1
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Reinken H, Menzel AM. Vortex Pattern Stabilization in Thin Films Resulting from Shear Thickening of Active Suspensions. PHYSICAL REVIEW LETTERS 2024; 132:138301. [PMID: 38613265 DOI: 10.1103/physrevlett.132.138301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Revised: 01/17/2024] [Accepted: 02/29/2024] [Indexed: 04/14/2024]
Abstract
The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path toward functionalization through patterning of thin films and membranes.
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Affiliation(s)
- Henning Reinken
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
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2
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de Wit XM, Fruchart M, Khain T, Toschi F, Vitelli V. Pattern formation by turbulent cascades. Nature 2024; 627:515-521. [PMID: 38509279 PMCID: PMC10954557 DOI: 10.1038/s41586-024-07074-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 01/15/2024] [Indexed: 03/22/2024]
Abstract
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation1-6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state7. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems8-12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales4. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows13-19, stellar plasma such as the solar wind20-22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades23-25.
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Affiliation(s)
- Xander M de Wit
- Department of Applied Physics and Science Education, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Michel Fruchart
- Gulliver, ESPCI Paris, Université PSL, CNRS, Paris, France
- James Franck Institute, The University of Chicago, Chicago, IL, USA
| | - Tali Khain
- James Franck Institute, The University of Chicago, Chicago, IL, USA
| | - Federico Toschi
- Department of Applied Physics and Science Education, Eindhoven University of Technology, Eindhoven, The Netherlands.
- CNR-IAC, Rome, Italy.
| | - Vincenzo Vitelli
- James Franck Institute, The University of Chicago, Chicago, IL, USA.
- Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL, USA.
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3
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Topology, vorticity, and limit cycle in a stabilized Kuramoto-Sivashinsky equation. Proc Natl Acad Sci U S A 2022; 119:e2211359119. [PMID: 36459639 PMCID: PMC9894259 DOI: 10.1073/pnas.2211359119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022] Open
Abstract
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex-like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.
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4
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Chen L, Lee CF, Maitra A, Toner J. Incompressible Polar Active Fluids with Quenched Random Field Disorder in Dimensions d>2. PHYSICAL REVIEW LETTERS 2022; 129:198001. [PMID: 36399725 DOI: 10.1103/physrevlett.129.198001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 07/24/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.
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Affiliation(s)
- Leiming Chen
- School of Material Science and Physics, China University of Mining and Technology, Xuzhou Jiangsu, 221116, People's Republic of China
| | - Chiu Fan Lee
- Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Ananyo Maitra
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, F-95302 Cergy-Pontoise Cedex, France
| | - John Toner
- Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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5
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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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6
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Piñeros WD, Tlusty T. Spontaneous chiral symmetry breaking in a random driven chemical system. Nat Commun 2022; 13:2244. [PMID: 35474070 PMCID: PMC9042824 DOI: 10.1038/s41467-022-29952-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2021] [Accepted: 04/09/2022] [Indexed: 11/09/2022] Open
Abstract
Living systems have evolved to efficiently consume available energy sources using an elaborate circuitry of chemical reactions which, puzzlingly, bear a strict restriction to asymmetric chiral configurations. While autocatalysis is known to promote such chiral symmetry breaking, whether a similar phenomenon may also be induced in a more general class of configurable chemical systems—via energy exploitation—is a sensible yet underappreciated possibility. This work examines this question within a model of randomly generated complex chemical networks. We show that chiral symmetry breaking may occur spontaneously and generically by harnessing energy sources from external environmental drives. Key to this transition are intrinsic fluctuations of achiral-to-chiral reactions and tight matching of system configurations to the environmental drives, which together amplify and sustain diverged enantiomer distributions. These asymmetric states emerge through steep energetic transitions from the corresponding symmetric states and sharply cluster as highly-dissipating states. The results thus demonstrate a generic mechanism in which energetic drives may give rise to homochirality in an otherwise totally symmetrical environment, and from an early-life perspective, might emerge as a competitive, energy-harvesting advantage. “A hallmark of living systems is their homochirality, the selection of specific mirror symmetry in their molecules. Here, the authors show that chiral symmetry can be spontaneously broken in complex, random chemical systems via exploitation of environmental energy sources – a possible mechanism for the emergence of homochirality in life.”
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Affiliation(s)
- William D Piñeros
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan, 44919, Korea
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan, 44919, Korea. .,Department of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Korea. .,Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Korea.
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7
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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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8
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Nejad MR, Doostmohammadi A, Yeomans JM. Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics. SOFT MATTER 2021; 17:2500-2511. [PMID: 33503081 DOI: 10.1039/d0sm01794a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive limit, we show that, as the friction is increased, memory effects become more prominent and +1/2 topological defects leave increasingly persistent trails in the director field as they pass. The trails are preferential sites for defect formation and they tend to impose polar order on any new +1/2 defects. In the absence of noise and for high friction, it becomes very difficult to create defects, but trails formed by any defects present at the beginning of the simulations persist and organise into parallel arch-like patterns in the director field. We show aligned arches of equal width are approximate steady state solutions of the equations of motion which co-exist with the nematic state. We compare our results to other models in the literature, in particular dry systems with no hydrodynamics, where trails, arches and polar defect ordering have also been observed.
