1
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Ghosh S, Joshi C, Baskaran A, Hagan MF. Spatiotemporal control of structure and dynamics in a polar active fluid. SOFT MATTER 2024. [PMID: 39188251 DOI: 10.1039/d4sm00547c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/28/2024]
Abstract
We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.
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Affiliation(s)
- Saptorshi Ghosh
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Chaitanya Joshi
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Aparna Baskaran
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.
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2
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Murphy P, Perepelitsa M, Timofeyev I, Lieber-Kotz M, Islas B, Igoshin OA. Breakdown of Boltzmann-type models for the alignment of self-propelled rods. Math Biosci 2024; 376:109266. [PMID: 39127094 DOI: 10.1016/j.mbs.2024.109266] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 07/23/2024] [Accepted: 08/03/2024] [Indexed: 08/12/2024]
Abstract
Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's "molecular chaos" hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.
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Affiliation(s)
- Patrick Murphy
- Department of Mathematics and Statistics, San Jose State University, San Jose, CA 95192, United States of America.
| | - Misha Perepelitsa
- Department of Mathematics, University of Houston, TX 77204, United States of America
| | - Ilya Timofeyev
- Department of Mathematics, University of Houston, TX 77204, United States of America
| | - Matan Lieber-Kotz
- Department of Bioengineering, Rice University, Houston, TX 77005, United States of America
| | - Brandon Islas
- Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, United States of America
| | - Oleg A Igoshin
- Department of Bioengineering, Rice University, Houston, TX 77005, United States of America; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, United States of America; Department of Chemistry, Rice University, Houston, TX 77005, United States of America; Department of Biosciences, Rice University, Houston, TX 77005, United States of America
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3
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Soto R, Pinto M, Brito R. Kinetic Theory of Motility Induced Phase Separation for Active Brownian Particles. PHYSICAL REVIEW LETTERS 2024; 132:208301. [PMID: 38829083 DOI: 10.1103/physrevlett.132.208301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2024] [Accepted: 04/22/2024] [Indexed: 06/05/2024]
Abstract
When two active Brownian particles collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann-Enskog-like kinetic theory is built. A linear stability analysis of the homogeneous state predicts a density instability resulting from the effective velocity reduction of tagged particles predicted by the theory.
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Affiliation(s)
- Rodrigo Soto
- Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile
| | - Martín Pinto
- Departamento de Física, FCFM, Universidad de Chile, Santiago, Chile
| | - Ricardo Brito
- Departamento de Estructura de la Materia, Física Térmica y Electrónica and GISC, Universidad Complutense de Madrid, Spain
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4
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Heins C, Millidge B, Da Costa L, Mann RP, Friston KJ, Couzin ID. Collective behavior from surprise minimization. Proc Natl Acad Sci U S A 2024; 121:e2320239121. [PMID: 38630721 PMCID: PMC11046639 DOI: 10.1073/pnas.2320239121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 03/08/2024] [Indexed: 04/19/2024] Open
Abstract
Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and "social forces" such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modeling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically observed collective phenomena, including cohesion, milling, and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference-without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal nontrivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.
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Affiliation(s)
- Conor Heins
- Department of Collective Behaviour, Max Planck Institute of Animal Behavior, KonstanzD-78457, Germany
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, KonstanzD-78457, Germany
- Department of Biology, University of Konstanz, KonstanzD-78457, Germany
- VERSES Research Lab, Los Angeles, CA90016
| | - Beren Millidge
- Medical Research Council Brain Networks Dynamics Unit, University of Oxford, OxfordOX1 3TH, United Kingdom
| | - Lancelot Da Costa
- VERSES Research Lab, Los Angeles, CA90016
- Department of Mathematics, Imperial College London, LondonSW7 2AZ, United Kingdom
- Wellcome Centre for Human Neuroimaging, University College London, LondonWC1N 3AR, United Kingdom
| | - Richard P. Mann
- Department of Statistics, School of Mathematics, University of Leeds, LeedsLS2 9JT, United Kingdom
| | - Karl J. Friston
- VERSES Research Lab, Los Angeles, CA90016
- Wellcome Centre for Human Neuroimaging, University College London, LondonWC1N 3AR, United Kingdom
| | - Iain D. Couzin
- Department of Collective Behaviour, Max Planck Institute of Animal Behavior, KonstanzD-78457, Germany
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, KonstanzD-78457, Germany
- Department of Biology, University of Konstanz, KonstanzD-78457, Germany
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5
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Cordes J, Schadschneider A, Nicolas A. Dimensionless numbers reveal distinct regimes in the structure and dynamics of pedestrian crowds. PNAS NEXUS 2024; 3:pgae120. [PMID: 38577258 PMCID: PMC10994203 DOI: 10.1093/pnasnexus/pgae120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Accepted: 03/07/2024] [Indexed: 04/06/2024]
Abstract
In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers, which quantify the intrusions into the pedestrians' personal spaces and the imminency of the collisions that they face, respectively. Using an extensive dataset, we show that these numbers delineate regimes where distinct variables characterize the crowd's arrangement, namely, Euclidean distances at low Avoidance number and times-to-collision at low Intrusion number. On the basis of these findings, a perturbative expansion of the individual pedestrian dynamics is carried out around the noninteracting state, in quite general terms. Simulations confirm that this expansion performs well in its expected regime of applicability.
