1
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Matsukiyo H, Fukuda JI. Oscillating edge current in polar active fluid. Phys Rev E 2024; 109:054604. [PMID: 38907507 DOI: 10.1103/physreve.109.054604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Accepted: 04/11/2024] [Indexed: 06/24/2024]
Abstract
Dense bacterial suspensions exhibit turbulent behavior called bacterial turbulence. The behavior of the bulk unconstrained bacterial turbulence is described well by the Toner-Tu-Swift-Hohenberg (TTSH) equation for the velocity field. However, it remains unclear how we should treat boundary conditions on bacterial turbulence in contact with some boundaries (e.g., solid walls). To be more specific, although the importance of the edge current, the flow along the boundary, has been demonstrated in several experimental studies on confined bacterial suspensions, previous numerical studies based on the TTSH equation employ nonslip boundary conditions and do not seem to properly describe the behavior of bacteria near the boundaries. In this paper, we impose a slip boundary condition on the TTSH equation to describe the bacterial motion at boundaries. We develop a method to implement the slip boundary condition. Using this method, we have successfully produced edge current and discovered that the direction of the edge current temporally oscillates. The oscillation can be attributable to the advection term in the TTSH equation. Our paper demonstrates that boundary conditions could play an important role in the collective dynamics of active systems.
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Affiliation(s)
- Hiroki Matsukiyo
- Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - Jun-Ichi Fukuda
- Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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2
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Xu H, Wu Y. Self-enhanced mobility enables vortex pattern formation in living matter. Nature 2024; 627:553-558. [PMID: 38480895 DOI: 10.1038/s41586-024-07114-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 01/24/2024] [Indexed: 03/22/2024]
Abstract
Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.
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Affiliation(s)
- Haoran Xu
- Department of Physics and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, P.R. China
| | - Yilin Wu
- Department of Physics and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, P.R. China.
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3
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Lequy T, Menzel AM. Stochastic motion under nonlinear friction representing shear thinning. Phys Rev E 2023; 108:064606. [PMID: 38243489 DOI: 10.1103/physreve.108.064606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Accepted: 11/12/2023] [Indexed: 01/21/2024]
Abstract
We study stochastic motion under a nonlinear frictional force that levels off with increasing velocity. Specifically, our frictional force is of the so-called Coulomb-tanh type. At small speed, it increases approximately linearly with velocity, while at large speed, it approaches a constant magnitude, similarly to solid (dry, Coulomb) friction. In one spatial dimension, a formal analogy between the associated Fokker-Planck equation and the Schrödinger equation for a quantum mechanical oscillator in a nonharmonic Pöschl-Teller potential is revealed. Then, the stationary velocity statistics can be treated analytically. From such analytical considerations, we determine associated diffusion coefficients, which we confirm by agent-based simulations. Moreover, from such simulations and from numerically solving the associated Fokker-Planck equation, we find that the spatial distribution function, starting from an initial Gaussian shape, develops tails that appear exponential at intermediate timescales. At small magnitudes of stochastic driving, the velocity distribution resembles the case of linear friction, while at large magnitudes, it rather approaches the case of solid (dry, Coulomb) friction. The same is true for diffusion coefficients. In a certain sense thus interpolating between the two extreme cases of linear friction and solid (dry, Coulomb) friction, our approach should be useful to describe several cases of practical relevance. For instance, a reduced increase in friction with increasing relative speed is typical of shear-thinning behavior. Therefore, driven motion in shear-thinning environments is one specific example to which our description may be applied.
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Affiliation(s)
- Theo Lequy
- Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
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4
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Puggioni L, Boffetta G, Musacchio S. Flocking turbulence of microswimmers in confined domains. Phys Rev E 2023; 107:055107. [PMID: 37329031 DOI: 10.1103/physreve.107.055107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
We extensively study the Toner-Tu-Swift-Hohenberg model of motile active matter by means of direct numerical simulations in a two-dimensional confined domain. By exploring the space of parameters of the model we investigate the emergence of a new state of active turbulence which occurs when the aligning interactions and the self-propulsion of the swimmers are strong. This regime of flocking turbulence is characterized by a population of few strong vortices, each surrounded by an island of coherent flocking motion. The energy spectrum of flocking turbulence displays a power-law scaling with an exponent which depends weakly on the model parameters. By increasing the confinement we observe that the system, after a long transient characterized by power-law-distributed transition times, switches to the ordered state of a single giant vortex.
