51
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Passucci G, Brasch ME, Henderson JH, Zaburdaev V, Manning ML. Identifying the mechanism for superdiffusivity in mouse fibroblast motility. PLoS Comput Biol 2019; 15:e1006732. [PMID: 30763309 PMCID: PMC6392322 DOI: 10.1371/journal.pcbi.1006732] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Revised: 02/27/2019] [Accepted: 12/20/2018] [Indexed: 12/02/2022] Open
Abstract
We seek to characterize the motility of mouse fibroblasts on 2D substrates. Utilizing automated tracking techniques, we find that cell trajectories are super-diffusive, where displacements scale faster than t1/2 in all directions. Two mechanisms have been proposed to explain such statistics in other cell types: run and tumble behavior with Lévy-distributed run times, and ensembles of cells with heterogeneous speed and rotational noise. We develop an automated toolkit that directly compares cell trajectories to the predictions of each model and demonstrate that ensemble-averaged quantities such as the mean-squared displacements and velocity autocorrelation functions are equally well-fit by either model. However, neither model correctly captures the short-timescale behavior quantified by the displacement probability distribution or the turning angle distribution. We develop a hybrid model that includes both run and tumble behavior and heterogeneous noise during the runs, which correctly matches the short-timescale behaviors and indicates that the run times are not Lévy distributed. The analysis tools developed here should be broadly useful for distinguishing between mechanisms for superdiffusivity in other cells types and environments.
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Affiliation(s)
- Giuseppe Passucci
- Physics Department, Syracuse University, Syracuse, New York, United States of America
| | - Megan E. Brasch
- Biomedical and Chemical Engineering Department, Syracuse University, Syracuse, New York, United States of America
| | - James H. Henderson
- Biomedical and Chemical Engineering Department, Syracuse University, Syracuse, New York, United States of America
- Syracuse Biomaterials Institute, Syracuse University, Syracuse, New York, United States of America
| | - Vasily Zaburdaev
- Institute of Supercomputing Technologies, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - M. Lisa Manning
- Physics Department, Syracuse University, Syracuse, New York, United States of America
- Syracuse Biomaterials Institute, Syracuse University, Syracuse, New York, United States of America
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52
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Feng MK, Hou ZH. Mode-Coupling theory for glass transition of active-passive binary mixture. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806148] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Meng-kai Feng
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at the Microscales, iChEM, University of Science and Technology of China, Hefei 230026, China
| | - Zhong-huai Hou
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at the Microscales, iChEM, University of Science and Technology of China, Hefei 230026, China
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53
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Abstract
How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodeled by activity. However, different simulations of dense assemblies of active particles, parametrized by a self-propulsion force, [Formula: see text], and persistence time, [Formula: see text], appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here, we extend the random first-order transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy through an effective model of a single particle in a caging potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas [Formula: see text] always inhibits glassiness, the effect of [Formula: see text] is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step toward a more rigorous analytical treatment of active glass.
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54
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Dietrich K, Volpe G, Sulaiman MN, Renggli D, Buttinoni I, Isa L. Active Atoms and Interstitials in Two-Dimensional Colloidal Crystals. PHYSICAL REVIEW LETTERS 2018; 120:268004. [PMID: 30004717 DOI: 10.1103/physrevlett.120.268004] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Revised: 05/29/2018] [Indexed: 06/08/2023]
Abstract
We study experimentally and numerically the motion of a self-phoretic active particle in two-dimensional loosely packed colloidal crystals at fluid interfaces. Two scenarios emerge depending on the interactions between the active particle and the lattice: the active particle either navigates throughout the crystal as an interstitial or is part of the lattice and behaves as an active atom. Active interstitials undergo a run-and-tumble-like motion, with the passive colloids of the crystal acting as tumbling sites. Instead, active atoms exhibit an intermittent motion, stemming from the interplay between the periodic potential landscape of the passive crystal and the particle's self-propulsion. Our results constitute the first step towards the realization of non-close-packed crystalline phases with internal activity.
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Affiliation(s)
- Kilian Dietrich
- Laboratory for Interfaces, Soft Matter and Assembly, Department of Materials, ETH Zurich, Zurich 8093, Switzerland
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Göteborg 41296, Sweden
| | | | - Damian Renggli
- Laboratory for Interfaces, Soft Matter and Assembly, Department of Materials, ETH Zurich, Zurich 8093, Switzerland
| | - Ivo Buttinoni
- Laboratory for Interfaces, Soft Matter and Assembly, Department of Materials, ETH Zurich, Zurich 8093, Switzerland
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, Oxford OX1 3QZ, United Kingdom
| | - Lucio Isa
- Laboratory for Interfaces, Soft Matter and Assembly, Department of Materials, ETH Zurich, Zurich 8093, Switzerland
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55
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Blanch-Mercader C, Yashunsky V, Garcia S, Duclos G, Giomi L, Silberzan P. Turbulent Dynamics of Epithelial Cell Cultures. PHYSICAL REVIEW LETTERS 2018; 120:208101. [PMID: 29864293 DOI: 10.1103/physrevlett.120.208101] [Citation(s) in RCA: 67] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Revised: 02/12/2018] [Indexed: 05/23/2023]
Abstract
We investigate the large length and long time scales collective flows and structural rearrangements within in vitro human bronchial epithelial cell (HBEC) cultures. Activity-driven collective flows result in ensembles of vortices randomly positioned in space. By analyzing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequency is size independent, both being characteristic features of the chaotic dynamics of active nematic suspensions. Indeed, we find that HBECs self-organize in nematic domains of several cell lengths. Nematic defects are found at the interface between domains with a total number that remains constant due to the dynamical balance of nucleation and annihilation events. The mean velocity fields in the vicinity of defects are well described by a hydrodynamic theory of extensile active nematics.
