebraska-Lincoln (Principal Investigator)

Jae Sung Park, University of Nebraska-Lincoln (Co-Investigator)

Michael M. Norton, Pennsylvania State University, (Co-Investigator)

Active matter is a class of materials composed of interacting, energy-consuming and self-propelling constituents. The emergent spatiotemporal structures can span multiple spatial and temporal scales. In nature, active matter is present at different scales: from bacteria and cellular matter to schools of fish and flocks of birds. In recent years, synthetic active matter has been experimentally realized in several different settings. However, there are several outstanding challenges in characterizing and controlling active matter. In this proposal, we put forth a new theoretical and computational framework to address those challenges. Specifically, we focus on active nematics, which are suspensions of active, rod-like, and apolar components. This focus is motivated by the potential of exploiting the rich phenomenology of active nematics, including spontaneous coherent flows, dynamical vortex patterns, and chaotic hydrodynamics (i.e., low Reynolds number ‘active/mesoscale turbulence’), for material design. 

Our strategy is based on the hypothesis that the far-from-equilibrium behavior of active matter can be effectively described within the framework of deterministic nonlinear dynamical systems. Such a framework does not require close-to-equilibrium or ‘equilibrium-like’ assumptions, such as linear response or the existence of a local free energy functional. Specifically, we propose to apply theoretical and computational tools from nonlinear dynamics to expose the global phase space of active nematic systems. This phase space is expected to be populated by Exact Coherent Structures (ECS), which are exact solutions of the physical dynamics with distinct and regular spatiotemporal structure; examples include unstable equilibria, periodic orbits, and traveling waves. The ECSs are connected by dynamical pathways called invariant manifolds. Our main hypothesis is that active/mesoscale turbulence corresponds to a trajectory meandering in this phase space, transitioning between neighborhoods of the ECSs by traveling on the invariant manifolds. The first objective of this project is to develop reduced-order, predictive models by identifying the dominant ECSs and the transition dynamics between them. Besides improving fundamental understanding of mesoscale turbulence in active nematics, this analysis will illuminate the mechanisms driving such systems into, and out of, the turbulent state. This strategy is motivated by recent successes of ECS-based techniques in characterizing the routes to high Reynolds number turbulence in passive fluids. 

Recent experimental advances – such as the development of light-activated motor protein complexes and magnetically actuated rotors – have created avenues for actively controlling active nematics, besides passive control via confinement or substrate patterning. In this light, the second objective of this proposal is to use our low-order models to develop exogenous, automatic, feedback-driven control algorithms for active nematics. The predictive models will enable the use of established principles of control theory to identify the set of achievable spatiotemporal states for given hardware capabilities (e.g., sensing and actuation). The control algorithms will exploit the network formed by ECSs and their invariant manifolds to find perturbations that stabilize or disrupt existing states, or switch into new states. 

Recognizing that truly programmable self-assembly should depend minimally on external hardware, the third objective is to develop a computational framework for designing bio-mimetic auxiliary systems (e.g., reaction-diffusion networks) that provide the required control endogenously when embedded within the active material. Towards this end, we will formulate and solve a class of inverse problems to identify embedded, auxiliary systems with flexible and robust control capabilities. 

The proposed project will address the DOE-BES grand challenge of characterizing and controlling matter far-from-equilibrium. Furthermore, the proposed predictive models and control framework will help guide experimental efforts to discover, manipulate, and control complex mesoscale architectures and emergent functionality.

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