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Ghosh S, Joshi C, Baskaran A, Hagan MF. Spatiotemporal control of structure and dynamics in a polar active fluid. SOFT MATTER 2024. [PMID: 39188251 DOI: 10.1039/d4sm00547c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/28/2024]
Abstract
We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.
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Affiliation(s)
- Saptorshi Ghosh
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Chaitanya Joshi
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
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2
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Sinigaglia C, Braghin F, Serra M. Optimal Control of Short-Time Attractors in Active Nematics. PHYSICAL REVIEW LETTERS 2024; 132:218302. [PMID: 38856253 DOI: 10.1103/physrevlett.132.218302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 04/17/2024] [Accepted: 04/24/2024] [Indexed: 06/11/2024]
Abstract
Objective Eulerian coherent structures (OECSs) and instantaneous Lyapunov exponents (iLEs) govern short-term material transport in fluid flows as Lagrangian coherent structures and the finite-time Lyapunov exponent do over longer times. Attracting OECSs and iLEs reveal short-time attractors and are computable from the Eulerian rate-of-strain tensor. Here, we devise for the first time an optimal control strategy to create short-time attractors in compressible, viscosity-dominated active nematic flows. By modulating the active stress intensity, our framework achieves a target profile of the minimum eigenvalue of the rate-of-strain tensor, controlling the location and shape of short-time attractors. We show that our optimal control strategy effectively achieves desired short-time attractors while rejecting disturbances. Combining optimal control and coherent structures, our work offers a new perspective to steer material transport in compressible active nematics, with applications to morphogenesis and synthetic active matter.
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Affiliation(s)
- Carlo Sinigaglia
- Politecnico di Milano, Department of Mechanical Engineering, Milan 20156, Italy
| | - Francesco Braghin
- Politecnico di Milano, Department of Mechanical Engineering, Milan 20156, Italy
| | - Mattia Serra
- University of California San Diego, Department of Physics, San Diego, California 92093, USA
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3
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Shankar S, Scharrer LVD, Bowick MJ, Marchetti MC. Design rules for controlling active topological defects. Proc Natl Acad Sci U S A 2024; 121:e2400933121. [PMID: 38748571 PMCID: PMC11127047 DOI: 10.1073/pnas.2400933121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 04/12/2024] [Indexed: 05/27/2024] Open
Abstract
Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.
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Affiliation(s)
- Suraj Shankar
- Department of Physics, Harvard University, Cambridge, MA02138
- Department of Physics, University of Michigan, Ann Arbor, MI48109
| | - Luca V. D. Scharrer
- Department of Physics, University of California, Santa Barbara, CA93106
- Department of Physics, The University of Chicago, Chicago, IL60637
| | - Mark J. Bowick
- Department of Physics, University of California, Santa Barbara, CA93106
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA93106
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4
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Langeslay B, Fahy W, Juarez G. Stress and alignment response to curved obstacles in growing bacterial monolayers. Phys Rev E 2024; 109:054608. [PMID: 38907398 DOI: 10.1103/physreve.109.054608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 05/09/2024] [Indexed: 06/24/2024]
Abstract
Monolayers of growing bacteria, confined within channel geometries, exhibit self-organization into a highly aligned laminar state along the axis of the channel. Although this phenomenon has been observed in experiments and simulations under various boundary conditions, the underlying physical mechanism driving this alignment remains unclear. In this study, we conduct simulations of growing bacteria in two-dimensional channel geometries perturbed by fixed obstacles, either circular or arc shaped, placed at the channel's center. Our findings reveal that even sizable obstacles cause only short-ranged disruptions to the baseline laminar state. These disruptions arise from a competition between local planar anchoring and bulk laminar alignment. At smaller obstacle sizes, bulk alignment fully dominates, while at larger sizes planar anchoring induces increasing local disruptions. Furthermore, our analysis indicates that the resulting configurations of the bacterial system display a striking resemblance to the arrangement of hard-rod smectic liquid crystals around circular obstacles. This suggests that modeling hard-rod bacterial monolayers as smectic, rather than nematic, liquid crystals may yield successful outcomes. The insights gained from our study contribute to the expanding body of research on bacterial growth in channels. Our work provides perspectives on the stability of the laminar state and extends our understanding to encompass more intricate confinement schemes.