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Affiliation(s)
- C Blanch-Mercader
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - V Yashunsky
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - S Garcia
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - G Duclos
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - P Silberzan
- Laboratoire PhysicoChimie Curie, Institut Curie, PSL Research University-Sorbonne Université, UPMC-CNRS-Equipe labellisée Ligue Contre le Cancer, 75005 Paris, France
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56
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Chepizhko O, Lionetti MC, Malinverno C, Giampietro C, Scita G, Zapperi S, La Porta CAM. From jamming to collective cell migration through a boundary induced transition. SOFT MATTER 2018; 14:3774-3782. [PMID: 29713711 DOI: 10.1039/c8sm00128f] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Cell monolayers provide an interesting example of active matter, exhibiting a phase transition from flowing to jammed states as they age. Here we report experiments and numerical simulations illustrating how a jammed cellular layer rapidly reverts to a flowing state after a wound. Quantitative comparison between experiments and simulations shows that cells change their self-propulsion and alignment strength so that the system crosses a phase transition line, which we characterize by finite-size scaling in an active particle model. This wound-induced unjamming transition is found to occur generically in epithelial, endothelial and cancer cells.
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Affiliation(s)
- Oleksandr Chepizhko
- Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstrasse 21a, A-6020 Innsbruck, Austria
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57
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Giavazzi F, Paoluzzi M, Macchi M, Bi D, Scita G, Manning ML, Cerbino R, Marchetti MC. Flocking transitions in confluent tissues. SOFT MATTER 2018; 14:3471-3477. [PMID: 29693694 PMCID: PMC5995478 DOI: 10.1039/c8sm00126j] [Citation(s) in RCA: 72] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Collective cell migration in dense tissues underlies important biological processes, such as embryonic development, wound healing and cancer invasion. While many aspects of single cell movements are now well established, the mechanisms leading to displacements of cohesive cell groups are still poorly understood. To elucidate the emergence of collective migration in mechanosensitive cells, we examine a self-propelled Voronoi (SPV) model of confluent tissues with an orientational feedback that aligns a cell's polarization with its local migration velocity. While shape and motility are known to regulate a density-independent liquid-solid transition in tissues, we find that aligning interactions facilitate collective motion and promote solidification, with transitions that can be predicted by extending statistical physics tools such as effective temperature to this far-from-equilibrium system. In addition to accounting for recent experimental observations obtained with epithelial monolayers, our model predicts structural and dynamical signatures of flocking, which may serve as gateway to a more quantitative characterization of collective motility.
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Affiliation(s)
- Fabio Giavazzi
- Università degli Studi di Milano, Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, 20090 Segrate, Italy.
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58
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Sussman DM, Merkel M. No unjamming transition in a Voronoi model of biological tissue. SOFT MATTER 2018; 14:3397-3403. [PMID: 29667689 DOI: 10.1039/c7sm02127e] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Vertex models are a popular approach to simulating the mechanical and dynamical properties of dense biological tissues, describing the tissue as a network of polygons. Recently a class of two-dimensional vertex models was shown to exhibit a disordered rigidity transition controlled by the preferred cellular geometry, which was subsequently echoed by experimental findings. An attractive variant of these models uses a Voronoi tessellation to describe the cells, which reduces the number of degrees of freedom as compared the original vertex model. The Voronoi model was also endowed with a non-equilibrium model of cellular motility, leading to rich, glassy behavior. This glassy behavior was suggested to be inextricably linked to an underlying jamming transition. We test this conjecture, exploring the low-effective-temperature limit of the 2D Voronoi model by studying cell trajectories from detailed dynamical simulations in combination with rigidity measurements of energy-minimized disordered cell configurations. We find that the zero-temperature limit of this model has no unjamming transition. We show that this absence of an unjamming transition is intimately linked to the marginality of the model, i.e. the fact that the constraints imposed on cell areas and perimeters precisely balance the number of degrees of freedom in the model. Our work suggests that constraint counting arguments are useful to understand rigidity in a broad class of models of dense biological tissues.
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Affiliation(s)
- Daniel M Sussman
- Department of Physics, Syracuse University, Physics Building, Syracuse, New York 13210, USA.
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59
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de Macedo Biniossek N, Löwen H, Voigtmann T, Smallenburg F. Static structure of active Brownian hard disks. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:074001. [PMID: 29271364 DOI: 10.1088/1361-648x/aaa3bf] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.
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Affiliation(s)
- N de Macedo Biniossek
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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60
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Liao Q, Xu N. Criticality of the zero-temperature jamming transition probed by self-propelled particles. SOFT MATTER 2018; 14:853-860. [PMID: 29308823 DOI: 10.1039/c7sm01909b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We perform simulations of athermal systems of self-propelled particles (SPPs) interacting via harmonic repulsion in the vicinity of the zero-temperature jamming transition at point J. Every particle is propelled by a constant force f pointing to a randomly assigned and fixed direction. When f is smaller than the yield force fy, the system is statically jammed. We find that fy increases with packing fraction and exhibits finite size scaling, implying the criticality of point J. When f > fy, SPPs flow forever and their velocities satisfy the k-Gamma distribution. Velocity distributions at various packing fractions and f collapse when the particle velocity is scaled by the average velocity v[combining macron], suggesting that v[combining macron] is a reasonable quantity to characterize the response to f. We thus define a response function R(ϕ,f) = v[combining macron](ϕ,f)/f. The function exhibits critical scaling nicely, implying again the criticality of point J. Our analysis and results indicate that systems of SPPs behave analogically to sheared systems, although their driving mechanisms are apparently distinct.
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Affiliation(s)
- Qinyi Liao
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale & Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
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61
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Liluashvili A, Ónody J, Voigtmann T. Mode-coupling theory for active Brownian particles. Phys Rev E 2017; 96:062608. [PMID: 29347410 DOI: 10.1103/physreve.96.062608] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Indexed: 06/07/2023]
Abstract
We present a mode-coupling theory (MCT) for the slow dynamics of two-dimensional spherical active Brownian particles (ABPs). The ABPs are characterized by a self-propulsion velocity v_{0} and by their translational and rotational diffusion coefficients D_{t} and D_{r}, respectively. Based on the integration-through-transients formalism, the theory requires as input only the equilibrium static structure factors of the passive system (where v_{0}=0). It predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity, and rotational diffusivity that arise because at high densities, the persistence length of active swimming ℓ_{p}=v_{0}/D_{r} interferes with the interaction length ℓ_{c} set by the caging of particles. While the low-density dynamics of ABPs is characterized by a single Péclet number Pe=v_{0}^{2}/D_{r}D_{t}, close to the glass transition the dynamics is found to depend on Pe and ℓ_{p} separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to speed up, while decreasing the persistence length slows down the relaxation. The active-MCT glass is a nonergodic state that is qualitatively different from the passive glass. In it, correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.