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Affiliation(s)
- L Puggioni
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - G Boffetta
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
- Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan
| | - S Musacchio
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
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5
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Montana F, Camporeale C, Porporato A, Rondoni L. Inertial and geometrical effects of self-propelled elliptical Brownian particles. Phys Rev E 2023; 107:054607. [PMID: 37328983 DOI: 10.1103/physreve.107.054607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/11/2023] [Indexed: 06/18/2023]
Abstract
Active particles that self-propel by transforming energy into mechanical motion represent a growing area of research in mathematics, physics, and chemistry. Here we investigate the dynamics of nonspherical inertial active particles moving in a harmonic potential, introducing geometric parameters which take into account the role of eccentricity for nonspherical particles. A comparison between the overdamped and underdamped models for elliptical particles is performed. The model of overdamped active Brownian motion has been used to describe most of the basic aspects of micrometer-sized particles moving in a liquid ("microswimmers"). We consider active particles by extending the active Brownian motion model to incorporate translation and rotation inertia and account for the role of eccentricity. We show how the overdamped and the underdamped models behave in the same way for small values of activity (Brownian case) if eccentricity is equal to zero, but increasing eccentricity leads the two dynamics to substantially depart from each other-in particular, the action of a torque induced by external forces, induced a marked difference close to the walls of the domain if eccentricity is high. Effects induced by inertia include an inertial delay time of the self-propulsion direction from the particle velocity, and the differences between the overdamped and underdamped systems are particularly evident in the first and second moments of the particle velocities. Comparison with the experimental results of vibrated granular particles shows good agreement and corroborates the notion that self-propelling massive particles moving in gaseous media are dominated by inertial effects.
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Affiliation(s)
- Federica Montana
- Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy and INFN, Sezione di Torino, Turin, Italy
| | - Carlo Camporeale
- Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, Turin, Italy
| | - Amilcare Porporato
- Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey, USA and High Meadows Environmental Institute, Princeton University, Princeton, New Jersey, USA
| | - Lamberto Rondoni
- Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy and INFN, Sezione di Torino, Turin, Italy
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6
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Puggioni L, Boffetta G, Musacchio S. Giant vortex dynamics in confined bacterial turbulence. Phys Rev E 2022; 106:055103. [PMID: 36559438 DOI: 10.1103/physreve.106.055103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Accepted: 10/13/2022] [Indexed: 06/17/2023]
Abstract
We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.
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Affiliation(s)
- L Puggioni
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - G Boffetta
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - S Musacchio
- Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
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7
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Zantop AW, Stark H. Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence. SOFT MATTER 2022; 18:6179-6191. [PMID: 35822601 DOI: 10.1039/d2sm00449f] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.
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Affiliation(s)
- Arne W Zantop
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
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8
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Menzel AM. Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions. J Chem Phys 2022; 157:011102. [DOI: 10.1063/5.0093598] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.
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Affiliation(s)
- Andreas M. Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
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9
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Aranson IS. Bacterial active matter. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:076601. [PMID: 35605446 DOI: 10.1088/1361-6633/ac723d] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.
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Affiliation(s)
- Igor S Aranson
- Departments of Biomedical Engineering, Chemistry, and Mathematics, Pennsylvania State University, University Park, PA 16802, United States of America
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10
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Bickmann J, Bröker S, Jeggle J, Wittkowski R. Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers. J Chem Phys 2022; 156:194904. [DOI: 10.1063/5.0085122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. The agreement between results from theory and simulations is found to be good.
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Affiliation(s)
- Jens Bickmann
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Stephan Bröker
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Julian Jeggle
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
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11
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Reinken H, Heidenreich S, Bär M, Klapp SHL. Ising-like Critical Behavior of Vortex Lattices in an Active Fluid. PHYSICAL REVIEW LETTERS 2022; 128:048004. [PMID: 35148157 DOI: 10.1103/physrevlett.128.048004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Revised: 11/29/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.