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5
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Klapp SHL, Zakharova A, Schneider I. Introduction to focus issue: Control of self-organizing nonlinear systems. CHAOS (WOODBURY, N.Y.) 2024; 34:010402. [PMID: 38285723 DOI: 10.1063/5.0195548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 01/03/2024] [Indexed: 01/31/2024]
Affiliation(s)
- Sabine H L Klapp
- Institute of Theoretical Physics, Technical University Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Anna Zakharova
- Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany
| | - Isabelle Schneider
- Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany
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6
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Mitchell KA, Sabbir MMH, Geumhan K, Smith SA, Klein B, Beller DA. Maximally mixing active nematics. Phys Rev E 2024; 109:014606. [PMID: 38366395 DOI: 10.1103/physreve.109.014606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Accepted: 11/30/2023] [Indexed: 02/18/2024]
Abstract
Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.
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Affiliation(s)
- Kevin A Mitchell
- Physics Department, University of California, Merced, California 95344, USA
| | | | - Kevin Geumhan
- Physics Department, University of California, Merced, California 95344, USA
| | - Spencer A Smith
- Physics Department, Mount Holyoke College, South Hadley, Massachusetts 01075, USA
| | - Brandon Klein
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Daniel A Beller
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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7
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Zarei Z, Berezney J, Hensley A, Lemma L, Senbil N, Dogic Z, Fraden S. Light-activated microtubule-based two-dimensional active nematic. SOFT MATTER 2023; 19:6691-6699. [PMID: 37609884 DOI: 10.1039/d3sm00270e] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/24/2023]
Abstract
We assess the ability of two light responsive kinesin motor clusters to drive dynamics of microtubule-based active nematics: opto-K401, a processive motor, and opto-K365, a non-processive motor. Measurements reveal an order of magnitude improvement in the contrast of nematic flow speeds between maximally- and minimally-illuminated states for opto-K365 motors when compared to opto-K401 construct. For opto-K365 nematics, we characterize both the steady-state flow and defect density as a function of applied light. We also examine the transient behavior as the system switches between steady-states upon changes in light intensities. Although nematic flows reach a steady state within tens of seconds, the defect density exhibits transient behavior for up to 10 minutes, showing a separation between small-scale active flows and system-scale structural states. Our work establishes an experimental platform that can exploit spatiotemporally-heterogeneous patterns of activity to generate targeted dynamical states.
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Affiliation(s)
- Zahra Zarei
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - John Berezney
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - Alexander Hensley
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - Linnea Lemma
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
- The Department of Chemical and Biological Engineering, Princeton, NJ 08544, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Nesrin Senbil
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
| | - Zvonimir Dogic
- Department of Physics, University of California, Santa Barbara, California 93106, USA
- Biomolecular Science and Engineering, University of California, Santa Barbara, California 93106, USA
| | - Seth Fraden
- The Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.
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8
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Schimming CD, Reichhardt CJO, Reichhardt C. Friction-mediated phase transition in confined active nematics. Phys Rev E 2023; 108:L012602. [PMID: 37583137 DOI: 10.1103/physreve.108.l012602] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 06/28/2023] [Indexed: 08/17/2023]
Abstract
Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.