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Affiliation(s)
- Alexander Liluashvili
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
| | - Jonathan Ónody
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
- Department of Physics, Heinrich-Heine Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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62
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Nishizawa K, Fujiwara K, Ikenaga M, Nakajo N, Yanagisawa M, Mizuno D. Universal glass-forming behavior of in vitro and living cytoplasm. Sci Rep 2017; 7:15143. [PMID: 29123156 PMCID: PMC5680342 DOI: 10.1038/s41598-017-14883-y] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Accepted: 10/18/2017] [Indexed: 11/30/2022] Open
Abstract
Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.
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Affiliation(s)
- Kenji Nishizawa
- Department of Physics, Graduate School of Sciences, Kyushu University, Fukuoka, 819-0395, Japan
| | - Kei Fujiwara
- Department of Biosciences & Informatics, Keio University, Yokohama, 223-8522, Japan
| | - Masahiro Ikenaga
- Department of Physics, Graduate School of Sciences, Kyushu University, Fukuoka, 819-0395, Japan
| | - Nobushige Nakajo
- Department of Biology, Graduate School of Sciences, Kyushu University, Fukuoka, 819-0395, Japan
| | - Miho Yanagisawa
- Department of Applied Physics, Tokyo University of Agriculture and Technology, Tokyo, 184-8588, Japan
| | - Daisuke Mizuno
- Department of Physics, Graduate School of Sciences, Kyushu University, Fukuoka, 819-0395, Japan.
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63
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Tjhung E, Berthier L. Discontinuous fluidization transition in time-correlated assemblies of actively deforming particles. Phys Rev E 2017; 96:050601. [PMID: 29347785 DOI: 10.1103/physreve.96.050601] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 06/07/2023]
Abstract
Tracking experiments in dense biological tissues reveal a diversity of sources for local energy injection at the cell scale. The effect of cell motility has been largely studied, but much less is known about the effect of the observed volume fluctuations of individual cells. We consider a microscopic model of "actively deforming" particles where local fluctuations of the particle size constitute a unique source of motion. We demonstrate that collective motion can emerge under the sole influence of such active volume fluctuations. We interpret the onset of diffusive motion as a nonequilibrium first-order phase transition, which arises at a well-defined amplitude of self-deformation. This behavior contrasts with the glassy dynamics produced by self-propulsion, but resembles the mechanical response of soft solids under mechanical deformation. It thus constitutes an example of an active yielding transition.
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Affiliation(s)
- Elsen Tjhung
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier, 34095 Montpellier, France
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier, 34095 Montpellier, France
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64
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Oswald L, Grosser S, Smith DM, Käs JA. Jamming transitions in cancer. JOURNAL OF PHYSICS D: APPLIED PHYSICS 2017; 50:483001. [PMID: 29628530 PMCID: PMC5884432 DOI: 10.1088/1361-6463/aa8e83] [Citation(s) in RCA: 86] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patients.
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Affiliation(s)
- Linda Oswald
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
| | - Steffen Grosser
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
| | - David M Smith
- Fraunhofer Institute for Cell Therapy and Immunology, Perlickstr. 1,
04103 Leipzig, Germany
| | - Josef A Käs
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
- Author to whom any correspondence should be addressed.
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65
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Nandi SK, Gov NS. Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles. SOFT MATTER 2017; 13:7609-7616. [PMID: 29028064 DOI: 10.1039/c7sm01648d] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f0 and a persistence time τp. Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature Teff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent Teff that approaches a constant in the long-time limit, which depends on the activity parameters f0 and τp. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that τα, the α-relaxation time, behaves as τα ∼ f0-2γ, where γ = 1.74 is the MCT exponent for the passive system. τα may increase or decrease as a function of τp depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent γ. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.
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Affiliation(s)
- Saroj Kumar Nandi
- Department of Materials and Interfaces, The Weizmann Institute of Science, P.O. Box 26, 234 Herzl Street, Rehovot 7610001, Israel.
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66
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Mandal R, Bhuyan PJ, Chaudhuri P, Rao M, Dasgupta C. Glassy swirls of active dumbbells. Phys Rev E 2017; 96:042605. [PMID: 29347636 DOI: 10.1103/physreve.96.042605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Indexed: 06/07/2023]
Abstract
Is an active glass different from a conventional passive glass? To address this, we study the dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations. This dense assembly shows dynamical arrest, first to a translational and then to a rotational glass, as one reduces temperature T or the self-propulsion force f. We monitor the dynamics along an iso-relaxation-time contour in the (T-f) plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity, which characterize the onset of glass formation-the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and it appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers. We construct continuum hydrodynamic equations for the simulated system, and we show that the observed behavior of this growing dynamic length scale can be understood from these equations.
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Affiliation(s)
- Rituparno Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Pranab Jyoti Bhuyan
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | | | - Madan Rao
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences (TIFR), Bangalore 560065, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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67
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Janssen LMC, Kaiser A, Löwen H. Aging and rejuvenation of active matter under topological constraints. Sci Rep 2017; 7:5667. [PMID: 28720777 PMCID: PMC5516002 DOI: 10.1038/s41598-017-05569-6] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2017] [Accepted: 05/30/2017] [Indexed: 12/15/2022] Open
Abstract
The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these non-equilibrium processes, and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. Our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.
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Affiliation(s)
- Liesbeth M C Janssen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany.