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Affiliation(s)
- Henning Reinken
- Technische Universität Berlin, Institute of Theoretical Physics, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Sebastian Heidenreich
- Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Department of Mathematical Modelling and Data Analysis, Abbestraße 2-12, 10587 Berlin, Germany
| | - Markus Bär
- Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Department of Mathematical Modelling and Data Analysis, Abbestraße 2-12, 10587 Berlin, Germany
| | - Sabine H L Klapp
- Technische Universität Berlin, Institute of Theoretical Physics, Straße des 17. Juni 135, 10623 Berlin, Germany
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12
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Worlitzer VM, Ariel G, Be'er A, Stark H, Bär M, Heidenreich S. Turbulence-induced clustering in compressible active fluids. SOFT MATTER 2021; 17:10447-10457. [PMID: 34762091 DOI: 10.1039/d1sm01276b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay between self-advection of the aligned swimmers and their defect topology. The typical cluster size is determined by the characteristic vortex size. Our results are obtained by investigating a continuum model of compressible polar active fluids, which incorporates typical experimental observations in bacterial suspensions, in particular a non-monotone dependence of speed on density.
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Affiliation(s)
- Vasco M Worlitzer
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
| | - Gil Ariel
- Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
| | - Avraham Be'er
- Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Midreshet Ben-Gurion, Israel
- Department of Physics, Ben-Gurion University of the Negev, 84105 Beer Sheva, Israel
| | - Holger Stark
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
| | - Markus Bär
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
| | - Sebastian Heidenreich
- Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische, Bundesanstalt Braunschweig und Berlin, Abbestrasse 2-12, D-10587 Berlin, Germany.
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13
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Zantop AW, Stark H. Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods. J Chem Phys 2021; 155:134904. [PMID: 34624984 DOI: 10.1063/5.0064558] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.
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Affiliation(s)
- Arne W Zantop
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Holger Stark
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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14
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James M, Suchla DA, Dunkel J, Wilczek M. Emergence and melting of active vortex crystals. Nat Commun 2021; 12:5630. [PMID: 34561437 PMCID: PMC8463610 DOI: 10.1038/s41467-021-25545-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/18/2021] [Indexed: 11/09/2022] Open
Abstract
Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.
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Affiliation(s)
- Martin James
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany
| | - Dominik Anton Suchla
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany.,Faculty of Physics, University of Göttingen, Göttingen, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany. .,Faculty of Physics, University of Göttingen, Göttingen, Germany.
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15
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Mukherjee S, Singh RK, James M, Ray SS. Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence. PHYSICAL REVIEW LETTERS 2021; 127:118001. [PMID: 34558935 DOI: 10.1103/physrevlett.127.118001] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behavior of microorganisms, our Letter underlines the essential differences between active and inertial turbulence.
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Affiliation(s)
- Siddhartha Mukherjee
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Rahul K Singh
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | | | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
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16
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Sprenger AR, Shaik VA, Ardekani AM, Lisicki M, Mathijssen AJTM, Guzmán-Lastra F, Löwen H, Menzel AM, Daddi-Moussa-Ider A. Towards an analytical description of active microswimmers in clean and in surfactant-covered drops. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:58. [PMID: 32920676 DOI: 10.1140/epje/i2020-11980-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Accepted: 08/10/2020] [Indexed: 05/24/2023]
Abstract
Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.