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Affiliation(s)
- Cody D Schimming
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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9
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Lemma LM, Varghese M, Ross TD, Thomson M, Baskaran A, Dogic Z. Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids. PNAS NEXUS 2023; 2:pgad130. [PMID: 37168671 PMCID: PMC10165807 DOI: 10.1093/pnasnexus/pgad130] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/11/2022] [Revised: 02/27/2023] [Accepted: 04/03/2023] [Indexed: 05/13/2023]
Abstract
Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
- Department of Physics, University of California, Santa Barbara, 93106 CA, USA
| | - Minu Varghese
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
| | - Tyler D Ross
- Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd. Pasadena, 91125 CA, USA
| | - Matt Thomson
- Division of Biology and Biological Engineering, California Institute of Technology, 1200 E California Blvd., Pasadena, 91125 CA, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, 415 South St., Waltham, 02453 MA, USA
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10
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McDonald MN, Zhu Q, Paxton WF, Peterson CK, Tree DR. Active control of equilibrium, near-equilibrium, and far-from-equilibrium colloidal systems. SOFT MATTER 2023; 19:1675-1694. [PMID: 36790855 DOI: 10.1039/d2sm01447e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The development of top-down active control over bottom-up colloidal assembly processes has the potential to produce materials, surfaces, and objects with applications in a wide range of fields spanning from computing to materials science to biomedical engineering. In this review, we summarize recent progress in the field using a taxonomy based on how active control is used to guide assembly. We find there are three distinct scenarios: (1) navigating kinetic pathways to reach a desirable equilibrium state, (2) the creation of a desirable metastable, kinetically trapped, or kinetically arrested state, and (3) the creation of a desirable far-from-equilibrium state through continuous energy input. We review seminal works within this framework, provide a summary of important application areas, and present a brief introduction to the fundamental concepts of control theory that are necessary for the soft materials community to understand this literature. In addition, we outline current and potential future applications of actively-controlled colloidal systems, and we highlight important open questions and future directions.
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Affiliation(s)
- Mark N McDonald
- Department of Chemical Engineering, Brigham Young University, Provo, Utah, USA.
| | - Qinyu Zhu
- Department of Chemical Engineering, Brigham Young University, Provo, Utah, USA.
| | - Walter F Paxton
- Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah, USA
| | - Cameron K Peterson
- Department of Electrical and Computer Engineering, Brigham Young University, Provo, Utah, USA
| | - Douglas R Tree
- Department of Chemical Engineering, Brigham Young University, Provo, Utah, USA.
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11
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de Oliveira E, Mirantsev L, Lyra M, de Oliveira I. Orientational ordering of active nematics confined to a 2D nanoscopic ring-shaped cavity. J Mol Liq 2023. [DOI: 10.1016/j.molliq.2023.121513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
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12
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Sciortino A, Neumann LJ, Krüger T, Maryshev I, Teshima TF, Wolfrum B, Frey E, Bausch AR. Polarity and chirality control of an active fluid by passive nematic defects. NATURE MATERIALS 2023; 22:260-268. [PMID: 36585435 PMCID: PMC9894751 DOI: 10.1038/s41563-022-01432-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/22/2022] [Accepted: 11/03/2022] [Indexed: 06/17/2023]
Abstract
Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.
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Affiliation(s)
- Alfredo Sciortino
- Lehrstuhl für Zellbiophysik E27, Technische Universität München, Garching, Germany
- Center for Functional Protein Assemblies, Garching bei München, Germany
| | - Lukas J Neumann
- Lehrstuhl für Zellbiophysik E27, Technische Universität München, Garching, Germany
- Center for Functional Protein Assemblies, Garching bei München, Germany
| | - Timo Krüger
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität, München, Germany
| | - Ivan Maryshev
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität, München, Germany
| | - Tetsuhiko F Teshima
- Neuroelectronics, Department of Electrical Engineering, Technische Universität München, Garching, Germany
- Medical & Health Informatics Laboratories, NTT Research Incorporated, Sunnyvale, CA, USA
| | - Bernhard Wolfrum
- Neuroelectronics, Department of Electrical Engineering, Technische Universität München, Garching, Germany
- Medical & Health Informatics Laboratories, NTT Research Incorporated, Sunnyvale, CA, USA
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität, München, Germany
- Matter to Life Program, Max Planck School, München, Germany
| | - Andreas R Bausch
- Lehrstuhl für Zellbiophysik E27, Technische Universität München, Garching, Germany.
- Center for Functional Protein Assemblies, Garching bei München, Germany.
- Matter to Life Program, Max Planck School, München, Germany.
- Center for Organoid Systems and Tissue Engineering (COS), Technische Universität München, Garching, Germany.
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13
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Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity. Nat Commun 2022; 13:6573. [PMID: 36323696 PMCID: PMC9630547 DOI: 10.1038/s41467-022-34396-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 10/24/2022] [Indexed: 11/06/2022] Open
Abstract
Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.