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB, Eindhoven, The Netherlands.
| | - Andreas Kaiser
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Av, Illinois, 60439, USA
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
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68
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Merkel M, Manning ML. Using cell deformation and motion to predict forces and collective behavior in morphogenesis. Semin Cell Dev Biol 2017; 67:161-169. [PMID: 27496334 PMCID: PMC5290285 DOI: 10.1016/j.semcdb.2016.07.029] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2016] [Revised: 07/05/2016] [Accepted: 07/27/2016] [Indexed: 12/20/2022]
Abstract
In multi-cellular organisms, morphogenesis translates processes at the cellular scale into tissue deformation at the scale of organs and organisms. To understand how biochemical signaling regulates tissue form and function, we must understand the mechanical forces that shape cells and tissues. Recent progress in developing mechanical models for tissues has led to quantitative predictions for how cell shape changes and polarized cell motility generate forces and collective behavior on the tissue scale. In particular, much insight has been gained by thinking about biological tissues as physical materials composed of cells. Here we review these advances and discuss how they might help shape future experiments in developmental biology.
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Affiliation(s)
- Matthias Merkel
- Department of Physics, Syracuse University, Syracuse, NY 13244, United States
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, NY 13244, United States.
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69
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Feng M, Hou Z. Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles. SOFT MATTER 2017; 13:4464-4481. [PMID: 28580481 DOI: 10.1039/c7sm00852j] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient D[combining macron] and a nontrivial structural function S2(q) with q being the magnitude of wave vector q. D[combining macron] and S2(q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor fq and relaxation time τα as functions of the persistence time τp of self-propulsion, the single particle effective temperature Teff as well as the number density ρ. Consequently, we find the critical density ρc for given τp shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T for fixed ρ as well as its dependence on τp. We find that T increases with τp and in the limit τp → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.
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Affiliation(s)
- Mengkai Feng
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China.
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70
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Mahapatra PS, Kulkarni A, Mathew S, Panchagnula MV, Vedantam S. Transitions between multiple dynamical states in a confined dense active-particle system. Phys Rev E 2017; 95:062610. [PMID: 28709325 DOI: 10.1103/physreve.95.062610] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Indexed: 06/07/2023]
Abstract
We study the collective motion of a dense suspension of active swimmers in a viscous fluid medium. The swimmers are modeled as soft spheres moving in a highly viscous fluid medium. The magnitude of the propelling thrust exerted by each particle is taken to be a constant and the direction is aligned to its velocity. Depending on the magnitude of the exerted thrust, several nonequilibrium steady states are observed. The transitions between the steady states are characterized using the total dissipation as a function of the magnitude of the thrust. The transitions between the nonequilibrium states are characterized by changes in exponent at low thrust values. At high thrust values, hysteretic transitions between ordered and disordered states are observed.
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Affiliation(s)
- Pallab Sinha Mahapatra
- Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ajinkya Kulkarni
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Sam Mathew
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Mahesh V Panchagnula
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Srikanth Vedantam
- Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India
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71
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Matoz-Fernandez DA, Martens K, Sknepnek R, Barrat JL, Henkes S. Cell division and death inhibit glassy behaviour of confluent tissues. SOFT MATTER 2017; 13:3205-3212. [PMID: 28398448 DOI: 10.1039/c6sm02580c] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the effects of cell division and apoptosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apoptosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phase, a gel-like phase, and a dense confluent (tissue) phase. Most striking is the observation that the tissue is self-melting through its own internal activity, ruling out the existence of any glassy phase.
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72
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Ding H, Jiang H, Hou Z. Study of dynamic heterogeneity of an active particle system. Phys Rev E 2017; 95:052608. [PMID: 28618538 DOI: 10.1103/physreve.95.052608] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Indexed: 06/07/2023]
Abstract
We have studied spatial and temporal dynamic heterogeneity (DH) in a system of hard-sphere particles, subjected to active forces with constant amplitude and random direction determined by rotational diffusion with correlation time τ. We have used a variety of observables to characterize the DH behavior, including the deviation from standard Stokes-Einstein (SE) relation, a non-Gaussian parameter α_{2}(Δt) for the distribution of particle displacement within a certain time interval Δt, a four-point susceptibility χ_{4}(Δt,ΔL) for the correlation in dynamics between any two points in space separated by distance ΔL within some time window Δt, and a vector spatial-temporal correlation function S_{vec}(R,Δt) for vector displacements within time interval Δt of particle pairs originally separated by R. By mapping the particle motion into a continuous-time random walk with constant jump length, we can obtain the average waiting time 〈t_{x}〉∝D_{s}^{-1} and persistence time 〈t_{p}〉∝η, with D_{s} the self-diffusion coefficient and η the shear viscosity, such that the observable λ=〈t_{p}〉/〈t_{x}〉∝D_{s}η can be calculated as a function of the control parameter τ to show how it deviates from its SE value λ_{0}. Interestingly, we find λ/λ_{0} shows a nonmonotonic behavior for large volume fraction φ_{a}, wherein λ/λ_{0} undergoes a minimum at a certain intermediate value of τ, indicating that both small and large particle activity may lead to strong DH. Such a reentrance phenomenon is further demonstrated in terms of the non-Gaussian parameters α_{2}, four-point susceptibility χ_{4}, and vector spatiotemporal correlation functions S_{vec}, respectively. Detail analysis shows that it is the competition between the dual roles of particle activity, namely, activity-induced higher effective temperature and activity-induced clustering, that leads to such nontrivial nonmonotonic behaviors. In addition, we find that DH may also show a maximum level at an intermediate value of φ_{a} if τ is large enough, implying that a more crowded system may be less heterogeneous than a less crowded one for a system with high particle activity.
