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Li Z, Ye H, Lin J, Ouyang Z. Analysis of the number of topological defects in active nematic fluids under applied shear flow. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:43. [PMID: 38900310 DOI: 10.1140/epje/s10189-024-00437-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2024] [Accepted: 05/31/2024] [Indexed: 06/21/2024]
Abstract
The number of topological defects in the shear flow of active nematic fluids is numerically investigated in this study. The evolution of the flow state of extensile active nematic fluids is explored by increasing the activity of active nematic fluids. Evidently, medium-activity active nematic fluids exhibit a highly ordered vortex lattice fluid state. However, high-activity active nematic fluids exhibit a meso-scale turbulent flow accompanied by topological defects. The number of topological defects (Ndef) increases with increasing shear Reynolds number (Res). Fluid viscosity strongly influences Ndef, while the influence of fluid density is relatively weak. Ndef decreases with increasing activity length scale (lζ) value. A small Res value strongly influences Ndef, whereas a large lζ value only weakly influences Ndef. As the activity increases, Ndef in contractile active nematic fluids becomes larger than that of extensile active nematic fluids.
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Affiliation(s)
- Zhenna Li
- State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China
| | - Hao Ye
- State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China
| | - Jianzhong Lin
- State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China.
- Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Ningbo University, Ningbo, 315201, China.
| | - Zhenyu Ouyang
- Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Ningbo University, Ningbo, 315201, China
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2
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Barakat JM, Modica KJ, Lu L, Anujarerat S, Choi KH, Takatori SC. Surface Topography Induces and Orients Nematic Swarms of Active Filaments: Considerations for Lab-On-A-Chip Devices. ACS APPLIED NANO MATERIALS 2024; 7:12142-12152. [PMID: 38808306 PMCID: PMC11129142 DOI: 10.1021/acsanm.4c02020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2024] [Revised: 04/15/2024] [Accepted: 04/16/2024] [Indexed: 05/30/2024]
Abstract
Surface-bound molecular motors can drive the collective motion of cytoskeletal filaments in the form of nematic bands and polar flocks in reconstituted gliding assays. Although these "swarming transitions" are an emergent property of active filament collisions, they can be controlled and guided by tuning the surface chemistry or topography of the substrate. To date, the impact of surface topography on collective motion in active nematics is only partially understood, with most experimental studies focusing on the escape of a single filament from etched channels. Since the late 1990s, significant progress has been made to utilize the nonequilibrium properties of active filaments and create a range of functional nanodevices relevant to biosensing and parallel computation; however, the complexity of these swarming transitions presents a challenge when attempting to increase filament surface concentrations. In this work, we etch shallow, linear trenches into glass substrates to induce the formation of swarming nematic bands and investigate the mechanisms by which surface topography regulates the two-dimensional (2D) collective motion of driven filamentous actin (F-actin). We demonstrate that nematic swarms only appear at intermediate trench spacings and vanish if the trenches are made too narrow, wide, or tortuous. To rationalize these results, we simulate the F-actin as self-propelled, semiflexible chains subject to a soft, spatially modulated potential that encodes the energetic cost of bending a filament along the edge of a trench. In our model, we hypothesize that an individual filament experiences a penalty when its projected end-to-end distance is smaller than the trench spacing ("bending and turning"). However, chains that span the channel width glide above the trenches in a force- and torque-free manner ("crowd-surfing"). Our simulations demonstrate that collections of filaments form nematic bands only at intermediate trench spacings, consistent with our experimental findings.
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Affiliation(s)
| | | | - Le Lu
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Stephanie Anujarerat
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Kyu Hwan Choi
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
| | - Sho C. Takatori
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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3
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Híjar H, Majumdar A. Particle-based and continuum models for confined nematics in two dimensions. SOFT MATTER 2024; 20:3755-3770. [PMID: 38629234 DOI: 10.1039/d3sm01684f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2024]
Abstract
We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.
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Affiliation(s)
| | - Apala Majumdar
- Department of Mathematics and Statistics, University of Strathclyde, UK
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4
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Keogh RR, Kozhukhov T, Thijssen K, Shendruk TN. Active Darcy's Law. PHYSICAL REVIEW LETTERS 2024; 132:188301. [PMID: 38759204 DOI: 10.1103/physrevlett.132.188301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 03/11/2024] [Indexed: 05/19/2024]
Abstract
While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.
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Affiliation(s)
- Ryan R Keogh
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Timofey Kozhukhov
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Kristian Thijssen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, Denmark
| | - Tyler N Shendruk
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
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5
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Redford SA, Colen J, Shivers JL, Zemsky S, Molaei M, Floyd C, Ruijgrok PV, Vitelli V, Bryant Z, Dinner AR, Gardel ML. Motor crosslinking augments elasticity in active nematics. SOFT MATTER 2024; 20:2480-2490. [PMID: 38385209 PMCID: PMC10933839 DOI: 10.1039/d3sm01176c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Accepted: 01/12/2024] [Indexed: 02/23/2024]
Abstract
In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.