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Affiliation(s)
- Jakob Cordes
- Institute of Advanced Simulation, Forschungszentrum Jülich, 52428 Jülich, Germany
- Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
| | | | - Alexandre Nicolas
- Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, UMR5306, F-69100 Villeurbanne, France
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6
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Triguero-Platero G, Ziebert F, Bonilla LL. Coarse-graining the vertex model and its response to shear. Phys Rev E 2023; 108:044118. [PMID: 37978645 DOI: 10.1103/physreve.108.044118] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Accepted: 09/21/2023] [Indexed: 11/19/2023]
Abstract
Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the active vertex model exist and yield reasonable agreement with experimental observations such as tissue fluidization or fingering. However, a good and well-founded continuum description for tissues remains to be developed. In this work, we derive a macroscopic description for a two-dimensional cell monolayer by coarse-graining the vertex model through the Poisson bracket approach. We obtain equations for cell density, velocity, and the cellular shape tensor. We then study the homogeneous steady states, their stability (which coincides with thermodynamic stability), and especially their behavior under an externally applied shear. Our results contribute to elucidate the interplay between flow and cellular shape. The obtained macroscopic equations present a good starting point for adding cell motion, morphogenetic, and other biologically relevant processes.
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Affiliation(s)
| | - Falko Ziebert
- Institute for Theoretical Physics, Heidelberg University, D-69120 Heidelberg, Germany
| | - Luis L Bonilla
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain and G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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7
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Vats A, Yadav PK, Banerjee V, Puri S. Symbiotic dynamics in living liquid crystals. Phys Rev E 2023; 108:024701. [PMID: 37723723 DOI: 10.1103/physreve.108.024701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 06/22/2023] [Indexed: 09/20/2023]
Abstract
An amalgam of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and microcargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours coalignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.
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Affiliation(s)
- Aditya Vats
- Department of Physics, Indian Institute of Technology Delhi, New Delhi-110016, India
| | - Pradeep Kumar Yadav
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology Delhi, New Delhi-110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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8
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González-Albaladejo R, Carpio A, Bonilla LL. Scale-free chaos in the confined Vicsek flocking model. Phys Rev E 2023; 107:014209. [PMID: 36797962 DOI: 10.1103/physreve.107.014209] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 01/05/2023] [Indexed: 06/18/2023]
Abstract
The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite-size effects and criticality in the three-dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable "condensed" nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function, and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.
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Affiliation(s)
- R González-Albaladejo
- Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - A Carpio
- Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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9
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Perepelitsa M, Timofeyev I, Murphy P, Igoshin OA. Mean-field model for nematic alignment of self-propelled rods. Phys Rev E 2022; 106:034613. [PMID: 36266908 DOI: 10.1103/physreve.106.034613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.
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Affiliation(s)
| | - Ilya Timofeyev
- Department of Mathematics, University of Houston, Texas 77204, USA
| | - Patrick Murphy
- Department of Bioengineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Oleg A Igoshin
- Department of Bioengineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Biosciences, Rice University, Houston, Texas 77005, USA
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10
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Codina J, Mahault B, Chaté H, Dobnikar J, Pagonabarraga I, Shi XQ. Small Obstacle in a Large Polar Flock. PHYSICAL REVIEW LETTERS 2022; 128:218001. [PMID: 35687474 DOI: 10.1103/physrevlett.128.218001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 05/03/2022] [Indexed: 06/15/2023]
Abstract
We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counterpropagating dense bands leading to reversals of the flow. In very large systems, these bands interact, yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.
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Affiliation(s)
- Joan Codina
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325001, China
- Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Benoît Mahault
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100193, China
- Sorbonne Université, CNRS UMR7600, Laboratoire de Physique Théorique de la Matière Condensée, 75005 Paris, France
| | - Jure Dobnikar
- Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems, 08028 Barcelona, Spain
- Centre Européen de Calcul Atomique et Moléculaire, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
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11
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Hiraiwa T. Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:16. [PMID: 35212814 PMCID: PMC8881282 DOI: 10.1140/epje/s10189-022-00161-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
Understanding how migrating cells can establish both dynamic structures and coherent dynamics may provide mechanistic insights to study how living systems acquire complex structures and functions. Recent studies revealed that intercellular contact communication plays a crucial role for establishing cellular dynamic self-organization (DSO) and provided a theoretical model of DSO for migrating solitary cells in a free space. However, to apply those understanding to situations in living organisms, we need to know the role of cell-cell communication for tissue dynamics under spatial confinements and epithelial integrity. Here, we expand the previous numerical studies on DSO to migrating cells subjected spatial confinement and/or epithelial integrity. An epithelial monolayer is simulated by combining the model of cellular DSO and the cellular vertex model in two dimensions for apical integrity. Under confinement to a small space, theoretical models of both solitary and epithelial cells exhibit characteristic coherent dynamics, including apparent swirling. We also find that such coherent dynamics can allow the cells to overcome the strong constraint due to spatial confinement and epithelial integrity. Furthermore, we demonstrate how epithelial cell clusters behave without spatial confinement and find various cluster dynamics, including spinning, migration and elongation.
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Affiliation(s)
- Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, Singapore, Singapore, 117411.
- Universal Biology Institute, The University of Tokyo, Hongo, Tokyo, 113-0033, Japan.
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12
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Ouellette N. A physics perspective on collective animal behavior. Phys Biol 2022; 19. [PMID: 35038691 DOI: 10.1088/1478-3975/ac4bef] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 01/17/2022] [Indexed: 11/12/2022]
Abstract
The beautiful dynamic patterns and coordinated motion displayed by groups of social animals are a beautiful example of self-organization in natural farfrom-equilibrium systems. Recent advances in active-matter physics have enticed physicists to begin to consider how their results can be extended from microscale physical or biological systems to groups of real, macroscopic animals. At the same time, advances in measurement technology have led to the increasing availability of high-quality empirical data for the behavior of animal groups both in the laboratory and in the wild. In this review, I survey this available data and the ways that it has been analyzed. I then describe how physicists have approached synthesizing, modeling, and interpreting this information, both at the level of individual animals and at the group scale. In particular, I focus on the kinds of analogies that physicists have made between animal groups and more traditional areas of physics.