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Affiliation(s)
- Huai Ding
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Huijun Jiang
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
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73
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Matoz-Fernandez DA, Agoritsas E, Barrat JL, Bertin E, Martens K. Nonlinear Rheology in a Model Biological Tissue. PHYSICAL REVIEW LETTERS 2017; 118:158105. [PMID: 28452505 DOI: 10.1103/physrevlett.118.158105] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2016] [Indexed: 06/07/2023]
Abstract
The rheological response of dense active matter is a topic of fundamental importance for many processes in nature such as the mechanics of biological tissues. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with an increasing shear rate. To rationalize this nonlinear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are, respectively, generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
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Affiliation(s)
| | - Elisabeth Agoritsas
- Université Grenoble Alpes & CNRS, LIPHY, F-38000 Grenoble, France
- Laboratoire de Physique Théorique, ENS & PSL University, UPMC & Sorbonne Universités, F- 75005 Paris, France
| | | | - Eric Bertin
- Université Grenoble Alpes & CNRS, LIPHY, F-38000 Grenoble, France
| | - Kirsten Martens
- Université Grenoble Alpes & CNRS, LIPHY, F-38000 Grenoble, France
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74
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Tjhung E, Kawasaki T. Excitation of vibrational soft modes in disordered systems using active oscillation. SOFT MATTER 2016; 13:111-118. [PMID: 27221647 DOI: 10.1039/c6sm00788k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional athermal jammed system by giving a small amplitude of active oscillation to each particle's size with an identical driving frequency. The response is then obtained as the real time displacements of the particles. We show remarkable correlations between the real time displacements and the eigen vectors obtained from conventional normal mode analysis. More importantly, from these real time displacements, we can measure the participation ratio and spatial polarization of particles' vibrations. From these measurements, we find three distinct frequency regimes which characterize the spatial distribution and correlation of particles' vibrations in jammed amorphous solids. Furthermore, we can possibly apply this method to a much larger system to examine the low frequency behaviour of amorphous solids with a much higher resolution of the frequency space.
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Affiliation(s)
- Elsen Tjhung
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier, Montpellier 34095, France
| | - Takeshi Kawasaki
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan.
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75
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Paoluzzi M, Di Leonardo R, Marchetti MC, Angelani L. Shape and Displacement Fluctuations in Soft Vesicles Filled by Active Particles. Sci Rep 2016; 6:34146. [PMID: 27678166 PMCID: PMC5039690 DOI: 10.1038/srep34146] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 09/07/2016] [Indexed: 11/09/2022] Open
Abstract
We investigate numerically the dynamics of shape and displacement fluctuations of two-dimensional flexible vesicles filled with active particles. At low concentration most of the active particles accumulate at the boundary of the vesicle where positive particle number fluctuations are amplified by trapping, leading to the formation of pinched spots of high density, curvature and pressure. At high concentration the active particles cover the vesicle boundary almost uniformly, resulting in fairly homogeneous pressure and curvature, and nearly circular vesicle shape. The change between polarized and spherical shapes is driven by the number of active particles. The center-of-mass of the vesicle performs a persistent random walk with a long time diffusivity that is strongly enhanced for elongated active particles due to orientational correlations in their direction of propulsive motion. In our model shape-shifting induces directional sensing and the cell spontaneously migrate along the polarization direction.
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Affiliation(s)
- Matteo Paoluzzi
- Department of Physics and Syracuse Soft Matter Program, Syracuse University, Syracuse NY 13244, USA
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
| | - Roberto Di Leonardo
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory, Piazzale A. Moro 2, I-00185, Roma, Italy
| | - M. Cristina Marchetti
- Department of Physics and Syracuse Soft Matter Program, Syracuse University, Syracuse NY 13244, USA
| | - Luca Angelani
- Dipartimento di Fisica Università Sapienza, P.le A Moro 2, 00185 Rome, Italy
- ISC-CNR, Institute for Complex Systems, Piazzale A. Moro 2, I-00185 Roma, Italy
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76
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Zhou Y, Milner ST. Structural entropy of glassy systems from graph isomorphism. SOFT MATTER 2016; 12:7281-7288. [PMID: 27510729 DOI: 10.1039/c6sm01355d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Configurational entropy plays a central role in thermodynamic scenarios of the glass transition. As a measure of the number of basins in the potential energy landscape, configurational entropy for a glass-forming liquid can be evaluated by explicitly counting distinct inherent structures. In this work, we propose a graph-theory based method to examine local structure and obtain the corresponding entropy of hard-particle systems. Voronoi diagrams of associated clusters are classified using a graph isomorphism algorithm. The statistics of these clusters reveal structural motifs such as icosahedron-like order, and also allow us to calculate the structural entropy SG. We find the structural entropy of an n-particle subsystem grows linearly with n. Thus the structural entropy per particle can be obtained from the slope dSG/dn. Our results are consistent with previous values for configurational entropy obtained via thermodynamic integration. Structural entropies per particle are measured for hard-disk and hard-sphere polydisperse systems, and extrapolated for monodisperse hard disks, all of which are nonzero at the dynamic glass transition.
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Affiliation(s)
- Yuxing Zhou
- Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USA.
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77
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Flenner E, Szamel G, Berthier L. The nonequilibrium glassy dynamics of self-propelled particles. SOFT MATTER 2016; 12:7136-7149. [PMID: 27499055 DOI: 10.1039/c6sm01322h] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process, characterized by a persistence time and an effective temperature, and particles interact via a Lennard-Jones potential that yields well-studied glassy behavior in the Brownian limit, which is obtained as the persistence time vanishes. By increasing the persistence time, the system departs more strongly from thermal equilibrium and we provide a comprehensive numerical analysis of the structure and dynamics of the resulting active fluid. Finite persistence times profoundly affect the static structure of the fluid and give rise to nonequilibrium velocity correlations that are absent in thermal systems. Despite these nonequilibrium features, for any value of the persistence time we observe a nonequilibrium glass transition as the effective temperature is decreased. Surprisingly, increasing departure from thermal equilibrium is found to promote (rather than suppress) the glassy dynamics. Overall, our results suggest that with increasing persistence time, microscopic properties of the active fluid change quantitatively, but the general features of the nonequilibrium glassy dynamics observed with decreasing the effective temperature remain qualitatively similar to those of thermal glass-formers.
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Affiliation(s)
- Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA.