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Affiliation(s)
- Steven A Redford
- The Graduate Program in Biophysical Sciences, University of Chicago, Chicago, IL 60637, USA
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
| | - Jonathan Colen
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
| | - Jordan L Shivers
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Sasha Zemsky
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
- Program in Biophysics, Stanford University, Stanford, CA 94305, USA
| | - Mehdi Molaei
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
| | - Carlos Floyd
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Paul V Ruijgrok
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - Vincenzo Vitelli
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
| | - Zev Bryant
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
- Department of Structural Biology, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Aaron R Dinner
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
| | - Margaret L Gardel
- Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA.
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
- James Franck Institute, University of Chicago, Chicago, IL 60637, USA
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
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6
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Partovifard A, Grawitter J, Stark H. Controlling active turbulence by activity patterns. SOFT MATTER 2024; 20:1800-1814. [PMID: 38305449 DOI: 10.1039/d3sm01050c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
By patterning activity in space, one can control active turbulence. To show this, we use Doi's hydrodynamic equations of a semidilute solution of active rods. A linear stability analysis reveals the resting isotropic fluid to be unstable above an absolute pusher activity. The emergent activity-induced paranematic state displays active turbulence, which we characterize by different quantities including the energy spectrum, which shows the typical power-law decay with exponent -4. Then, we control the active turbulence by a square lattice of circular spots where activity is switched off. In the parameter space lattice constant versus surface-to-surface distance of the spots, we identify different flow states. Most interestingly, for lattice constants below the vorticity correlation length and for spot distances smaller than the nematic coherence length, we observe a multi-lane flow state, where flow lanes with alternating flow directions are separated by a street of vortices. The flow pattern displays pronounced multistability and also appears transiently at the transition to the isotropic active-turbulence state. At larger lattice constants a trapped vortex state is identified with a non-Gaussian vorticity distribution due to the low flow vorticity at the spots. It transitions to conventional active turbulence for increasing spot distance.
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Affiliation(s)
- Arghavan Partovifard
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
| | - Josua Grawitter
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
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7
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Ye H, Ouyang Z, Lin J. On particle motion in a confined square domain filled with active fluids. SOFT MATTER 2024; 20:1786-1799. [PMID: 38305105 DOI: 10.1039/d3sm01321a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
The motion of passive particles in a confined square domain filled with active fluids has been numerically simulated using a direct-fictitious domain method. The ratio of particle diameter to the side length of the square domain (dp/L) is adopted to classify the degree of confinement (i.e., strong or weak confinement). The translational mean-squared displacement (MSDT) of weakly-confined particles scales well with the reported theoretical and experimental results in a short time and eventually reaches a plateau because of the confined environment. Additionally, the radial probability densities of the particle positions gradually increase with increasing distance from the center of the square domain at relatively high activity levels, displaying an apparent rise near the boundary and maximize near the corner. Conversely, the strongly confined particles migrate toward the center of the square domain or approach the corner with continuous rotation. In addition, the localized minima of the angular velocity of the particles show a periodic behavior, with the vortices periodically becoming more organized. Moreover, with increasing activity, two distinct linearly correlated regimes emerge in the relationship between the particle's rotational velocity and the activity. A comprehensive analysis of the collective dynamics reveals that the cutoff length is Rc ≈ 0.19(2.375dp), pointing to the distance at which the velocities of two particles are uncorrelated. Moreover, the spatial correlation function (Ip) shows a small peak at Rr ≈ 0.12(1.5dp), suggesting a relatively strong correlation between a given particle and another particle located at a distance Rr from it. Interestingly, both Rc and Rr are smaller than those observed in an unbounded flow, which indicates that boundary confinement significantly influences the ability of the particles to form coherent structures.
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Affiliation(s)
- Hao Ye
- Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China.
| | - Zhenyu Ouyang
- Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, 315210 Ningbo, China.
| | - Jianzhong Lin
- Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, China.
- Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, 315210 Ningbo, China.
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8
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Macías-Durán J, Duarte-Alaniz V, Híjar H. Active nematic liquid crystals simulated by particle-based mesoscopic methods. SOFT MATTER 2023; 19:8052-8069. [PMID: 37700612 DOI: 10.1039/d3sm00481c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.
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Affiliation(s)
- Jesús Macías-Durán
- La Salle University Mexico, Benjamin Franklin 45, 06140, Mexico City, Mexico.
| | | | - Humberto Híjar
- La Salle University Mexico, Benjamin Franklin 45, 06140, Mexico City, Mexico.
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9
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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: 0] [Impact Index Per Article: 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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10
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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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11
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Joshi C, Ray S, Lemma LM, Varghese M, Sharp G, Dogic Z, Baskaran A, Hagan MF. Data-Driven Discovery of Active Nematic Hydrodynamics. PHYSICAL REVIEW LETTERS 2022; 129:258001. [PMID: 36608242 DOI: 10.1103/physrevlett.129.258001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.