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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, 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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9
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Global potential, topology, and pattern selection in a noisy stabilized Kuramoto-Sivashinsky equation. Proc Natl Acad Sci U S A 2020; 117:23227-23234. [PMID: 32917812 DOI: 10.1073/pnas.2012364117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We formulate a general method to extend the decomposition of stochastic dynamics developed by Ao et al. [J. Phys. Math. Gen. 37, L25-L30 (2004)] to nonlinear partial differential equations which are nonvariational in nature and construct the global potential or Lyapunov functional for a noisy stabilized Kuramoto-Sivashinsky equation. For values of the control parameter where singly periodic stationary solutions exist, we find a topological network of a web of saddle points of stationary states interconnected by unstable eigenmodes flowing between them. With this topology, a global landscape of the steady states is found. We show how to predict the noise-selected pattern which agrees with those from stochastic simulations. Our formalism and the topology might offer an approach to explore similar systems, such as the Navier Stokes equation.
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10
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El Hasadi YM, Crapper M. Self-propelled nanofluids a coolant inspired from nature with enhanced thermal transport properties. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113548] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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11
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Linkmann M, Marchetti MC, Boffetta G, Eckhardt B. Condensate formation and multiscale dynamics in two-dimensional active suspensions. Phys Rev E 2020; 101:022609. [PMID: 32168685 DOI: 10.1103/physreve.101.022609] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Accepted: 02/05/2020] [Indexed: 11/07/2022]
Abstract
The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
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12
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Zhao H, Storey BD, Braatz RD, Bazant MZ. Learning the Physics of Pattern Formation from Images. PHYSICAL REVIEW LETTERS 2020; 124:060201. [PMID: 32109085 DOI: 10.1103/physrevlett.124.060201] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Revised: 12/09/2019] [Accepted: 01/21/2020] [Indexed: 05/21/2023]
Abstract
Using a framework of partial differential equation-constrained optimization, we demonstrate that multiple constitutive relations can be extracted simultaneously from a small set of images of pattern formation. Examples include state-dependent properties in phase-field models, such as the diffusivity, kinetic prefactor, free energy, and direct correlation function, given only the general form of the Cahn-Hilliard equation, Allen-Cahn equation, or dynamical density functional theory (phase-field crystal model). Constraints can be added based on physical arguments to accelerate convergence and avoid spurious results. Reconstruction of the free energy functional, which contains nonlinear dependence on the state variable and differential or convolutional operators, opens the possibility of learning nonequilibrium thermodynamics from only a few snapshots of the dynamics.
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Affiliation(s)
- Hongbo Zhao
- Department of Chemical Engineering, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Brian D Storey
- Toyota Research Institute, Cambridge, Massachusetts 02139, USA
- Olin College, Needham, Massachusetts 02492, USA
| | - Richard D Braatz
- Department of Chemical Engineering, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Martin Z Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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13
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Linkmann M, Boffetta G, Marchetti MC, Eckhardt B. Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence. PHYSICAL REVIEW LETTERS 2019; 122:214503. [PMID: 31283308 DOI: 10.1103/physrevlett.122.214503] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Indexed: 06/09/2023]
Abstract
The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small-scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense suspension of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2D bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.
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Affiliation(s)
- Moritz Linkmann
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - M Cristina Marchetti
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Bruno Eckhardt
- Fachbereich Physik, Philipps-Universität of Marburg, D-35032 Marburg, Germany
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14
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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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15
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Mickelin O, Słomka J, Burns KJ, Lecoanet D, Vasil GM, Faria LM, Dunkel J. Anomalous Chained Turbulence in Actively Driven Flows on Spheres. PHYSICAL REVIEW LETTERS 2018; 120:164503. [PMID: 29756929 DOI: 10.1103/physrevlett.120.164503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Indexed: 06/08/2023]
Abstract
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of antiferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.
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Affiliation(s)
- Oscar Mickelin
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jonasz Słomka
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Keaton J Burns
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Daniel Lecoanet
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Geoffrey M Vasil
- School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Luiz M Faria
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
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16
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Sahoo G, Alexakis A, Biferale L. Discontinuous Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence. PHYSICAL REVIEW LETTERS 2017; 118:164501. [PMID: 28474929 DOI: 10.1103/physrevlett.118.164501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2017] [Indexed: 06/07/2023]
Abstract
Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three-dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflections, and scale transforms) as the original equations. It is demonstrated that the examined system displays a change in the direction of the energy cascade when varying the value of a free parameter which controls the relative weights of the triadic interactions between different helical Fourier modes. The transition from a forward to inverse cascade is shown to occur at a critical point in a discontinuous manner with diverging fluctuations close to criticality. Our work thus supports the observation that purely isotropic and three-dimensional flow configurations can support inverse energy transfer when interactions are altered and that inside all turbulent flows there is a competition among forward and backward transfer mechanisms which might lead to multiple energy-containing turbulent states.
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Affiliation(s)
- Ganapati Sahoo
- Department of Physics and INFN, University of Rome 'Tor Vergata,' Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Alexandros Alexakis
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université Pierre et Marié Curie, Université Paris Diderot, 24 rue Lhomond, 75005 Paris, France
| | - Luca Biferale
- Department of Physics and INFN, University of Rome 'Tor Vergata,' Via della Ricerca Scientifica 1, 00133 Rome, Italy
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