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Affiliation(s)
- Nicholas Ouellette
- Department of Civil and Environmental Engineering, Stanford University, 473 Via Ortega, Stanford, California, 94305-6104, UNITED STATES
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13
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Ben-Ari A, Ben-Ari L, Bisker G. Nonequilibrium self-assembly of multiple stored targets in a dimer-based system. J Chem Phys 2021; 155:234113. [PMID: 34937365 DOI: 10.1063/5.0069161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.
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Affiliation(s)
- Adi Ben-Ari
- Faculty of Engineering, School of Electrical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Liron Ben-Ari
- Faculty of Engineering, School of Electrical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Gili Bisker
- Faculty of Engineering, Department of Biomedical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
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14
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Mayer J, Obermüller M, Denk J, Frey E. Snowdrift game induces pattern formation in systems of self-propelled particles. Phys Rev E 2021; 104:044408. [PMID: 34781521 DOI: 10.1103/physreve.104.044408] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 07/29/2021] [Indexed: 11/07/2022]
Abstract
Evolutionary games between species are known to lead to intriguing spatiotemporal patterns in systems of diffusing agents. However, the role of interspecies interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions-a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatiotemporal patterns as well as game-induced pattern formation.
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Affiliation(s)
- Johanna Mayer
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Michael Obermüller
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
| | - Jonas Denk
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany.,Department of Physics, University of California, Berkeley, California 94720, USA.,Department of Integrative Biology, University of California, Berkeley, California 94720, USA
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
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15
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Kürsten R, Ihle T. Quantitative kinetic theory of flocking with three-particle closure. Phys Rev E 2021; 104:034604. [PMID: 34654183 DOI: 10.1103/physreve.104.034604] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 08/13/2021] [Indexed: 12/27/2022]
Abstract
We consider aligning self-propelled particles in two dimensions. Their motion is given by Langevin equations and includes nonadditive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean-field theory, the flocking transition is shifted significantly toward lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.
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Affiliation(s)
- Rüdiger Kürsten
- Institut für Physik, Universität Greifswald, Felix-Hausdorff-Strasse 6, 17489 Greifswald, Germany
| | - Thomas Ihle
- Institut für Physik, Universität Greifswald, Felix-Hausdorff-Strasse 6, 17489 Greifswald, Germany
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16
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Auschra S, Holubec V. Density and polarization of active Brownian particles in curved activity landscapes. Phys Rev E 2021; 103:062604. [PMID: 34271717 DOI: 10.1103/physreve.103.062604] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Accepted: 04/12/2021] [Indexed: 11/07/2022]
Abstract
Suspensions of motile active particles with space-dependent activity form characteristic polarization and density patterns. Recent single-particle studies for planar activity landscapes identified several quantities associated with emergent density-polarization patterns that are solely determined by bulk variables. Naive thermodynamic intuition suggests that these results might hold for arbitrary activity landscapes mediating bulk regions, and thus could be used as benchmarks for simulations and theories. However, the considered system operates in a nonequilibrium steady state and we prove by construction that the quantities in question lose their simple form for curved activity landscapes. Specifically, we provide a detailed analytical study of polarization and density profiles induced by radially symmetric activity steps, and of the total polarization for the case of a general radially symmetric activity landscape. While the qualitative picture is similar to the planar case, all the investigated variables depend not only on bulk variables but also comprise geometry-induced contributions. We verified that all our analytical results agree with exact numerical calculations.
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Affiliation(s)
- Sven Auschra
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Viktor Holubec
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany.,Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
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17
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Auschra S, Holubec V, Söker NA, Cichos F, Kroy K. Polarization-density patterns of active particles in motility gradients. Phys Rev E 2021; 103:062601. [PMID: 34271745 DOI: 10.1103/physreve.103.062601] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 04/21/2021] [Indexed: 11/07/2022]
Abstract
The colocalization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. We employ the active-Brownian-particle model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step. Our analysis allows for an optional (but not necessary) orientation-dependent propulsion speed, as often employed in force-free particle steering. The results agree well with measurement data for a thermophoretic microswimmer presented in the companion paper [Söker et al., Phys. Rev. Lett. 126, 228001 (2021)10.1103/PhysRevLett.126.228001], and they can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species "run-and-tumble" model.
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Affiliation(s)
- Sven Auschra
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
| | - Viktor Holubec
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany.,Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, CZ-180 00 Prague, Czech Republic
| | - Nicola Andreas Söker
- Peter Debye Institute for Soft Matter Physics, Leipzig University, 04103 Leipzig, Germany
| | - Frank Cichos
- Peter Debye Institute for Soft Matter Physics, Leipzig University, 04103 Leipzig, Germany
| | - Klaus Kroy
- Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
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18
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Abstract
Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.
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19
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Martin D, Chaté H, Nardini C, Solon A, Tailleur J, Van Wijland F. Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion. PHYSICAL REVIEW LETTERS 2021; 126:148001. [PMID: 33891435 DOI: 10.1103/physrevlett.126.148001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including models in which particles interact with their "topological" neighbors that have been believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.