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Affiliation(s)
- Chaitanya Joshi
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Sattvic Ray
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Minu Varghese
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 USA
| | - Graham Sharp
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Zvonimir Dogic
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Aparna Baskaran
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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12
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Active boundary layers in confined active nematics. Nat Commun 2022; 13:6675. [PMID: 36335213 PMCID: PMC9637202 DOI: 10.1038/s41467-022-34336-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 10/21/2022] [Indexed: 11/08/2022] Open
Abstract
The role of boundary layers in conventional liquid crystals is commonly related to the mesogen anchoring on confining walls. In the classical view, anchoring enslaves the orientational field of the passive material under equilibrium conditions. In this work, we show that an active nematic can develop active boundary layers that topologically polarize the confining walls. We find that negatively-charged defects accumulate in the boundary layer, regardless of the wall curvature, and they influence the overall dynamics of the system to the point of fully controlling the behavior of the active nematic in situations of strong confinement. Further, we show that wall defects exhibit behaviors that are essentially different from those of their bulk counterparts, such as high motility or the ability to recombine with another defect of like-sign topological charge. These exotic behaviors result from a change of symmetry induced by the wall in the director field around the defect. Finally, we suggest that the collective dynamics of wall defects might be described in terms of a model equation for one-dimensional spatio-temporal chaos.
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13
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Coelho RCV, Araújo NAM, Telo da Gama MM. Dispersion of activity at an active-passive nematic interface. SOFT MATTER 2022; 18:7642-7653. [PMID: 36169262 DOI: 10.1039/d2sm00988a] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems known as active nematics. However, the dynamics of this mixing is non-trivial as there is a coupling between nutrients concentration and velocity field. To address this question, we solve the hydrodynamic equation for active nematics to model the bacterial swarms coupled to an advection-diffusion equation for the activity field, which is proportional to the concentration of nutrients. At the interface between active and passive nematics the activity field is transported by the interfacial flows and in turn it modifies them through the generation of active stresses. We find that the dispersion of this conserved activity field is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects.
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Affiliation(s)
- Rodrigo C V Coelho
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Nuno A M Araújo
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
| | - Margarida M Telo da Gama
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
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14
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Kumar S, Mishra S. Active nematic gel with quenched disorder. Phys Rev E 2022; 106:044603. [PMID: 36397569 DOI: 10.1103/physreve.106.044603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2022] [Accepted: 09/22/2022] [Indexed: 06/16/2023]
Abstract
With quenched disorder, we introduce two-dimensional active nematics suspended in an incompressible fluid. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density, orientation, and flow fields. The quenched disorder is introduced such that it interacts with the local orientation at every point with some strength. Disorder strength is tuned from zero to large values. We numerically study the defect dynamics and system kinetics and find that the finite disorder slows the ordering. The presence of fluid induces large fluctuation in the orientation field, further disturbing the ordering. The large fluctuation in the orientation field due to the fluid is so dominant that it reduces the effect of the quenched disorder. We have also found that the disorder effect is almost the same for both the contractile and extensile nature of active stresses in the system. This study can help to understand the impact of quenched disorder on the ordering kinetics of active gels with nematic interaction among the constituent objects.
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Affiliation(s)
- Sameer Kumar
- Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
| | - Shradha Mishra
- Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
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15
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Vafa F, Mahadevan L. Active Nematic Defects and Epithelial Morphogenesis. PHYSICAL REVIEW LETTERS 2022; 129:098102. [PMID: 36083666 DOI: 10.1103/physrevlett.129.098102] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Revised: 04/11/2022] [Accepted: 05/25/2022] [Indexed: 06/15/2023]
Abstract
Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.
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Affiliation(s)
- Farzan Vafa
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L Mahadevan
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Departments of Physics, and Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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16
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Kozhukhov T, Shendruk TN. Mesoscopic simulations of active nematics. SCIENCE ADVANCES 2022; 8:eabo5788. [PMID: 36001669 PMCID: PMC9401632 DOI: 10.1126/sciadv.abo5788] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a substantial role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarse-grained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multiparticle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active nematic MPCD (AN-MPCD) simulations not only exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing simulations of composite active-passive systems.
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17
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Keogh RR, Chandragiri S, Loewe B, Ala-Nissila T, Thampi SP, Shendruk TN. Helical flow states in active nematics. Phys Rev E 2022; 106:L012602. [PMID: 35974522 DOI: 10.1103/physreve.106.l012602] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.
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Affiliation(s)
- Ryan R Keogh
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Santhan Chandragiri
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Benjamin Loewe
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Tapio Ala-Nissila
- MSP Group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
- Interdisciplinary Centre for Mathematical Modelling, Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Sumesh P Thampi
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Tyler N Shendruk
- School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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18
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Nejad MR, Yeomans JM. Active Extensile Stress Promotes 3D Director Orientations and Flows. PHYSICAL REVIEW LETTERS 2022; 128:048001. [PMID: 35148135 DOI: 10.1103/physrevlett.128.048001] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Revised: 08/21/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist type in extensile or wedge type in contractile materials.