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78
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Briand G, Dauchot O. Crystallization of Self-Propelled Hard Discs. PHYSICAL REVIEW LETTERS 2016; 117:098004. [PMID: 27610889 DOI: 10.1103/physrevlett.117.098004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2016] [Indexed: 06/06/2023]
Abstract
We experimentally study the crystallization of a monolayer of vibrated discs with a built-in polar asymmetry, a model system of active liquids, and contrast it with that of vibrated isotropic discs. Increasing the packing fraction ϕ, the quasicontinuous crystallization reported for isotropic discs is replaced by a transition, or a crossover, towards a "self-melting" crystal. Starting from the liquid phase and increasing the packing fraction, clusters of dense hexagonal-ordered packed discs spontaneously form, melt, split, and merge, leading to a highly intermittent and heterogeneous dynamics. For a packing fraction larger than ϕ^{*}, a few large clusters span the system size. The cluster size distribution is monotonically decreasing for ϕ<ϕ^{*}, nonmonotonic for ϕ>ϕ^{*}, and is a power law at the transition. The system is, however, never dynamically arrested. The clusters permanently melt from place to place, forming droplets of an active liquid which rapidly propagate across the system. This self-melting crystalline state subsists up to the highest possible packing fraction, questioning the stability of the crystal for active discs unless it is at ordered close packing.
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Affiliation(s)
- G Briand
- EC2M, UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| | - O Dauchot
- EC2M, UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
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79
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Mandal R, Bhuyan PJ, Rao M, Dasgupta C. Active fluidization in dense glassy systems. SOFT MATTER 2016; 12:6268-6276. [PMID: 27380935 DOI: 10.1039/c5sm02950c] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Dense soft glasses show strong collective caging behavior at sufficiently low temperatures. Using molecular dynamics simulations of a model glass former, we show that the incorporation of activity or self-propulsion, f0, can induce cage breaking and fluidization, resulting in the disappearance of the glassy phase beyond a critical f0. The diffusion coefficient crosses over from being strongly to weakly temperature dependent as f0 is increased. In addition, we demonstrate that activity induces a crossover from a fragile to a strong glass and a tendency of active particles to cluster. Our results are of direct relevance to the collective dynamics of dense active colloidal glasses and to recent experiments on tagged particle diffusion in living cells.
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Affiliation(s)
- Rituparno Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
| | - Pranab Jyoti Bhuyan
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
| | - Madan Rao
- Raman Research Institute, Bangalore 560080, India and National Centre for Biological Sciences (TIFR), Bangalore 560065, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
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80
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Fodor É, Hayakawa H, Visco P, van Wijland F. Active cage model of glassy dynamics. Phys Rev E 2016; 94:012610. [PMID: 27575182 DOI: 10.1103/physreve.94.012610] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2016] [Indexed: 06/06/2023]
Abstract
We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.
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Affiliation(s)
- Étienne Fodor
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Paolo Visco
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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81
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Abstract
We construct a phase-field model for collective cell migration based on a Ginzburg-Landau free-energy formulation. We model adhesion, surface tension, repulsion, coattraction, and polarization, enabling us to follow the cells' morphologies and the effect of their membranes fluctuations on collective motion. We were able to measure the tissue surface tension as a function of the individual cell cortical tension and adhesion and identify a density threshold for cell-sheet formation.
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Affiliation(s)
- Sara Najem
- Graduate Aerospace Laboratories (GALCIT), California Institute of Technology, Pasadena, California 91125, USA
| | - Martin Grant
- Physics Department, Rutherford Building, 3600 rue University, McGill University, Montréal, Québec, Canada H3A 2T8
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82
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Bi D, Yang X, Marchetti MC, Manning ML. Motility-driven glass and jamming transitions in biological tissues. PHYSICAL REVIEW. X 2016; 6:021011. [PMID: 28966874 PMCID: PMC5619672 DOI: 10.1103/physrevx.6.021011] [Citation(s) in RCA: 270] [Impact Index Per Article: 33.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.
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Affiliation(s)
- Dapeng Bi
- Department of Physics, Syracuse University, Syracuse, NY, USA
| | - Xingbo Yang
- Department of Physics, Syracuse University, Syracuse, NY, USA
| | - M Cristina Marchetti
- Department of Physics, Syracuse University, Syracuse, NY, USA
- Syracuse Biomaterials Institute, Syracuse, NY, USA
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, NY, USA
- Syracuse Biomaterials Institute, Syracuse, NY, USA
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83
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Hagan MF, Baskaran A. Emergent self-organization in active materials. Curr Opin Cell Biol 2016; 38:74-80. [PMID: 26971116 DOI: 10.1016/j.ceb.2016.02.020] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2015] [Revised: 02/04/2016] [Accepted: 02/25/2016] [Indexed: 11/20/2022]
Abstract
Biological systems exhibit large-scale self-organized dynamics and structures which enable organisms to perform the functions of life. The field of active matter strives to develop and understand microscopically driven nonequilibrium materials, with emergent properties comparable to those of living systems. This review will describe two recently developed classes of active matter systems, in which simple building blocks-self-propelled colloidal particles or extensile rod-like particles-self-organize to form macroscopic structures with features not possible in equilibrium systems. We summarize the recent experimental and theoretical progress on each of these systems, and we present simple descriptions of the physics underlying their emergent behaviors.
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Affiliation(s)
- Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
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84
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Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter. Curr Opin Colloid Interface Sci 2016. [DOI: 10.1016/j.cocis.2016.01.003] [Citation(s) in RCA: 114] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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85
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Tennenbaum M, Liu Z, Hu D, Fernandez-Nieves A. Mechanics of fire ant aggregations. NATURE MATERIALS 2016; 15:54-9. [PMID: 26501413 DOI: 10.1038/nmat4450] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2014] [Accepted: 09/17/2015] [Indexed: 05/02/2023]
Abstract
Fire ants link their bodies to form aggregations; these can adopt a variety of structures, they can drip and spread, or withstand applied loads. Here, by using oscillatory rheology, we show that fire ant aggregations are viscoelastic. We find that, at the lowest ant densities probed and in the linear regime, the elastic and viscous moduli are essentially identical over the spanned frequency range, which highlights the absence of a dominant mode of structural relaxation. As ant density increases, the elastic modulus rises, which we interpret by alluding to ant crowding and subsequent jamming. When deformed beyond the linear regime, the aggregation flows, exhibiting shear-thinning behaviour with a stress load that is comparable to the maximum load the aggregation can withstand before individual ants are torn apart. Our findings illustrate the rich, collective mechanical behaviour that can arise in aggregations of active, interacting building blocks.