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Affiliation(s)
- David Martin
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100193, China
| | - Cesare Nardini
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Alexandre Solon
- Sorbonne Université, CNRS, Laboratoire Physique Théorique de la Matière Condensée, 75005 Paris, France
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Frédéric Van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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20
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Speck T, Jayaram A. Vorticity Determines the Force on Bodies Immersed in Active Fluids. PHYSICAL REVIEW LETTERS 2021; 126:138002. [PMID: 33861089 DOI: 10.1103/physrevlett.126.138002] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Revised: 11/18/2020] [Accepted: 03/04/2021] [Indexed: 06/12/2023]
Abstract
When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by-but far away from-the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a nonvanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Ashreya Jayaram
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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21
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Fazli Z, Naji A. Active particles with polar alignment in ring-shaped confinement. Phys Rev E 2021; 103:022601. [PMID: 33736018 DOI: 10.1103/physreve.103.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 01/13/2021] [Indexed: 12/17/2022]
Abstract
We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.
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Affiliation(s)
- Zahra Fazli
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.,School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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22
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Kuan HS, Pönisch W, Jülicher F, Zaburdaev V. Continuum Theory of Active Phase Separation in Cellular Aggregates. PHYSICAL REVIEW LETTERS 2021; 126:018102. [PMID: 33480767 DOI: 10.1103/physrevlett.126.018102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 11/29/2020] [Indexed: 06/12/2023]
Abstract
Dense cellular aggregates are common in biology, ranging from bacterial biofilms to organoids, cell spheroids, and tumors. Their dynamics, driven by intercellular forces, is intrinsically out of equilibrium. Motivated by bacterial colonies as a model system, we present a continuum theory to study dense, active, cellular aggregates. We describe the process of aggregate formation as an active phase separation phenomenon, while the merging of aggregates is rationalized as a coalescence of viscoelastic droplets where the key timescales are linked to the turnover of the active force. Our theory provides a general framework for studying the rheology and nonequilibrium dynamics of dense cellular aggregates.
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Affiliation(s)
- Hui-Shun Kuan
- Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Max Planck Zentrum für Physik und Medizin, 91058 Erlangen, Germany
| | - Wolfram Pönisch
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- MRC Laboratory for Molecular Cell Biology, University College London, WC1E 6BT London, United Kingdom
- Department of Physiology, Development and Neuroscience, University of Cambridge, CB2 3DY Cambridge, United Kingdom
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, 01307 Dresden, Germany
| | - Vasily Zaburdaev
- Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Max Planck Zentrum für Physik und Medizin, 91058 Erlangen, Germany
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23
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Hiraiwa T. Dynamic Self-Organization of Idealized Migrating Cells by Contact Communication. PHYSICAL REVIEW LETTERS 2020; 125:268104. [PMID: 33449791 DOI: 10.1103/physrevlett.125.268104] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
This Letter investigates what forms of cellular dynamic self-organization are caused through intercellular contact communication based on a theoretical model in which migrating cells perform contact following and contact inhibition and attraction of locomotion. Tuning those strengths causes varieties of dynamic patterns. This further includes a novel form of collective migration, snakelike dynamic assembly. Scrutinizing this pattern reveals that cells in this state can accurately respond to an external directional cue but have no spontaneous global polar order.
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Affiliation(s)
- Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, 117411, Singapore and Universal Biology Institute, The University of Tokyo, Hongo, Tokyo 113-0033, Japan
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24
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Abstract
The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.
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25
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O'Byrne J, Tailleur J. Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals. PHYSICAL REVIEW LETTERS 2020; 125:208003. [PMID: 33258650 DOI: 10.1103/physrevlett.125.208003] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.
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Affiliation(s)
- J O'Byrne
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - J Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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26
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Exceptional non-Hermitian topological edge mode and its application to active matter. Nat Commun 2020; 11:5745. [PMID: 33184296 PMCID: PMC7665040 DOI: 10.1038/s41467-020-19488-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 10/14/2020] [Indexed: 11/08/2022] Open
Abstract
Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in non-Hermitian systems with dissipations and injections, the fundamental principle of their edge modes has not fully been established. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity around an exceptional point, at which eigenvectors coalesce and the Hamiltonian becomes nondiagonalizable. Their characteristic complex eigenenergy spectra are applicable to realize lasing wave packets that propagate along the edge of the sample. We numerically confirm the emergence and the robustness of the proposed edge modes in the prototypical lattice models. Furthermore, we show that these edge modes appear in a model of chiral active matter based on the hydrodynamic description, demonstrating that active matter can exhibit an inherently non-Hermitian topological feature. The proposed general mechanism would serve as an alternative designing principle to realize scattering-free edge current in non-Hermitian devices, going beyond the existing frameworks of non-Hermitian topological phases.
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27
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Kürsten R, Ihle T. Dry Active Matter Exhibits a Self-Organized Cross Sea Phase. PHYSICAL REVIEW LETTERS 2020; 125:188003. [PMID: 33196272 DOI: 10.1103/physrevlett.125.188003] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2020] [Revised: 08/03/2020] [Accepted: 10/06/2020] [Indexed: 06/11/2023]
Abstract
The Vicsek model of self-propelled particles is known in three different phases: a polar ordered homogeneous phase, also called the Toner-Tu phase, a phase of polar ordered regularly arranged high density bands with surrounding low density regions without polar order, and a homogeneous phase without polar order. Here, we show that the standard Vicsek model has a fourth phase for large system sizes: a polar ordered cross sea phase. We demonstrate that the cross sea phase is not just a superposition of two waves, but it is an independent complex pattern with an inherently selected crossing angle.
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Affiliation(s)
- Rüdiger Kürsten
- Institut für Physik, Universität Greifswald, Felix-Hausdorff-Straße 6, 17489 Greifswald, Germany
| | - Thomas Ihle
- Institut für Physik, Universität Greifswald, Felix-Hausdorff-Straße 6, 17489 Greifswald, Germany
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28
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A particle-field approach bridges phase separation and collective motion in active matter. Nat Commun 2020; 11:5365. [PMID: 33097711 PMCID: PMC7584633 DOI: 10.1038/s41467-020-18978-5] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 09/21/2020] [Indexed: 12/20/2022] Open
Abstract
Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media. Interacting self-propelled particles exhibit phase separation or collective motion depending on particle shape. A unified theory connecting these paradigms represents a major challenge in active matter, which the authors address here by modeling active particles as continuum fields.