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Affiliation(s)
- Mehrana R Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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19
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Koch CM, Wilczek M. Role of Advective Inertia in Active Nematic Turbulence. PHYSICAL REVIEW LETTERS 2021; 127:268005. [PMID: 35029495 DOI: 10.1103/physrevlett.127.268005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 10/22/2021] [Indexed: 06/14/2023]
Abstract
Suspensions of active agents with nematic interactions exhibit complex spatiotemporal dynamics such as mesoscale turbulence. Since the Reynolds number of microscopic flows is very small on the scale of individual agents, inertial effects are typically excluded in continuum theories of active nematic turbulence. Whether active stresses can collectively excite inertial flows is currently unclear. To address this question, we investigate a two-dimensional continuum theory for active nematic turbulence. In particular, we compare mesoscale turbulence with and without the effects of advective inertia. We find that inertial effects can influence the flow already close to the onset of the turbulent state and, moreover, give rise to large-scale fluid motion for strong active driving. A detailed analysis of the kinetic energy budget reveals an energy transfer to large scales mediated by inertial advection. While this transfer is small in comparison to energy injection and dissipation, its effects accumulate over time. The inclusion of friction, which is typically present in experiments, can compensate for this effect. The findings suggest that the inclusion of inertia and friction may be necessary for dynamically consistent theories of active nematic turbulence.
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Affiliation(s)
- Colin-Marius Koch
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany and Faculty of Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany and Faculty of Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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20
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Abstract
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is uniform across the system, the Turing patterns dissociate when the flux from active advection balances that from the reaction-diffusion process. If the activity is coupled to the concentration of Turing morphogens, and neighbouring stripes have equal and opposite activity, the system self organises into a pattern of shearing flows, with stripes tending to fracture and slip sideways to join their neighbours. We discuss the role of active instabilities in controlling the crossover between these limits. Our results are of relevance to mechanochemical coupling in biological systems.
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Affiliation(s)
- Saraswat Bhattacharyya
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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21
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Samui A, Yeomans JM, Thampi SP. Flow transitions and length scales of a channel-confined active nematic. SOFT MATTER 2021; 17:10640-10648. [PMID: 34788355 DOI: 10.1039/d1sm01434j] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We perform lattice Boltzmann simulations of an active nematic fluid confined in a two-dimensional channel to study the range of flow states that are stabilised by the confinement: unidirectional flow, oscillatory flow, the dancing state, localised active turbulence and fully-developed active turbulence. We analyse the flows in Fourier space, and measure a range of different length scales which describe the flows. We argue that the different states occur as a result of flow instabilities inherent to the system. As a consequence the characteristic length scale for oscillatory flow, the dancing state and localised active turbulence is set by the channel width. Fully-developed active turbulence occurs only when the channel width is larger than the intrinsic, active length scale of the bulk fluid. The results clarify why the activity number is a control parameter for the flow transitions.
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Affiliation(s)
- Abhik Samui
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
| | - Sumesh P Thampi
- Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
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22
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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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23
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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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24
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Mitchell KA, Tan AJ, Arteaga J, Hirst LS. Fractal generation in a two-dimensional active-nematic fluid. CHAOS (WOODBURY, N.Y.) 2021; 31:073125. [PMID: 34340333 DOI: 10.1063/5.0050795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 06/18/2021] [Indexed: 06/13/2023]
Abstract
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k-β for large wavenumbers k. The parameter β is measured for several experimental realizations. Though β is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k-β seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between β and a single dimensionless quantity r, which characterizes the compressibility.
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Affiliation(s)
- Kevin A Mitchell
- Physics Department, University of California, Merced, Merced, California 95344, USA
| | - Amanda J Tan
- Physics Department, University of California, Merced, Merced, California 95344, USA
| | - Jorge Arteaga
- Physics Department, University of California, Merced, Merced, California 95344, USA
| | - Linda S Hirst
- Physics Department, University of California, Merced, Merced, California 95344, USA
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25
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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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26
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Vafa F, Bowick MJ, Shraiman BI, Marchetti MC. Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells. SOFT MATTER 2021; 17:3068-3073. [PMID: 33596291 DOI: 10.1039/d0sm02027c] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.
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Affiliation(s)
- Farzan Vafa
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
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27
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Colen J, Han M, Zhang R, Redford SA, Lemma LM, Morgan L, Ruijgrok PV, Adkins R, Bryant Z, Dogic Z, Gardel ML, de Pablo JJ, Vitelli V. Machine learning active-nematic hydrodynamics. Proc Natl Acad Sci U S A 2021; 118:e2016708118. [PMID: 33653956 PMCID: PMC7958379 DOI: 10.1073/pnas.2016708118] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.