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Affiliation(s)
- Michael Tennenbaum
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Zhongyang Liu
- School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - David Hu
- School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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86
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Szamel G. Theory for the dynamics of dense systems of athermal self-propelled particles. Phys Rev E 2016; 93:012603. [PMID: 26871118 DOI: 10.1103/physreve.93.012603] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start from the equation of motion for the joint distribution of particles' positions and self-propulsions and we integrate out the self-propulsions. In this way we derive an approximate, many-particle evolution equation for the probability distribution of the particles' positions. Second, we use this evolution equation to describe the time dependence of steady-state density correlations. We derive a memory function representation of the density correlation function and then we use a factorization approximation to obtain an approximate expression for the memory function. In the final equation of motion for the density correlation function the nonequilibrium character of the active system manifests itself through the presence of a new steady-state correlation function that quantifies spatial correlations of the velocities of the particles. This correlation function enters into the frequency term, and thus it describes the dependence of the short-time dynamics on the properties of the self-propulsions. More importantly, the correlation function of particles' velocities enters into the vertex of the memory function and through the vertex it modifies the long-time glassy dynamics.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA and Laboratoire Charles Coulomb, UMR 5221 CNRS, Université Montpellier, Montpellier, France
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87
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Navarro RM, Fielding SM. Clustering and phase behaviour of attractive active particles with hydrodynamics. SOFT MATTER 2015; 11:7525-7546. [PMID: 26278520 DOI: 10.1039/c5sm01061f] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We simulate clustering, phase separation and hexatic ordering in a monolayered suspension of active squirming disks subject to an attractive Lennard-Jones-like pairwise interaction potential, taking hydrodynamic interactions between the particles fully into account. By comparing the hydrodynamic case with counterpart simulations for passive and active Brownian particles, we elucidate the relative roles of self-propulsion, interparticle attraction, and hydrodynamic interactions in determining clustering and phase behaviour. Even in the presence of an attractive potential, we find that hydrodynamic interactions strongly suppress the motility induced phase separation that might a priori have been expected in a highly active suspension. Instead, we find only a weak tendency for the particles to form stringlike clusters in this regime. At lower activities we demonstrate phase behaviour that is broadly equivalent to that of the counterpart passive system at low temperatures, characterized by regimes of gas-liquid, gas-solid and liquid-solid phase coexistence. In this way, we suggest that a dimensionless quantity representing the level of activity relative to the strength of attraction plays the role of something like an effective non-equilibrium temperature, counterpart to the (dimensionless) true thermodynamic temperature in the passive system. However there are also some important differences from the equilibrium case, most notably with regards the degree of hexatic ordering, which we discuss carefully.
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Affiliation(s)
- Ricard Matas Navarro
- Department of Physics, University of Durham, Science Laboratories, South Road, DH1 3LE, Durham, UK.
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88
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Park JA, Kim JH, Bi D, Mitchel JA, Qazvini NT, Tantisira K, Park CY, McGill M, Kim SH, Gweon B, Notbohm J, Steward R, Burger S, Randell SH, Kho AT, Tambe DT, Hardin C, Shore SA, Israel E, Weitz DA, Tschumperlin DJ, Henske EP, Weiss ST, Lisa Manning M, Butler JP, Drazen JM, Fredberg JJ. Unjamming and cell shape in the asthmatic airway epithelium. NATURE MATERIALS 2015; 14:1040-8. [PMID: 26237129 PMCID: PMC4666305 DOI: 10.1038/nmat4357] [Citation(s) in RCA: 344] [Impact Index Per Article: 38.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2015] [Accepted: 06/18/2015] [Indexed: 05/14/2023]
Abstract
From coffee beans flowing in a chute to cells remodelling in a living tissue, a wide variety of close-packed collective systems-both inert and living-have the potential to jam. The collective can sometimes flow like a fluid or jam and rigidify like a solid. The unjammed-to-jammed transition remains poorly understood, however, and structural properties characterizing these phases remain unknown. Using primary human bronchial epithelial cells, we show that the jamming transition in asthma is linked to cell shape, thus establishing in that system a structural criterion for cell jamming. Surprisingly, the collapse of critical scaling predicts a counter-intuitive relationship between jamming, cell shape and cell-cell adhesive stresses that is borne out by direct experimental observations. Cell shape thus provides a rigorous structural signature for classification and investigation of bronchial epithelial layer jamming in asthma, and potentially in any process in disease or development in which epithelial dynamics play a prominent role.
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Affiliation(s)
- Jin-Ah Park
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- Correspondence and requests for materials should be addressed to J.-A.P.