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Affiliation(s)
- Alexander R Sprenger
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany.
| | - Vaseem A Shaik
- School of Mechanical Engineering, Purdue University, 47907, West Lafayette, IN, USA
| | - Arezoo M Ardekani
- School of Mechanical Engineering, Purdue University, 47907, West Lafayette, IN, USA
| | - Maciej Lisicki
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
| | - Arnold J T M Mathijssen
- Department of Bioengineering, Stanford University, 443 Via Ortega, 94305, Stanford, CA, USA
- Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, 19104, Philadelphia, PA, USA
| | - Francisca Guzmán-Lastra
- Centro de Investigación DAiTA Lab, Facultad de Estudios Interdisciplinarios, Universidad Mayor, Av. Manuel Montt 367, Providencia, Santiago de Chile, Chile
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany
| | - Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany
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17
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Zantop AW, Stark H. Squirmer rods as elongated microswimmers: flow fields and confinement. SOFT MATTER 2020; 16:6400-6412. [PMID: 32582901 DOI: 10.1039/d0sm00616e] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Microswimmers or active elements, such as bacteria and active filaments, have an elongated shape, which determines their individual and collective dynamics. There is still a need to identify what role long-range hydrodynamic interactions play in their fascinating dynamic structure formation. We construct rods of different aspect ratios using several spherical squirmer model swimmers. With the help of the mesoscale simulation method of multi-particle collision dynamics we analyze the flow fields of these squirmer rods both in a bulk fluid and in Hele-Shaw geometries of different slab widths. Based on the hydrodynamic multipole expansion either for bulk or confinement between two parallel plates, we categorize the different multipole contributions of neutral as well as pusher-type squirmer rods. We demonstrate how confinement alters the radial decay of the flow fields for a given force or source multipole moment compared to the bulk fluid.
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Affiliation(s)
- Arne W Zantop
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
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18
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Arold D, Schmiedeberg M. Active phase field crystal systems with inertial delay and underdamped dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:47. [PMID: 32642832 DOI: 10.1140/epje/i2020-11971-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 06/23/2020] [Indexed: 06/11/2023]
Abstract
Active matter systems often are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic systems but also for many mesoscopic ones particle mass can become relevant for the dynamics. For such systems we recently proposed an underdamped continuum model which captures translationally inertial dynamics via two contributions. First, convection and second a damping time scale of inertial motion. In this paper, we ask how both of these features influence the collective behavior compared to overdamped dynamics by studying the example of the active phase field crystal model. We first focus on the case of suppressed convection to study the role of the damping time. We quantify that the relaxation process to the steady collective motion state is considerably prolonged with damping time due to the increasing occurrence of transient groups of circularly moving density peaks. Finally, we illustrate the fully underdamped case with convection. Instead of collective motion of density peaks we then find a coexistence of constant high and low density phases reminiscent of motility-induced phase separation.
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Affiliation(s)
- Dominic Arold
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany
| | - Michael Schmiedeberg
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany.
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19
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Arold D, Schmiedeberg M. Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:315403. [PMID: 32396529 DOI: 10.1088/1361-648x/ab849b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2019] [Accepted: 03/30/2020] [Indexed: 06/11/2023]
Abstract
Many active matter systems, especially on the microscopic scale, are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic active systems but also for many mesoscopic systems the time scale of translational inertial motion can become large enough to be relevant for the dynamics. This raises the question how collective dynamics and the resulting states in active matter are influenced by inertia. Therefore, we propose a coarse-grained continuum model for underdamped active matter based on a mean field description for passive systems. Furthermore, as an example, we apply the model to a system with interactions that support an alignment on short distances and an anti-alignment on longer length scales as known in the context of pattern formation due to orientational interactions. Our numerical calculations of the under- and overdamped dynamics both predict a structured laning state. However, activity induced convective flows that are only present in the underdamped model destabilize this state when the anti-alignment is weakened, leading to a collective motion state which does not occur in the overdamped limit. A turbulent transition regime between the two states can be characterized by strong density fluctuations and the absence of global ordering.