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Affiliation(s)
- Jonathan Colen
- Department of Physics, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Ming Han
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637
| | - Rui Zhang
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637
- Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR, People's Republic of China
| | - Steven A Redford
- James Franck Institute, University of Chicago, Chicago, IL 60637
- Graduate Program in Biophysical Sciences, University of Chicago, Chicago, IL 60637
| | - Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, MA 02454
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Link Morgan
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Paul V Ruijgrok
- Department of Bioengineering, Stanford University, Stanford, CA 94305
| | - Raymond Adkins
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Zev Bryant
- Department of Bioengineering, Stanford University, Stanford, CA 94305
- Department of Structural Biology, Stanford University Medical Center, Stanford, CA 94305
| | - Zvonimir Dogic
- Department of Physics, University of California, Santa Barbara, CA 92111
| | - Margaret L Gardel
- Department of Physics, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Juan J de Pablo
- Pritzer School of Molecular Engineering, University of Chicago, Chicago, IL 60637;
- Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL 60439
| | - Vincenzo Vitelli
- Department of Physics, University of Chicago, Chicago, IL 60637;
- James Franck Institute, University of Chicago, Chicago, IL 60637
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28
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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: 5] [Impact Index Per Article: 1.7] [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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29
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Thijssen K, Nejad MR, Yeomans JM. Role of Friction in Multidefect Ordering. PHYSICAL REVIEW LETTERS 2020; 125:218004. [PMID: 33275020 DOI: 10.1103/physrevlett.125.218004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 07/30/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
We use continuum simulations to study the impact of friction on the ordering of defects in an active nematic. Even in a frictionless system, +1/2 defects tend to align side by side and orient antiparallel reflecting their propensity to form, and circulate with, flow vortices. Increasing friction enhances the effectiveness of the defect-defect interactions, and defects form dynamically evolving, large-scale, positionally, and orientationally ordered structures, which can be explained as a competition between hexagonal packing, preferred by the -1/2 defects, and rectangular packing, preferred by the +1/2 defects.
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Affiliation(s)
- Kristian Thijssen
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Mehrana R Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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30
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Hardoüin J, Laurent J, Lopez-Leon T, Ignés-Mullol J, Sagués F. Active microfluidic transport in two-dimensional handlebodies. SOFT MATTER 2020; 16:9230-9241. [PMID: 32926045 DOI: 10.1039/d0sm00610f] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.
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Affiliation(s)
- Jérôme Hardoüin
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
| | - Justine Laurent
- Laboratoire de Physique et Mécanique des Milieux hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, Paris, France and Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Teresa Lopez-Leon
- Laboratoire de Physique et Mécanique des Milieux hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, Paris, France and Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Jordi Ignés-Mullol
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
| | - Francesc Sagués
- Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain. and Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, Spain
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31
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Krajnik Ž, Kos Ž, Ravnik M. Spectral energy analysis of bulk three-dimensional active nematic turbulence. SOFT MATTER 2020; 16:9059-9068. [PMID: 32901629 DOI: 10.1039/c9sm02492a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We perform energy spectrum analysis of the active turbulence in a 3D bulk active nematic using continuum numerical modelling. Specifically, we calculate the spectra of the two main energy contributions - kinetic energy and nematic elastic energy - and combine this with the geometrical analysis of the nematic order and flow fields, based on direct defect tracking and calculation of autocorrelations. We show that the active nematic elastic energy is concentrated at scales corresponding to the effective defect-to-defect separation, scaling with activity as ∼ζ0.5, whereas the kinetic energy is largest at somewhat larger scales of typically several 100 nematic correlation lengths. Nematic biaxiality is shown to have no role in active turbulence at most length scales, but can affect the nematic elastic energy by an order of magnitude at scales of the active defect core size. The effect of an external aligning field on the 3D active turbulence is explored, showing a transition from an effective active turbulent to an aligned regime. The work is aimed at providing a contribution towards understanding active turbulence in general three-dimensions, from the perspective of main energy-relevant mechanisms at different length scales of the system.
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Affiliation(s)
- Žiga Krajnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
| | - Žiga Kos
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
| | - Miha Ravnik
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia. and JoŽef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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32
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Vliegenthart GA, Ravichandran A, Ripoll M, Auth T, Gompper G. Filamentous active matter: Band formation, bending, buckling, and defects. SCIENCE ADVANCES 2020; 6:eaaw9975. [PMID: 32832652 PMCID: PMC7439626 DOI: 10.1126/sciadv.aaw9975] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2019] [Accepted: 06/05/2020] [Indexed: 06/01/2023]
Abstract
Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.
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33
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Coelho RCV, Araújo NAM, Telo da Gama MM. Propagation of active nematic-isotropic interfaces on substrates. SOFT MATTER 2020; 16:4256-4266. [PMID: 32301453 DOI: 10.1039/c9sm02306b] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Motivated by results for the propagation of active-passive interfaces of bacterial Serratia marcescens swarms [Nat. Commun., 2018, 9, 5373], we used a hydrodynamic multiphase model to investigate the propagation of interfaces of active nematics on substrates. We characterized the active nematic phase of the model through the calculation of the spatial and temporal auto correlation functions and the energy spectrum and discussed its description of the statistical dynamics of the swarms reported in the experiment. We then studied the propagation of circular and flat active-passive interfaces. We found that the closing time of the circular passive domain decays quadratically with the activity and that the structure factor of the flat interface is similar to that reported for the swarms, with an activity dependent exponent. Finally, the effect of the substrate friction was investigated. We found an activity dependent threshold, above which the turbulent active nematic forms isolated islands that shrink until the system becomes isotropic and below which the active nematic expands, with a well defined propagating interface. We also found that the interface becomes static in the presence of a friction gradient.