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14
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Najma B, Varghese M, Tsidilkovski L, Lemma L, Baskaran A, Duclos G. Competing instabilities reveal how to rationally design and control active crosslinked gels. Nat Commun 2022; 13:6465. [PMID: 36309493 PMCID: PMC9617906 DOI: 10.1038/s41467-022-34089-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Accepted: 10/13/2022] [Indexed: 12/25/2022] Open
Abstract
How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.
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Affiliation(s)
- Bibi Najma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Minu Varghese
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.214458.e0000000086837370Department of Physics, University of Michigan, Ann Arbor, MI 48109 USA
| | - Lev Tsidilkovski
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Linnea Lemma
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA ,grid.133342.40000 0004 1936 9676Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106 USA ,grid.16750.350000 0001 2097 5006Present Address: Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544 USA
| | - Aparna Baskaran
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
| | - Guillaume Duclos
- grid.253264.40000 0004 1936 9473Department of Physics, Brandeis University, Waltham, MA 02453 USA
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15
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Optimal transport and control of active drops. Proc Natl Acad Sci U S A 2022; 119:e2121985119. [PMID: 36001692 PMCID: PMC9436341 DOI: 10.1073/pnas.2121985119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.
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16
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Zhang DQ, Li ZY, Li B. Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics. Phys Rev E 2022; 105:064607. [PMID: 35854599 DOI: 10.1103/physreve.105.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 05/27/2022] [Indexed: 06/15/2023]
Abstract
Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.
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Affiliation(s)
- De-Qing Zhang
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Zhong-Yi Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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17
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Schildknecht D, Popova AN, Stellwagen J, Thomson M. Reinforcement learning reveals fundamental limits on the mixing of active particles. SOFT MATTER 2022; 18:617-625. [PMID: 34929723 DOI: 10.1039/d1sm01400e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The control of far-from-equilibrium physical systems, including active materials, requires advanced control strategies due to the non-linear dynamics and long-range interactions between particles, preventing explicit solutions to optimal control problems. In such situations, Reinforcement Learning (RL) has emerged as an approach to derive suitable control strategies. However, for active matter systems, it is an important open question how the mathematical structure and the physical properties determine the tractability of RL. In this paper, we demonstrate that RL can only find good mixing strategies for active matter systems that combine attractive and repulsive interactions. Using analytic results from dynamical systems theory, we show that combining both interaction types is indeed necessary for the existence of mixing-inducing hyperbolic dynamics and therefore the ability of RL to find homogeneous mixing strategies. In particular, we show that for drag-dominated translational-invariant particle systems, mixing relies on combined attractive and repulsive interactions. Therefore, our work demonstrates which experimental developments need to be made to make protein-based active matter applicable, and it provides some classification of microscopic interactions based on macroscopic behavior.
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Affiliation(s)
- Dominik Schildknecht
- Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA.
| | - Anastasia N Popova
- Applied and Computational Mathematics, California Institute of Technology, Pasadena CA, USA
| | - Jack Stellwagen
- School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA
| | - Matt Thomson
- Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA.
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Wagner CG, Norton MM, Park JS, Grover P. Exact Coherent Structures and Phase Space Geometry of Preturbulent 2D Active Nematic Channel Flow. PHYSICAL REVIEW LETTERS 2022; 128:028003. [PMID: 35089772 DOI: 10.1103/physrevlett.128.028003] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic "active turbulence." Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact coherent structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant exact coherent structures and connecting orbits in a preturbulent active nematic channel flow, which enables a fully nonlinear but highly reduced-order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate- to high-activity regime.
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Affiliation(s)
- Caleb G Wagner
- Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
| | - Michael M Norton
- School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Jae Sung Park
- Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
| | - Piyush Grover
- Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
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19
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Susser AL, Kralj S, Rosenblatt C. Co-revolving topological defects in a nematic liquid crystal. SOFT MATTER 2021; 17:9616-9623. [PMID: 34622261 PMCID: PMC8573773 DOI: 10.1039/d1sm01124c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +1/2. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E, these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency ν, where the threshold field for full co-revolution scales as ν1/2. Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency "phase diagram" compellingly suggests that the induced fluctuations and eventual co-revolutions of the ordinarily static defects are coupled strongly to-and driven by-the presence of the hydrodynamic instability. The observed behaviour suggests a Lehmann-like mechanism that drives the co-revolution.