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Affiliation(s)
- Dominic Arold
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Michael Schmiedeberg
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
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20
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Maloney RC, Liao GJ, Klapp SHL, Hall CK. Clustering and phase separation in mixtures of dipolar and active particles. SOFT MATTER 2020; 16:3779-3791. [PMID: 32239046 DOI: 10.1039/c9sm02311a] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The self-assembly of colloidal particles in dynamic environments has become an important field of study because of potential applications in fabricating out-of-equilibrium materials. We investigate the phase behavior of mixtures of passive dipolar colloids and active soft spheres using Brownian dynamics simulations in two dimensions. The phase behaviors exhibited include dipolar percolated network, dipolar string-fluid, isotropic fluid, and a phase-separated state. We find that the clustering of dipolar colloids is enhanced in the presence of slow-moving active particles compared to the clustering of dipolar particles mixed with passive particles. When the active particle motility is high, the chains of dipolar particles are either broken into short chains or pushed into dense clusters. Motility-induced phase separation into dense and dilute phases is also present. The area fraction of particles in the dilute phase increases as the fraction of active particles in the system decreases, while the area fraction of particles in the dense phase remains constant. Our findings are relevant to the development of reconfigurable self-assembled materials.
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Affiliation(s)
- Ryan C Maloney
- Department of Chemical & Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695, USA.
| | - Guo-Jun Liao
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D10623 Berlin, Germany
| | - Carol K Hall
- Department of Chemical & Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695, USA.
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21
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Fürthauer S, Lemma B, Foster PJ, Ems-McClung SC, Yu CH, Walczak CE, Dogic Z, Needleman DJ, Shelley MJ. Self-straining of actively crosslinked microtubule networks. NATURE PHYSICS 2019; 15:1295-1300. [PMID: 32322291 PMCID: PMC7176317 DOI: 10.1038/s41567-019-0642-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 07/17/2019] [Indexed: 05/26/2023]
Abstract
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and densely crosslinked. Relating their large-scale dynamics to the properties of their constituents remains an unsolved problem. Here, we study an in vitro active gel made from aligned microtubules and XCTK2 kinesin motors. Using photobleaching, we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local microtubule polarity and motor concentration. This phenomenon is also observed, and remains unexplained, in spindles. We derive a general framework for coarse graining microtubule gels crosslinked by molecular motors from microscopic considerations. Using microtubule-microtubule coupling through a force-velocity relationship for kinesin, this theory naturally explains the experimental results: motors generate an active strain rate in regions of changing polarity, which allows microtubules of opposite polarities to slide past each other without stressing the material.
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Affiliation(s)
| | - Bezia Lemma
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics, Brandeis University, Waltham, MA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Peter J Foster
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | | | - Che-Hang Yu
- Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, USA
| | | | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - Daniel J Needleman
- Paulson School of Engineering & Applied Science and Department of Molecular & Cellular Biology, Harvard University, Cambridge, MA, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, NY, USA
- Courant Institute, New York University, New York, NY, USA
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22
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Daddi-Moussa-Ider A, Kurzthaler C, Hoell C, Zöttl A, Mirzakhanloo M, Alam MR, Menzel AM, Löwen H, Gekle S. Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface. Phys Rev E 2019; 100:032610. [PMID: 31639990 DOI: 10.1103/physreve.100.032610] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Indexed: 06/10/2023]
Abstract
The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.
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Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Christina Kurzthaler
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Andreas Zöttl
- Institute for Theoretical Physics, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
| | - Mehdi Mirzakhanloo
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | - Mohammad-Reza Alam
- Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
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23
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Hoell C, Löwen H, Menzel AM. Multi-species dynamical density functional theory for microswimmers: Derivation, orientational ordering, trapping potentials, and shear cells. J Chem Phys 2019. [DOI: 10.1063/1.5099554] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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24
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Abstract
Despite mounting evidence that the same gradients, which active colloids use for swimming, induce important cross-interactions (phoretic interactions), they are still ignored in most many-body descriptions, perhaps to avoid complexity and a zoo of unknown parameters. Here we derive a simple model, which reduces phoretic far-field interactions to a pair-interaction whose strength is mainly controlled by one genuine parameter (swimming speed). The model suggests that phoretic interactions are generically important for autophoretic colloids (unless effective screening of the phoretic fields is strong) and should dominate over hydrodynamic interactions for the typical case of half-coating and moderately nonuniform surface mobilities. Unlike standard minimal models, but in accordance with canonical experiments, our model generically predicts dynamic clustering in active colloids at a low density. This suggests that dynamic clustering can emerge from the interplay of screened phoretic attractions and active diffusion.