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Affiliation(s)
- Rodrigo C V Coelho
- Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
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34
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Patelli A, Djafer-Cherif I, Aranson IS, Bertin E, Chaté H. Understanding Dense Active Nematics from Microscopic Models. PHYSICAL REVIEW LETTERS 2019; 123:258001. [PMID: 31922774 DOI: 10.1103/physrevlett.123.258001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 09/13/2019] [Indexed: 06/10/2023]
Abstract
We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smecticlike arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.
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Affiliation(s)
- Aurelio Patelli
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Ilyas Djafer-Cherif
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
| | - Igor S Aranson
- Department of Biomedical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Eric Bertin
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100094, China
- LPTMC, Sorbonne Université, CNRS, 75005 Paris, France
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35
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Kempf F, Mueller R, Frey E, Yeomans JM, Doostmohammadi A. Active matter invasion. SOFT MATTER 2019; 15:7538-7546. [PMID: 31451816 DOI: 10.1039/c9sm01210a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.
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Affiliation(s)
- Felix Kempf
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München - Theresienstr. 37, D-80333 Munich, Germany
| | - Romain Mueller
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München - Theresienstr. 37, D-80333 Munich, Germany
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics - Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK.
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36
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Foffano G, Lintuvuori JS, Stratford K, Cates ME, Marenduzzo D. Dynamic clustering and re-dispersion in concentrated colloid-active gel composites. SOFT MATTER 2019; 15:6896-6902. [PMID: 31423501 DOI: 10.1039/c9sm01249d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the dynamics of quasi-two-dimensional concentrated suspensions of colloidal particles in active gels by computer simulations. Remarkably, we find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites. Our quasi-two-dimensional "inverse" dispersions of passive particles in active fluids (as opposed to the more common "direct" suspensions of active particles in passive fluids) provide a promising route towards the self-assembly of new soft materials.
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Affiliation(s)
- G Foffano
- Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, UMR 8626, 91405 Orsay, France
| | - J S Lintuvuori
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | - K Stratford
- EPCC, School of Physics and Astronomy, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - M E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK
| | - D Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Gutherie Tait Road, Edinburgh EH9 3FD, UK.
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37
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Pearce DJG. Activity Driven Orientational Order in Active Nematic Liquid Crystals on an Anisotropic Substrate. PHYSICAL REVIEW LETTERS 2019; 122:227801. [PMID: 31283272 DOI: 10.1103/physrevlett.122.227801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Indexed: 05/08/2023]
Abstract
We investigate the effect of an anisotropic substrate on the turbulent dynamics of a simulated two-dimensional active nematic. This is introduced as an anisotropic friction and an effective anisotropic viscosity, with the orientation of the anisotropy being defined by the substrate. In this system, we observe the emergence of global nematic order of topological defects that is controlled by the degree of anisotropy in the viscosity and the magnitude of the active stress. No global defect alignment is seen in passive liquid crystals with anisotropic viscosity or friction confirming that ordering is driven by the active stress. We then closely examine the active flow generated by a single defect to show that the net kinetic energy of the flow is dependent on the orientation of the defect relative to the substrate, resulting in a torque on the defect to align it with the anisotropy in the substrate.
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Affiliation(s)
- D J G Pearce
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland and Department of Biochemistry, University of Geneva, Geneva 1205, Switzerland
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38
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Lemma LM, DeCamp SJ, You Z, Giomi L, Dogic Z. Statistical properties of autonomous flows in 2D active nematics. SOFT MATTER 2019; 15:3264-3272. [PMID: 30920553 PMCID: PMC6924514 DOI: 10.1039/c8sm01877d] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs the motion of individual kinesin motors.
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Affiliation(s)
- Linnea M Lemma
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
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39
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Cai LB, Chaté H, Ma YQ, Shi XQ. Dynamical subclasses of dry active nematics. Phys Rev E 2019; 99:010601. [PMID: 30780307 DOI: 10.1103/physreve.99.010601] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Indexed: 06/09/2023]
Abstract
We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.
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Affiliation(s)
- Li-Bing Cai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Hugues Chaté
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100094, China
| | - Yu-Qiang Ma
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
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40
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Abstract
Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such "active nematics" systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here, we introduce an active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path toward more quantitative active matter research.