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Affiliation(s)
- Adam L Susser
- Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA.
| | - Samo Kralj
- Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia and Jožef Stefan Institute, Koroška cesta 160, SI-2000 Maribor, P.O. Box 3000, SI-1000 Ljubljana, Slovenia
| | - Charles Rosenblatt
- Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA.
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20
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Submersed micropatterned structures control active nematic flow, topology, and concentration. Proc Natl Acad Sci U S A 2021; 118:2106038118. [PMID: 34535551 DOI: 10.1073/pnas.2106038118] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/24/2021] [Indexed: 01/10/2023] Open
Abstract
Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.
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21
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Mirantsev LV. Behavior of chiral active nematics confined to nanoscopic circular region. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:112. [PMID: 34476624 DOI: 10.1140/epje/s10189-021-00120-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 08/26/2021] [Indexed: 06/13/2023]
Abstract
We performed molecular dynamic simulations of a model active nematic confined to a two-dimensional nanoscopic circular region under both tangential and radial anchoring boundary conditions. This active material is assumed to be composed of elongated chiral particles which interact with each other by means of isotropic Lennard-Jones and anisotropic Maier-Saupe-like potentials. These particles have the lateral appendage emitting a jet of some substance generated by a certain internal chemical reaction. As a result, such elongated particles are exposed to both the reactive self-propelled force and the torque that provide an additional translational movement of particles and a self-rotation with respect to their geometric centers. It has been found that the chiral active nematics under consideration form time-dependent vortex-like structures with two +1/2 topological defects which are similar to experimentally observed structures in active materials.
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Affiliation(s)
- L V Mirantsev
- Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoi 61, V. O., St., Saint Petersburg, Russia, 199178.
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Mozaffari A, Zhang R, Atzin N, de Pablo JJ. Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics. PHYSICAL REVIEW LETTERS 2021; 126:227801. [PMID: 34152186 DOI: 10.1103/physrevlett.126.227801] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 01/06/2021] [Accepted: 05/03/2021] [Indexed: 06/13/2023]
Abstract
Topological defects in active liquid crystals can be confined by introducing gradients of activity. Here, we examine the dynamical behavior of two defects confined by a sharp gradient of activity that separates an active circular region and a surrounding passive nematic material. Continuum simulations are used to explain how the interplay among energy injection into the system, hydrodynamic interactions, and frictional forces governs the dynamics of topologically required self-propelling +1/2 defects. Our findings are rationalized in terms of a phase diagram for the dynamical response of defects in terms of activity and frictional damping strength. Different regions of the underlying phase diagram correspond to distinct dynamical modes, namely immobile defects, steady rotation of defects, bouncing defects, bouncing-cruising defects, dancing defects, and multiple defects with irregular dynamics. These dynamic states raise the prospect of generating synchronized defect arrays for microfluidic applications.
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Affiliation(s)
- Ali Mozaffari
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Rui Zhang
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Noe Atzin
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, USA
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23
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Lavrentovich OD. Design of nematic liquid crystals to control microscale dynamics. LIQUID CRYSTALS REVIEWS 2021; 8:59-129. [PMID: 34956738 PMCID: PMC8698256 DOI: 10.1080/21680396.2021.1919576] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 04/11/2021] [Indexed: 05/25/2023]
Abstract
The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.
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Affiliation(s)
- Oleg D Lavrentovich
- Advanced Materials and Liquid Crystal Institute, Department of Physics, Materials Science Graduate Program, Kent State University, Kent, OH 44242, USA
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Zhou Z, Joshi C, Liu R, Norton MM, Lemma L, Dogic Z, Hagan MF, Fraden S, Hong P. Machine learning forecasting of active nematics. SOFT MATTER 2021; 17:738-747. [PMID: 33220675 DOI: 10.1039/d0sm01316a] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.
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