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29
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Mangeat M, Chatterjee S, Paul R, Rieger H. Flocking with a q-fold discrete symmetry: Band-to-lane transition in the active Potts model. Phys Rev E 2020; 102:042601. [PMID: 33212593 DOI: 10.1103/physreve.102.042601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 09/11/2020] [Indexed: 11/06/2022]
Abstract
We study the q-state active Potts model (APM) on a two-dimensional lattice in which self-propelled particles have q internal states corresponding to the q directions of motion. A local alignment rule inspired by the ferromagnetic q-state Potts model and self-propulsion via biased diffusion according to the internal particle states elicits collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory with which we compute the phase diagrams of the APM for q=4 and q=6 and analyze the flocking dynamics in the coexistence region, where the high-density (polar liquid) phase forms a fluctuating stripe of coherently moving particles on the background of the low-density (gas) phase. A reorientation transition of the phase-separated profiles from transversal band motion to longitudinal lane formation is found, which is absent in the Vicsek model and the active Ising model. The origin of this reorientation transition is revealed by a stability analysis: for large velocities the transverse diffusivity approaches zero and stabilizes lanes. Computer simulations corroborate the analytical predictions of the flocking and reorientation transitions and validate the phase diagrams of the APM.
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Affiliation(s)
- Matthieu Mangeat
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
| | - Swarnajit Chatterjee
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Raja Paul
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Heiko Rieger
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
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30
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Škultéty V, Birnšteinová Š, Lučivjanský T, Honkonen J. Universality in incompressible active fluid: Effect of nonlocal shear stress. Phys Rev E 2020; 102:032616. [PMID: 33075957 DOI: 10.1103/physreve.102.032616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen et al., New J. Phys. 17, 042002 (2015)10.1088/1367-2630/17/4/042002] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a nonlocal shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Lévy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of nonlocal shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual long-range Model A universality class not reported before, to our knowledge. Moreover, when the degree of nonlocality is sufficiently high all nonlinearities become irrelevant and the mean-field description is valid in any spatial dimension.
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Affiliation(s)
- V Škultéty
- SUPA, School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Š Birnšteinová
- Faculty of Sciences, P. J. Šafárik University, 04154 Košice, Slovakia
| | - T Lučivjanský
- Faculty of Sciences, P. J. Šafárik University, 04154 Košice, Slovakia
| | - J Honkonen
- Department of Military Technology, National Defence University, P.O. Box 7, 00861 Helsinki, Finland
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31
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Soni H, Kumar N, Nambisan J, Gupta RK, Sood AK, Ramaswamy S. Phases and excitations of active rod-bead mixtures: simulations and experiments. SOFT MATTER 2020; 16:7210-7221. [PMID: 32393926 DOI: 10.1039/c9sm02552a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We present a large-scale numerical study, supplemented by experimental observations, on a quasi-two-dimensional active system of polar rods and spherical beads confined between two horizontal plates and energised by vertical vibration. For a low rod concentration Φr, our observations are consistent with a direct phase transition, as bead concentration Φb is increased, from the isotropic phase to a homogeneous flock. For Φr above a threshold value, an ordered band dense in both rods and beads occurs between the disordered phase and the homogeneous flock, in both experiments and simulations. Within the size ranges accessible, we observe only a single band, whose width increases with Φr. Deep in the ordered state, we observe broken-symmetry "sound" modes and giant number fluctuations. The direction-dependent sound speeds and the scaling of fluctuations are consistent with the predictions of field theories of flocking; sound damping rates show departures from such theories, but the range of wavenumbers explored is modest. At very high densities, we see phase separation into rod-rich and bead-rich regions, both of which move coherently.
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Affiliation(s)
- Harsh Soni
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
| | - Nitin Kumar
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Jyothishraj Nambisan
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and School of Physics, Georgia Institute of Technology, 770 State Street NW, Atlanta, GA 30332-0430, USA
| | - Rahul Kumar Gupta
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
| | - A K Sood
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India.
| | - Sriram Ramaswamy
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India. and TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500 107, India
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32
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Nava-Sedeño JM, Voß-Böhme A, Hatzikirou H, Deutsch A, Peruani F. Modelling collective cell motion: are on- and off-lattice models equivalent? Philos Trans R Soc Lond B Biol Sci 2020; 375:20190378. [PMID: 32713300 DOI: 10.1098/rstb.2019.0378] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
Biological processes, such as embryonic development, wound repair and cancer invasion, or bacterial swarming and fruiting body formation, involve collective motion of cells as a coordinated group. Collective cell motion of eukaryotic cells often includes interactions that result in polar alignment of cell velocities, while bacterial patterns typically show features of apolar velocity alignment. For analysing the population-scale effects of these different alignment mechanisms, various on- and off-lattice agent-based models have been introduced. However, discriminating model-specific artefacts from general features of collective cell motion is challenging. In this work, we focus on equivalence criteria at the population level to compare on- and off-lattice models. In particular, we define prototypic off- and on-lattice models of polar and apolar alignment, and show how to obtain an on-lattice from an off-lattice model of velocity alignment. By characterizing the behaviour and dynamical description of collective migration models at the macroscopic level, we suggest the type of phase transitions and possible patterns in the approximative macroscopic partial differential equation descriptions as informative equivalence criteria between on- and off-lattice models. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.