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Affiliation(s)
- Benno Liebchen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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25
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Puljiz M, Menzel AM. Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments. Phys Rev E 2019; 99:012601. [PMID: 30780302 DOI: 10.1103/physreve.99.012601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2018] [Indexed: 06/09/2023]
Abstract
Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both viscoelastic environments of terminal fluidlike flow and of completely reversible damped elastic behavior are covered. For illustration and to highlight the role of the formalism in potential applications, we briefly address the relevant examples of dragging a rigid sphere through a viscoelastic environment together with subsequent relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel matrices, and the swimming behavior of active microswimmers in viscoelastic solutions. The approach provides a basis for more quantitative and extended investigations of these and related systems in the future.
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Affiliation(s)
- Mate Puljiz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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26
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Khadem SMJ, Klapp SHL. Delayed feedback control of active particles: a controlled journey towards the destination. Phys Chem Chem Phys 2019; 21:13776-13787. [PMID: 31210204 DOI: 10.1039/c9cp00495e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the direction of motion in the next time step. Here we estimate the orientation by comparing the delayed position of the particle with the actual one. This method does not require any real-time monitoring of the particle orientation and may thus be relevant also for controlling sub-micron sized particles, where the imaging process is not easily feasible. We apply the delayed feedback strategy to two experimentally relevant situations, namely, optical trapping and photon nudging. To investigate the performance of our strategy, we calculate the mean arrival time analytically (exploiting a small-delay approximation) and by simulations.
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Affiliation(s)
- S M J Khadem
- Institute of Theoretical Physics, Technical University Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.
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27
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Be’er A, Ariel G. A statistical physics view of swarming bacteria. MOVEMENT ECOLOGY 2019; 7:9. [PMID: 30923619 PMCID: PMC6419441 DOI: 10.1186/s40462-019-0153-9] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Accepted: 02/18/2019] [Indexed: 05/18/2023]
Abstract
Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.
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Affiliation(s)
- Avraham Be’er
- Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Midreshet Ben-Gurion, Israel
- Department of Physics, Ben-Gurion University of the Negev, 84105 Beer Sheva, Israel
| | - Gil Ariel
- Department of Mathematics, Bar-Ilan University, 52000 Ramat Gan, Israel
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28
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Theers M, Westphal E, Qi K, Winkler RG, Gompper G. Clustering of microswimmers: interplay of shape and hydrodynamics. SOFT MATTER 2018; 14:8590-8603. [PMID: 30339172 DOI: 10.1039/c8sm01390j] [Citation(s) in RCA: 66] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The spatiotemporal dynamics in systems of active self-propelled particles is controlled by the propulsion mechanism in combination with various direct interactions, such as steric repulsion and hydrodynamics. These direct interactions are typically anisotropic, and come in different "flavors", such as spherical and elongated particle shapes, pusher and puller flow fields, etc. The combination of the various aspects is expected to lead to new emergent behavior. However, it is a priori not evident whether shape and hydrodynamics act synergistically or antagonistically to generate motility-induced clustering (MIC) and phase separation (MIPS). We employ a model of prolate spheroidal microswimmers-called squirmers-in quasi-two-dimensional confinement to address this issue by mesoscale hydrodynamic simulations. For comparison, non-hydrodynamic active Brownian particles (ABPs) are considered to elucidate the contribution of hydrodynamic interactions. For spherical particles, the comparison between ABPs and hydrodynamic-squirmer ensembles reveals a suppression of MIPS due to hydrodynamic interactions. Yet, our analysis shows that dynamic clusters exist, with a broad size distribution. The fundamental difference between ABPs and squirmers is attributed to an increased reorientation of squirmers by hydrodynamic torques during their collisions. In contrast, for elongated squirmers, hydrodynamics interactions enhance MIPS. The transition to a phase-separated state strongly depends on the nature of the swimmer's flow field-with an increased tendency toward MIPS for pullers, and a reduced tendency for pushers. Thus, hydrodynamic interactions show opposing effects on MIPS for spherical and elongated microswimmers, and details of the propulsion mechanism of biological microswimmers may be very important to determine their collective behavior.