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41
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Kumar N, Zhang R, de Pablo JJ, Gardel ML. Tunable structure and dynamics of active liquid crystals. SCIENCE ADVANCES 2018; 4:eaat7779. [PMID: 30333990 PMCID: PMC6184751 DOI: 10.1126/sciadv.aat7779] [Citation(s) in RCA: 90] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2018] [Accepted: 08/31/2018] [Indexed: 05/21/2023]
Abstract
Active materials are capable of converting free energy into directional motion, giving rise to notable dynamical phenomena. Developing a general understanding of their structure in relation to the underlying nonequilibrium physics would provide a route toward control of their dynamic behavior and pave the way for potential applications. The active system considered here consists of a quasi-two-dimensional sheet of short (≈1 μm) actin filaments driven by myosin II motors. By adopting a concerted theoretical and experimental strategy, new insights are gained into the nonequilibrium properties of active nematics over a wide range of internal activity levels. In particular, it is shown that topological defect interactions can be led to transition from attractive to repulsive as a function of initial defect separation and relative orientation. Furthermore, by examining the +1/2 defect morphology as a function of activity, we found that the apparent elastic properties of the system (the ratio of bend-to-splay elastic moduli) are altered considerably by increased activity, leading to an effectively lower bend elasticity. At high levels of activity, the topological defects that decorate the material exhibit a liquid-like structure and adopt preferred orientations depending on their topological charge. Together, these results suggest that it should be possible to tune internal stresses in active nematic systems with the goal of designing out-of-equilibrium structures with engineered dynamic responses.
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Affiliation(s)
- Nitin Kumar
- James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
- Department of Physics, The University of Chicago, Chicago, IL 60637, USA
| | - Rui Zhang
- Institute for Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
| | - Juan J. de Pablo
- Institute for Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA
- Institute for Molecular Engineering, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Margaret L. Gardel
- James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
- Department of Physics, The University of Chicago, Chicago, IL 60637, USA
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, IL 60637, USA
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42
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Doostmohammadi A, Ignés-Mullol J, Yeomans JM, Sagués F. Active nematics. Nat Commun 2018; 9:3246. [PMID: 30131558 PMCID: PMC6104062 DOI: 10.1038/s41467-018-05666-8] [Citation(s) in RCA: 255] [Impact Index Per Article: 42.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Revised: 06/28/2018] [Accepted: 07/19/2018] [Indexed: 11/09/2022] Open
Abstract
Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.
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Affiliation(s)
- Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Rd., Oxford, OX1 3PU, UK.
| | - Jordi Ignés-Mullol
- Departament de Ciència de Materials i Química Física and Institute of Nanoscience and Nanotechnology, Universitat de Barcelona, Martí I Franquès 1, 08028, Barcelona, Catalonia, Spain
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Rd., Oxford, OX1 3PU, UK
| | - Francesc Sagués
- Departament de Ciència de Materials i Química Física and Institute of Nanoscience and Nanotechnology, Universitat de Barcelona, Martí I Franquès 1, 08028, Barcelona, Catalonia, Spain
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43
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Shendruk TN, Thijssen K, Yeomans JM, Doostmohammadi A. Twist-induced crossover from two-dimensional to three-dimensional turbulence in active nematics. Phys Rev E 2018; 98:010601. [PMID: 30110824 DOI: 10.1103/physreve.98.010601] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Indexed: 12/27/2022]
Abstract
While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-two-dimensional (quasi-2D) to three-dimensional (3D) chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. Above this critical activity highly contorted disclination lines and disclination loops are formed. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.
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Affiliation(s)
- Tyler N Shendruk
- The Rockefeller University, 1230 York Avenue, New York, New York 10021, USA
| | - Kristian Thijssen
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Amin Doostmohammadi
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
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44
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Norton MM, Baskaran A, Opathalage A, Langeslay B, Fraden S, Baskaran A, Hagan MF. Insensitivity of active nematic liquid crystal dynamics to topological constraints. Phys Rev E 2018; 97:012702. [PMID: 29448352 DOI: 10.1103/physreve.97.012702] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Indexed: 11/07/2022]
Abstract
Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.
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Affiliation(s)
- Michael M Norton
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Arvind Baskaran
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Achini Opathalage
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Blake Langeslay
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Seth Fraden
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Aparna Baskaran
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
| | - Michael F Hagan
- Physics Department, Brandeis University, Waltham, Massachusetts 02453, USA
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45
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Cortese D, Eggers J, Liverpool TB. Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals. Phys Rev E 2018; 97:022704. [PMID: 29548179 DOI: 10.1103/physreve.97.022704] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Indexed: 11/07/2022]
Abstract
We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q=1/2 and q=-1/2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.
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Affiliation(s)
- Dario Cortese
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
| | - Jens Eggers
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
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46
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Henkes S, Marchetti MC, Sknepnek R. Dynamical patterns in nematic active matter on a sphere. Phys Rev E 2018; 97:042605. [PMID: 29758687 DOI: 10.1103/physreve.97.042605] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Indexed: 01/24/2023]
Abstract
Using simulations of self-propelled agents with short-range repulsion and nematic alignment, we explore the dynamical phases of a dense active nematic confined to the surface of a sphere. We map the nonequilibrium phase diagram as a function of curvature, alignment strength, and activity. Our model reproduces several phases seen in recent experiments on active microtubule bundles confined the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a polar band wrapping around an equator, with large empty spherical caps corresponding to two +1 defects at the poles. Upon further increasing activity, the bands fold onto themselves, and the system eventually transitions to a turbulent state marked by the proliferation of pairs of topological defects. We highlight the key role of the nematic persistence length in controlling pattern formation in these confined systems with positive Gaussian curvature.