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Affiliation(s)
- Josué Manik Nava-Sedeño
- Technische Universität Dresden, Center for Information Services and High Performance Computing, Nöthnitzer Straße 46, 01062 Dresden, Germany
| | - Anja Voß-Böhme
- Technische Universität Dresden, Center for Information Services and High Performance Computing, Nöthnitzer Straße 46, 01062 Dresden, Germany.,Fakultät Informatik/Mathematik, Hochschule für Technik und Wirtschaft, Dresden, Germany
| | - Haralampos Hatzikirou
- Department of Systems Immunology and Braunschweig Integrated Center of Systems Biology, Helmholtz Center for Infection Research, Inhoffenstraße 7, 38124 Braunschweig, Germany
| | - Andreas Deutsch
- Technische Universität Dresden, Center for Information Services and High Performance Computing, Nöthnitzer Straße 46, 01062 Dresden, Germany
| | - Fernando Peruani
- Laboratoire J. A. Dieudonné, Université Côte d'Azur, UMR 7351 CNRS, Parc Valrose, 06108 Nice Cedex 02, France
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33
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Collective Dynamics of Model Pili-Based Twitcher-Mode Bacilliforms. Sci Rep 2020; 10:10747. [PMID: 32612117 PMCID: PMC7330051 DOI: 10.1038/s41598-020-67212-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2020] [Accepted: 05/27/2020] [Indexed: 11/29/2022] Open
Abstract
Pseudomonas aeruginosa, like many bacilliforms, are not limited only to swimming motility but rather possess many motility strategies. In particular, twitching-mode motility employs hair-like pili to transverse moist surfaces with a jittery irregular crawl. Twitching motility plays a critical role in redistributing cells on surfaces prior to and during colony formation. We combine molecular dynamics and rule-based simulations to study twitching-mode motility of model bacilliforms and show that there is a critical surface coverage fraction at which collective effects arise. Our simulations demonstrate dynamic clustering of twitcher-type bacteria with polydomains of local alignment that exhibit spontaneous correlated motions, similar to rafts in many bacterial communities.
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34
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Abstract
Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
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35
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Jayaram A, Fischer A, Speck T. From scalar to polar active matter: Connecting simulations with mean-field theory. Phys Rev E 2020; 101:022602. [PMID: 32168709 DOI: 10.1103/physreve.101.022602] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2019] [Accepted: 01/21/2020] [Indexed: 11/07/2022]
Abstract
We study numerically the phase behavior of self-propelled elliptical particles interacting through the "hard" repulsive Gay-Berne potential at infinite Péclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obtain a complete and consistent picture, unifying the paradigms of scalar and polar active matter.
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Affiliation(s)
- Ashreya Jayaram
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Andreas Fischer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
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36
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Liao GJ, Hall CK, Klapp SHL. Dynamical self-assembly of dipolar active Brownian particles in two dimensions. SOFT MATTER 2020; 16:2208-2223. [PMID: 32090218 DOI: 10.1039/c9sm01539f] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Based on Brownian Dynamics (BD) simulations, we study the dynamical self-assembly of active Brownian particles with dipole-dipole interactions, stemming from a permanent point dipole at the particle center. The propulsion direction of each particle is chosen to be parallel to its dipole moment. We explore a wide range of motilities and dipolar coupling strengths and characterize the corresponding behavior based on several order parameters. At low densities and low motilities, the most important structural phenomenon is the aggregation of the dipolar particles into chains. Upon increasing the particle motility, these chain-like structures break, and the system transforms into a weakly correlated isotropic fluid. At high densities, we observe that the motility-induced phase separation is strongly suppressed by the dipolar coupling. Once the dipolar coupling dominates the thermal energy, the phase separation disappears, and the system rather displays a flocking state, where particles form giant clusters and move collective along one direction. We provide arguments for the emergence of the flocking behavior, which is absent in the passive dipolar system.
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Affiliation(s)
- Guo-Jun Liao
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
| | - Carol K Hall
- Department of Chemical & Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695, USA
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
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37
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Katyal N, Dey S, Das D, Puri S. Coarsening dynamics in the Vicsek model of active matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:10. [PMID: 32025853 DOI: 10.1140/epje/i2020-11934-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as [Formula: see text] (with [Formula: see text] , while the velocity length scale grows much faster, viz., [Formula: see text] (with [Formula: see text] . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively.
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Affiliation(s)
- Nisha Katyal
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | - Supravat Dey
- Laboratoire Charles Coulomb Université Montpellier and CNRS, UMR 5221, 34095, Montpellier, France
| | - Dibyendu Das
- Department of Physics, Indian Institute of Technology Bombay, 400076, Powai, Mumbai, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India.
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38
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Netz RR. Approach to equilibrium and nonequilibrium stationary distributions of interacting many-particle systems that are coupled to different heat baths. Phys Rev E 2020; 101:022120. [PMID: 32168558 DOI: 10.1103/physreve.101.022120] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 01/23/2020] [Indexed: 06/10/2023]
Abstract
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy S_{free}(t), is constructed. For the stationary distribution S_{free}(t) becomes maximal and its time derivative, the free entropy production S[over ̇]_{free}(t), is minimal and vanishes. Thus, S_{free}(t) characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.
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Affiliation(s)
- Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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39
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Fischer A, Schmid F, Speck T. Quorum-sensing active particles with discontinuous motility. Phys Rev E 2020; 101:012601. [PMID: 32069622 DOI: 10.1103/physreve.101.012601] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Indexed: 06/10/2023]
Abstract
We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.