| | - Jae Hun Kim
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Dapeng Bi
- Syracuse University, Syracuse, New York 13244, USA
| | | | - Nader Taheri Qazvini
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- School of Chemistry, College of Science, University of Tehran, Tehran 14179, Iran
| | - Kelan Tantisira
- Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Chan Young Park
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Maureen McGill
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Sae-Hoon Kim
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Bomi Gweon
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Jacob Notbohm
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Robert Steward
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Stephanie Burger
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Scott H. Randell
- The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, USA
| | - Alvin T. Kho
- Children’s Hospital, Boston, Massachusetts 02215, USA
| | - Dhananjay T. Tambe
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- Department of Mechanical Engineering, University of South Alabama, Mobile, Alabama 36688, USA
| | - Corey Hardin
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Stephanie A. Shore
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
| | - Elliot Israel
- Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
| | | | | | - Elizabeth P. Henske
- Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Scott T. Weiss
- Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
| | | | - James P. Butler
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
- Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Jeffrey M. Drazen
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, USA
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89
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Gravish N, Gold G, Zangwill A, Goodisman MAD, Goldman DI. Glass-like dynamics in confined and congested ant traffic. SOFT MATTER 2015; 11:6552-6561. [PMID: 26106969 DOI: 10.1039/c5sm00693g] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The collective movement of animal groups often occurs in confined spaces. As animal groups are challenged to move at high density, their mobility dynamics may resemble the flow of densely packed non-living soft materials such as colloids, grains, or polymers. However, unlike inert soft-materials, self-propelled collective living systems often display social interactions whose influence on collective mobility are only now being explored. In this paper, we study the mobility of bi-directional traffic flow in a social insect (the fire ant Solenopsis invicta) as we vary the diameter of confining foraging tunnels. In all tunnel diameters, we observe the emergence of spatially heterogeneous regions of fast and slow traffic that are induced through two phenomena: physical obstruction, arising from the inability of individual ants to interpenetrate, and time-delay resulting from social interaction in which ants stop to briefly antennate. Density correlation functions reveal that the relaxation dynamics of high density traffic fluctuations scale linearly with fluctuation size and are sensitive to tunnel diameter. We separate the roles of physical obstruction and social interactions in traffic flow using cellular automata based simulation. Social interaction between ants is modeled as a dwell time (Tint) over which interacting ants remain stationary in the tunnel. Investigation over a range of densities and Tint reveals that the slowing dynamics of collective motion in social living systems are consistent with dynamics near a fragile glass transition in inert soft-matter systems. In particular, flow is relatively insensitive to density until a critical density is reached. As social interaction affinity is increased (increasing Tint) traffic dynamics change and resemble a strong glass transition. Thus, social interactions play an important role in the mobility of collective living systems at high density. Our experiments and model demonstrate that the concepts of soft-matter physics aid understanding of the mobility of collective living systems, and motivate further inquiry into the dynamics of densely confined social living systems.
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Affiliation(s)
- Nick Gravish
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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90
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Speck T, Menzel AM, Bialké J, Löwen H. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles. J Chem Phys 2015; 142:224109. [DOI: 10.1063/1.4922324] [Citation(s) in RCA: 85] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Julian Bialké
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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91
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Szamel G, Flenner E, Berthier L. Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062304. [PMID: 26172716 DOI: 10.1103/physreve.91.062304] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2014] [Indexed: 06/04/2023]
Abstract
We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. Our simulations reveal that when the persistence time of the self-propulsion is increased, the local structure becomes more pronounced, whereas the long-time dynamics first accelerates and then slows down. We explain these surprising findings by constructing a nonequilibrium microscopic theory that yields nontrivial predictions for the glassy dynamics. These predictions are in qualitative agreement with the simulations and reveal the importance of steady-state correlations of the local velocities to the nonequilibrium dynamics of dense self-propelled particles.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221 CNRS, Université Montpellier, Montpellier, France
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92
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Godfrey MJ, Moore MA. Understanding the ideal glass transition: lessons from an equilibrium study of hard disks in a channel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022120. [PMID: 25768471 DOI: 10.1103/physreve.91.022120] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2014] [Indexed: 06/04/2023]
Abstract
We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ϕ(K) that is less than the maximum possible ϕ(max), the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any real divergence of the pressure at ϕ(K). We give arguments that this avoided phase transition is a structural feature, the remnant in our narrow channel system of the hexatic to crystal transition, but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ξ̃(3) as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15σ at ϕ(K), which is larger than the penetration lengths that have been reported for three-dimensional systems. It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ϕ(K).
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Affiliation(s)
- M J Godfrey
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M A Moore
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
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93
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Pilkiewicz KR, Eaves JD. Reentrance in an active glass mixture. SOFT MATTER 2014; 10:7495-7501. [PMID: 25208297 DOI: 10.1039/c4sm01177e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are dynamically isolated from one another. While this defining characteristic is held in common, its origin is different in each case: for active systems, the irreversible driving forces can produce dynamically frozen states, while glassy systems vitrify when they get kinetically trapped on a rugged free energy landscape. In a mixture of active and glassy particles, the interplay between these two tendencies leads to novel phenomenology. We demonstrate this with a spin glass model that we generalize to include an active component. In the absence of a ferromagnetic bias, we find that the spin glass transition temperature depresses with the active fraction, consistent with what has been observed for fully active glassy systems. When a bias does exist, however, a new type of transition becomes possible: the system can be cooled out of the glassy phase. This unusual phenomenon, known as reentrance, has been observed before in a limited number of colloidal and micellar systems, but it has not yet been observed in active glass mixtures. Using low order perturbation theory, we study the origin of this reentrance and, based on the physical picture that results, suggest how our predictions might be measured experimentally.
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Affiliation(s)
- Kevin R Pilkiewicz
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado, USA.
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94
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Szamel G. Self-propelled particle in an external potential: existence of an effective temperature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012111. [PMID: 25122255 DOI: 10.1103/physreve.90.012111] [Citation(s) in RCA: 138] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2014] [Indexed: 06/03/2023]
Abstract
We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating internal driving force evolving according to the Ornstein-Uhlenbeck process, independently of the state of the particle. Without an external potential, in the long time limit, the self-propelled particle moving in a viscous medium performs diffusive motion, which allows one to identify an effective temperature. We show that in the presence of a linear external potential the stationary state distribution has an exponential form with the sedimentation length determined by the effective temperature of the free self-propelled particle. In the presence of a quadratic external potential the stationary state distribution has a Gaussian form. However, in general, this distribution is not determined by the effective temperature of the free self-propelled particle.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80525, USA
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95
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Reichhardt C, Olson Reichhardt CJ. Active matter transport and jamming on disordered landscapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012701. [PMID: 25122329 DOI: 10.1103/physreve.90.012701] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Indexed: 06/03/2023]
Abstract
We numerically examine the transport of active run-and-tumble particles with steric particle-particle interactions driven with a drift force over random disordered landscapes composed of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for transport of run-and-tumble type active matter through quenched disorder and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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96
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Levis D, Berthier L. Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062301. [PMID: 25019770 DOI: 10.1103/physreve.89.062301] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Indexed: 06/03/2023]
Abstract
We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.
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Affiliation(s)
- Demian Levis
- Laboratoire Charles Coulomb, UMR 5221 CNRS, and Université Montpellier 2, Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221 CNRS, and Université Montpellier 2, Montpellier, France
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