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Affiliation(s)
- Mario Theers
- Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation and Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany.
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29
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Hoell C, Löwen H, Menzel AM. Particle-scale statistical theory for hydrodynamically induced polar ordering in microswimmer suspensions. J Chem Phys 2018; 149:144902. [DOI: 10.1063/1.5048304] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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30
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Liao GJ, Klapp SHL. Clustering and phase separation of circle swimmers dispersed in a monolayer. SOFT MATTER 2018; 14:7873-7882. [PMID: 30221296 DOI: 10.1039/c8sm01366g] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We perform Brownian dynamics simulations in two dimensions to study the collective behavior of circle swimmers, which are driven by both, an (effective) translational and rotational self-propulsion, and interact via steric repulsion. We find that active rotation generally opposes motility-induced clustering and phase separation, as demonstrated by a narrowing of the coexistence region upon increase of the propulsion angular velocity. Moreover, although the particles are intrinsically assigned to rotate counterclockwise, a novel state of clockwise vortices emerges at an optimal value of the effective propulsion torque. We propose a simple gear-like model to capture the underlying mechanism of the clockwise vortices.
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Affiliation(s)
- Guo-Jun Liao
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
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31
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Daddi-Moussa-Ider A, Lisicki M, Mathijssen AJTM, Hoell C, Goh S, Bławzdziewicz J, Menzel AM, Löwen H. State diagram of a three-sphere microswimmer in a channel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:254004. [PMID: 29757157 DOI: 10.1088/1361-648x/aac470] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.
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Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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32
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Daddi-Moussa-Ider A, Lisicki M, Hoell C, Löwen H. Swimming trajectories of a three-sphere microswimmer near a wall. J Chem Phys 2018; 148:134904. [DOI: 10.1063/1.5021027] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Maciej Lisicki
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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33
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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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Doostmohammadi A, Shendruk TN, Thijssen K, Yeomans JM. Onset of meso-scale turbulence in active nematics. Nat Commun 2017; 8:15326. [PMID: 28508858 PMCID: PMC5440851 DOI: 10.1038/ncomms15326] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Accepted: 03/21/2017] [Indexed: 11/09/2022] Open
Abstract
Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at low Reynolds number in fluidized biological systems. This spatiotemporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here we show how the motion of active matter along a micro-channel transitions to meso-scale turbulence through the evolution of locally disordered patches (active puffs) from an ordered vortex-lattice flow state. We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in a channel coincide with the directed percolation universality class. This finding bridges our understanding of the onset of low-Reynolds-number meso-scale turbulence and traditional scale-invariant turbulence in confinement.
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Affiliation(s)
- Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
| | - Tyler N Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK.,Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - Kristian Thijssen
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
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Słomka J, Dunkel J. Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids. Proc Natl Acad Sci U S A 2017; 114:2119-2124. [PMID: 28193853 PMCID: PMC5338532 DOI: 10.1073/pnas.1614721114] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.
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Affiliation(s)
- Jonasz Słomka
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
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Oza AU, Heidenreich S, Dunkel J. Generalized Swift-Hohenberg models for dense active suspensions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:97. [PMID: 27815788 DOI: 10.1140/epje/i2016-16097-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2016] [Accepted: 09/20/2016] [Indexed: 06/06/2023]
Abstract
In describing the physics of living organisms, a mathematical theory that captures the generic ordering principles of intracellular and multicellular dynamics is essential for distinguishing between universal and system-specific features. Here, we compare two recently proposed nonlinear high-order continuum models for active polar and nematic suspensions, which aim to describe collective migration in dense cell assemblies and the ordering processes in ATP-driven microtubule-kinesin networks, respectively. We discuss the phase diagrams of the two models and relate their predictions to recent experiments. The satisfactory agreement with existing experimental data lends support to the hypothesis that non-equilibrium pattern formation phenomena in a wide range of active systems can be described within the same class of higher-order partial differential equations.
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Affiliation(s)
- Anand U Oza
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA.
| | - Sebastian Heidenreich
- Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Abbestr. 2-12, 10587, Berlin, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA
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