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Affiliation(s)
- Silke Henkes
- Institute for Complex Systems and Mathematical Biology, Department of Physics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - M Cristina Marchetti
- Department of Physics and Soft Matter Program, Syracuse University, Syracuse, New York 13244, USA
| | - Rastko Sknepnek
- School of Sciences and Engineering and School of Life Sciences, University of Dundee, Dundee DD1 4HN, United Kingdom
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47
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Reinken H, Klapp SHL, Bär M, Heidenreich S. Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions. Phys Rev E 2018; 97:022613. [PMID: 29548118 DOI: 10.1103/physreve.97.022613] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
In this paper, we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic model (pushers or pullers), which include hydrodynamic interactions on both small length scales (polar alignment of neighboring swimmers) and large length scales, where the solvent flow interacts with the order parameter field. The flow field is determined via the Stokes equation supplemented by an ansatz for the stress tensor. In addition to hydrodynamic interactions, we allow for nematic pair interactions stemming from excluded-volume effects. The results here substantially extend and generalize earlier findings [S. Heidenreich et al., Phys. Rev. E 94, 020601 (2016)2470-004510.1103/PhysRevE.94.020601], in which we derived a two-dimensional hydrodynamic theory. From the corresponding mean-field Fokker-Planck equation combined with a self-consistent closure scheme, we derive nonlinear field equations for the polar and the nematic order parameter, involving gradient terms of up to fourth order. We find that the effective microswimmer dynamics depends on the coupling between solvent flow and orientational order. For very weak coupling corresponding to a high viscosity of the suspension, the dynamics of mesoscale turbulence can be described by a simplified model containing only an effective microswimmer velocity.
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Affiliation(s)
- Henning Reinken
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
| | - Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587 Berlin, Germany
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48
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Shankar S, Ramaswamy S, Marchetti MC. Low-noise phase of a two-dimensional active nematic system. Phys Rev E 2018; 97:012707. [PMID: 29448420 DOI: 10.1103/physreve.97.012707] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Indexed: 06/08/2023]
Abstract
We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the two-dimensional fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long-ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist although now with strong finite-size effects and a nonuniversal scaling exponent. Nonlinear effects from the active currents lead to power-law correlations in the density field, thereby preventing macroscopic phase separation in the thermodynamic limit.
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Affiliation(s)
- Suraj Shankar
- Physics Department and Syracuse Soft & Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - M Cristina Marchetti
- Physics Department and Syracuse Soft & Living Matter Program, Syracuse University, Syracuse, New York 13244, USA
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Mandal R, Bhuyan PJ, Chaudhuri P, Rao M, Dasgupta C. Glassy swirls of active dumbbells. Phys Rev E 2017; 96:042605. [PMID: 29347636 DOI: 10.1103/physreve.96.042605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Indexed: 06/07/2023]
Abstract
Is an active glass different from a conventional passive glass? To address this, we study the dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations. This dense assembly shows dynamical arrest, first to a translational and then to a rotational glass, as one reduces temperature T or the self-propulsion force f. We monitor the dynamics along an iso-relaxation-time contour in the (T-f) plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity, which characterize the onset of glass formation-the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and it appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers. We construct continuum hydrodynamic equations for the simulated system, and we show that the observed behavior of this growing dynamic length scale can be understood from these equations.
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Affiliation(s)
- Rituparno Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Pranab Jyoti Bhuyan
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | | | - Madan Rao
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore 560065, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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50
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Guillamat P, Ignés-Mullol J, Sagués F. Taming active turbulence with patterned soft interfaces. Nat Commun 2017; 8:564. [PMID: 28916801 PMCID: PMC5601458 DOI: 10.1038/s41467-017-00617-1] [Citation(s) in RCA: 82] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Accepted: 07/13/2017] [Indexed: 11/30/2022] Open
Abstract
Active matter embraces systems that self-organize at different length and time scales, often exhibiting turbulent flows apparently deprived of spatiotemporal coherence. Here, we use a layer of a tubulin-based active gel to demonstrate that the geometry of active flows is determined by a single length scale, which we reveal in the exponential distribution of vortex sizes of active turbulence. Our experiments demonstrate that the same length scale reemerges as a cutoff for a scale-free power law distribution of swirling laminar flows when the material evolves in contact with a lattice of circular domains. The observed prevalence of this active length scale can be understood by considering the role of the topological defects that form during the spontaneous folding of microtubule bundles. These results demonstrate an unexpected strategy for active systems to adapt to external stimuli, and provide with a handle to probe the existence of intrinsic length and time scales. Active nematics consist of self-driven components that develop orientational order and turbulent flow. Here Guillamat et al. investigate an active nematic constrained in a quasi-2D geometrical setup and show that there exists an intrinsic length scale that determines the geometry in all forcing regimes.
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Affiliation(s)
- P Guillamat
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain.,Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain
| | - J Ignés-Mullol
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain.,Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain
| | - F Sagués
- Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain. .,Institute of Nanoscience and Nanotechnology (IN2UB), Universitat de Barcelona, Barcelona, 08028 Catalonia, Spain.
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