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Affiliation(s)
- Andreas Fischer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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40
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Chatterjee P, Goldenfeld N. Three-body interactions drive the transition to polar order in a simple flocking model. Phys Rev E 2019; 100:040602. [PMID: 31770962 DOI: 10.1103/physreve.100.040602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Indexed: 11/07/2022]
Abstract
A large class of mesoscopic or macroscopic flocking theories are coarse-grained from microscopic models that feature binary interactions as the chief aligning mechanism. However, while such theories seemingly predict the existence of polar order with just binary interactions, actomyosin motility assay experiments show that binary interactions are insufficient to obtain polar order, especially at high densities. To resolve this paradox, here we introduce a solvable one-dimensional flocking model and derive its stochastic hydrodynamics. We show that two-body interactions are insufficient to generate polar order unless the noise is non-Gaussian. We show that noisy three-body interactions in the microscopic theory allow us to capture all essential dynamical features of the flocking transition, in systems that achieve orientational order above a critical density.
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Affiliation(s)
- Purba Chatterjee
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
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41
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Nikoubashman A, Ihle T. Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations. Phys Rev E 2019; 100:042603. [PMID: 31770923 DOI: 10.1103/physreve.100.042603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Indexed: 11/07/2022]
Abstract
The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)1063-651X10.1103/PhysRevE.59.4894] for shearing simple liquids and measuring their viscosity is extended to the Vicsek model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.1226] and its metric-free version. The sheared systems exhibit a phenomenon that is similar to the skin effect of an alternating electric current: Momentum that is fed into the boundaries of a layer decays mostly exponentially toward the center of the layer. It is shown how two transport coefficients, i.e., the shear viscosity ν and the momentum amplification coefficient λ, can be obtained by fitting this decay with an analytical solution of the hydrodynamic equations for the VM. The viscosity of the VM consists of two parts, a kinetic and a collisional contribution. While analytical predictions already exist for the former, a novel expression for the collisional part is derived by an Enskog-like kinetic theory. To verify the predictions for the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of ν and 1-λ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the VM, compared to models obeying detailed balance such as multiparticle collision dynamics.
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Affiliation(s)
- Arash Nikoubashman
- Institute of Physics, Johannes-Gutenberg-University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Thomas Ihle
- Institute for Physics, University of Greifswald, Felix-Hausdorff-Strasse 6, 17489 Greifswald, Germany
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42
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Rana S, Samsuzzaman M, Saha A. Tuning the self-organization of confined active particles by the steepness of the trap. SOFT MATTER 2019; 15:8865-8878. [PMID: 31616877 DOI: 10.1039/c9sm01691k] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We consider the collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with small rotational fluctuations. They also interact with each other via soft, isotropic, repulsive potentials. The particles are confined in a circular trap. The steepness of the trap is tuneable. The average packing fraction of the particles is low. When the trap is steep, particles flock along its boundary. They form a polar cluster that spreads over the boundary. The cluster is not spatially ordered. We show that when the steepness is decreased beyond a threshold value, the cluster becomes round and compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order. We investigate the kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the cluster needs to roll around its centre of mass to be spatially ordered. We have studied the stability of the order when the trap is suddenly switched off. We find that for the particles with velocity alignment interaction, the decay of the spatial order is much slower than the particles without the alignment interaction.
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Affiliation(s)
- Shubhashis Rana
- S. N. Bose National Centre For Basic Sciences, Kolkata, 700098, India.
| | - Md Samsuzzaman
- Department of Physics, Savitribai Phule Pune University, Pune, 411007, India.
| | - Arnab Saha
- Department of Physics, Savitribai Phule Pune University, Pune, 411007, India.
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43
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Sone K, Ashida Y. Anomalous Topological Active Matter. PHYSICAL REVIEW LETTERS 2019; 123:205502. [PMID: 31809111 DOI: 10.1103/physrevlett.123.205502] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Indexed: 06/10/2023]
Abstract
Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. The quantum anomalous Hall effect thus provides design principles for realizing topological metamaterials. We propose and analyze the concrete minimal model and numerically calculate its band structure and eigenvectors, demonstrating the emergence of nonzero bulk topological invariants with the corresponding edge sound modes. This new type of topological active systems can potentially expand possibilities for their experimental realizations and may have broad applications to practical active metamaterials. Possible realization of non-Hermitian topological phenomena in active systems is also discussed.
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Affiliation(s)
- Kazuki Sone
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Yuto Ashida
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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44
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Sakaguchi H, Ishibashi K. Flip motion of solitary wave in an Ising-type Vicsek model. Phys Rev E 2019; 100:052113. [PMID: 31869910 DOI: 10.1103/physreve.100.052113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Indexed: 06/10/2023]
Abstract
An Ising-type Vicsek model is proposed for collective motion and sudden direction change in a population of self-propelled particles. Particles move on a linear lattice with velocity +1 or -1 in the one-dimensional model. The probability of the velocity of a particle at the next step is determined by the number difference of the right- and left-moving particles at the present lattice site and its nearest-neighboring sites. A solitary wave appears also in our model similarly to previous models. In some parameter range, the moving direction of the solitary wave sometimes changes rather suddenly, which is like the sudden change of direction of a flock of birds. We study the average reversal time of traveling direction numerically and compare the results with a mean-field theory. The one-dimensional model is generalized to a two-dimensional model. Flip motion of a bandlike soliton is observed in the two-dimensional model.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
| | - Kazuya Ishibashi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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45
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Papaspyros V, Bonnet F, Collignon B, Mondada F. Bidirectional interactions facilitate the integration of a robot into a shoal of zebrafish Danio rerio. PLoS One 2019; 14:e0220559. [PMID: 31430290 PMCID: PMC6701756 DOI: 10.1371/journal.pone.0220559] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Accepted: 07/18/2019] [Indexed: 11/21/2022] Open
Abstract
Many studies on collective animal behavior seek to identify the individual rules that underlie collective patterns. However, it was not until the recent advancements of micro-electronic and embedded systems that scientists were able to create mixed groups of sensor-rich robots and animals and study collective interactions from the within a bio-hybrid group. In recent work, scientists showed that a robot-controlled lure is capable of influencing the collective decisions of zebrafish Danio rerio shoals moving in a ring and a two-room setup. Here, we study a closely related topic, that is, the collective behavior patterns that emerge when different behavioral models are reproduced through the use of a robotic lure. We design a behavioral model that alternates between obeying and disobeying the collective motion decisions in order to become socially accepted by the shoal members. Subsequently, we compare it against two extreme cases: a reactive and an imposing decision model. For this, we use spatial, directional and information theoretic metrics to measure the degree of integration of the robotic agent. We show that our model leads to similar information flow as in freely roaming shoals of zebrafish and exhibits leadership skills more often than the open-loop models. Thus, in order for the robot to achieve higher degrees of integration in the zebrafish shoal, it must, like any other shoal member, be bidirectionally involved in the decision making process. These findings provide insight on the ability to form mixed societies of animals and robots and yield promising results on the degree to which a robot can influence the collective decision making.
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Affiliation(s)
- Vaios Papaspyros
- Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Frank Bonnet
- Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Bertrand Collignon
- Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- Unit of Social Ecology (USE), Université libre de Bruxelles (ULB), Bruxelles, Belgium
| | - Francesco Mondada
- Biorobotics Laboratory, Institute of Bioengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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46
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Partridge B, Lee CF. Critical Motility-Induced Phase Separation Belongs to the Ising Universality Class. PHYSICAL REVIEW LETTERS 2019; 123:068002. [PMID: 31491158 DOI: 10.1103/physrevlett.123.068002] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2018] [Indexed: 06/10/2023]
Abstract
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of a gas-liquid phase separation, known as motility-induced phase separation (MIPS). The nonequilibrium nature of the system is fundamental to the phase transition; however, it is unclear whether MIPS at criticality contributes a novel universality class to nonequilibrium physics. We demonstrate here that this is not the case by showing that a generic critical MIPS belongs to the Ising universality class with conservative dynamics.
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Affiliation(s)
- Benjamin Partridge
- Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Chiu Fan Lee
- Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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47
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Abstract
Collective motion is found in various animal systems, active suspensions, and robotic or virtual agents. This is often understood by using high-level models that directly encode selected empirical features, such as coalignment and cohesion. Can these features be shown to emerge from an underlying, low-level principle? We find that they emerge naturally under future state maximization (FSM). Here, agents perceive a visual representation of the world around them, such as might be recorded on a simple retina, and then move to maximize the number of different visual environments that they expect to be able to access in the future. Such a control principle may confer evolutionary fitness in an uncertain world by enabling agents to deal with a wide variety of future scenarios. The collective dynamics that spontaneously emerge under FSM resemble animal systems in several qualitative aspects, including cohesion, coalignment, and collision suppression, none of which are explicitly encoded in the model. A multilayered neural network trained on simulated trajectories is shown to represent a heuristic mimicking FSM. Similar levels of reasoning would seem to be accessible under animal cognition, demonstrating a possible route to the emergence of collective motion in social animals directly from the control principle underlying FSM. Such models may also be good candidates for encoding into possible future realizations of artificial "intelligent" matter, able to sense light, process information, and move.
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48
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Piwowarczyk R, Selin M, Ihle T, Volpe G. Influence of sensorial delay on clustering and swarming. Phys Rev E 2019; 100:012607. [PMID: 31499896 DOI: 10.1103/physreve.100.012607] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Indexed: 06/10/2023]
Abstract
We show that sensorial delay alters the collective motion of self-propelling agents with aligning interactions: In a two-dimensional Vicsek model, short delays enhance the emergence of clusters and swarms, while long or negative delays prevent their formation. In order to quantify this phenomenon, we introduce a global clustering parameter based on the Voronoi tessellation, which permits us to efficiently measure the formation of clusters. Thanks to its simplicity, sensorial delay might already play a role in the organization of living organisms and can provide a powerful tool to engineer and dynamically tune the behavior of large ensembles of autonomous robots.
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Affiliation(s)
- Rafal Piwowarczyk
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
- Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
| | - Martin Selin
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
- Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
| | - Thomas Ihle
- Institute of Physics, University of Greifswald, DE-17489 Greifswald, Germany
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
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49
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Chakraborti S, Pradhan P. Additivity and density fluctuations in Vicsek-like models of self-propelled particles. Phys Rev E 2019; 99:052604. [PMID: 31212568 DOI: 10.1103/physreve.99.052604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Indexed: 11/07/2022]
Abstract
We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation-the direct consequence of an additivity property-we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide evidence of the existence of an equilibriumlike chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.
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Affiliation(s)
- Subhadip Chakraborti
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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50
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Kourbane-Houssene M, Erignoux C, Bodineau T, Tailleur J. Exact Hydrodynamic Description of Active Lattice Gases. PHYSICAL REVIEW LETTERS 2018; 120:268003. [PMID: 30004761 DOI: 10.1103/physrevlett.120.268003] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Revised: 04/23/2018] [Indexed: 06/08/2023]
Abstract
We introduce lattice gas models of active matter systems whose coarse-grained "hydrodynamic" description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviors in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equations describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.
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Affiliation(s)
| | - Clément Erignoux
- Instituto de Matemática Pura e Aplicada, CEP 22460-320, Rio de Janeiro, Brazil
| | - Thierry Bodineau
- CMAP, Ecole polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France
| | - Julien Tailleur
- Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, 75205 Paris, France
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