1
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Paul T, Vadakkayil N, Das SK. Finite-size scaling in kinetics of phase separation in certain models of aligning active particles. Phys Rev E 2024; 109:064607. [PMID: 39020877 DOI: 10.1103/physreve.109.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Accepted: 05/14/2024] [Indexed: 07/19/2024]
Abstract
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.
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2
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Venkatareddy N, Mandal J, Maiti PK. Effect of confinement and topology: 2-TIPS vs. MIPS. SOFT MATTER 2023; 19:8561-8576. [PMID: 37905347 DOI: 10.1039/d3sm00796k] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
2-TIPS (two temperature induced phase separation) refers to the phase separation phenomenon observed in mixtures of active and passive particles which are modelled using scalar activity. The active particles are connected to a thermostat at high temperature while the passive particles are connected to the thermostat at low temperature and the relative temperature difference between "hot" and "cold" particles is taken as the measure of the activity χ of the non-equilibrium system. The study of such binary mixtures of hot and cold particles under various kinds of confinement is an important problem in many physical and biological processes. The nature and extent of phase separation are heavily influenced by the geometry of confinement, activity, and density of the non-equilibrium binary mixture. Investigating such 3D binary mixtures confined by parallel walls, we observe that the active and passive particles phase separate, but the extent of phase separation is reduced compared to bulk phase separation at high densities and enhanced at low densities. However, when the binary mixture of active and passive particles is confined inside a spherical cavity, the phase separation is radial for small radii of the confining sphere and the extent of phase separation is higher compared to their bulk counterparts. Confinement leads to interesting properties in the passive (cold) region like enhanced layering and high compression in the direction parallel to the confining wall. In 2D, both the bulk and confined systems of the binary mixture show a significant decrement in the extent of phase separation at higher densities. This observation is attributed to the trapping of active particles inside the passive cluster, which increases with density. Thus the 2D systems show structures more akin to dense-dilute phase co-existence, which is observed in motility induced phase separation in 2D active systems. The binary mixture constrained on the spherical surface also shows similar phase co-existence. Our analyses reveal that the coexistent densities observed in 2-TIPS on the spherical surface agree with the findings of previous studies on MIPS in active systems on a sphere.
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Affiliation(s)
- Nayana Venkatareddy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
| | - Jaydeep Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
| | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
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3
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Brandstätter T, Brückner DB, Han YL, Alert R, Guo M, Broedersz CP. Curvature induces active velocity waves in rotating spherical tissues. Nat Commun 2023; 14:1643. [PMID: 36964141 PMCID: PMC10039078 DOI: 10.1038/s41467-023-37054-2] [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: 10/26/2022] [Accepted: 02/26/2023] [Indexed: 03/26/2023] Open
Abstract
The multicellular organization of diverse systems, including embryos, intestines, and tumors relies on coordinated cell migration in curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes have been studied extensively in flat systems, the consequences of geometrical and topological constraints on collective migration in curved systems are largely unknown. Here, we discover a collective mode of cell migration in rotating spherical tissues manifesting as a propagating single-wavelength velocity wave. This wave is accompanied by an apparently incompressible supracellular flow pattern featuring topological defects as dictated by the spherical topology. Using a minimal active particle model, we reveal that this collective mode arises from the effect of curvature on the active flocking behavior of a cell layer confined to a spherical surface. Our results thus identify curvature-induced velocity waves as a mode of collective cell migration, impacting the dynamical organization of 3D curved tissues.
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Affiliation(s)
- Tom Brandstätter
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, The Netherlands
| | - David B Brückner
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria
| | - Yu Long Han
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Ricard Alert
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstr. 38, 01187, Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstr. 108, 01307, Dresden, Germany
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA
| | - Ming Guo
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333, Munich, Germany.
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV, Amsterdam, The Netherlands.
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4
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Schamberger B, Ziege R, Anselme K, Ben Amar M, Bykowski M, Castro APG, Cipitria A, Coles RA, Dimova R, Eder M, Ehrig S, Escudero LM, Evans ME, Fernandes PR, Fratzl P, Geris L, Gierlinger N, Hannezo E, Iglič A, Kirkensgaard JJK, Kollmannsberger P, Kowalewska Ł, Kurniawan NA, Papantoniou I, Pieuchot L, Pires THV, Renner LD, Sageman-Furnas AO, Schröder-Turk GE, Sengupta A, Sharma VR, Tagua A, Tomba C, Trepat X, Waters SL, Yeo EF, Roschger A, Bidan CM, Dunlop JWC. Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2206110. [PMID: 36461812 DOI: 10.1002/adma.202206110] [Citation(s) in RCA: 33] [Impact Index Per Article: 33.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 11/22/2022] [Indexed: 06/17/2023]
Abstract
Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.
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Affiliation(s)
- Barbara Schamberger
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Ricardo Ziege
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Karine Anselme
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Université de Strasbourg, F-67081, Strasbourg, France
| | - Martine Ben Amar
- Department of Physics, Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
| | - Michał Bykowski
- Department of Plant Anatomy and Cytology, Faculty of Biology, University of Warsaw, 02-096, Warsaw, Poland
| | - André P G Castro
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
- ESTS, Instituto Politécnico de Setúbal, 2914-761, Setúbal, Portugal
| | - Amaia Cipitria
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Group of Bioengineering in Regeneration and Cancer, Biodonostia Health Research Institute, 20014, San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, 48009, Bilbao, Spain
| | - Rhoslyn A Coles
- Cluster of Excellence, Matters of Activity, Humboldt-Universität zu Berlin, 10178, Berlin, Germany
| | - Rumiana Dimova
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Michaela Eder
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Sebastian Ehrig
- Max Delbrück Center for Molecular Medicine, 13125, Berlin, Germany
- Berlin Institute for Medical Systems Biology, 10115, Berlin, Germany
| | - Luis M Escudero
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013, Seville, Spain
- Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031, Madrid, Spain
| | - Myfanwy E Evans
- Institute for Mathematics, University of Potsdam, 14476, Potsdam, Germany
| | - Paulo R Fernandes
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
| | - Peter Fratzl
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - Liesbet Geris
- Biomechanics Research Unit, GIGA In Silico Medicine, University of Liège, 4000, Liège, Belgium
| | - Notburga Gierlinger
- Institute of Biophysics, Department of Nanobiotechnology, University of Natural Resources and Life Sciences Vienna (Boku), 1190, Vienna, Austria
| | - Edouard Hannezo
- Institute of Science and Technology Austria, 3400, Klosterneuburg, Austria
| | - Aleš Iglič
- Laboratory of Physics, Faculty of Electrical engineering, University of Ljubljana, Tržaška 25, SI-1000, Ljubljana, Slovenia
| | - Jacob J K Kirkensgaard
- Condensed Matter Physics, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100, København Ø, Denmark
- Ingredients and Dairy Technology, Department of Food Science, University of Copenhagen, Rolighedsvej 26, 1958, Frederiksberg, Denmark
| | - Philip Kollmannsberger
- Center for Computational and Theoretical Biology, University of Würzburg, 97074, Würzburg, Germany
| | - Łucja Kowalewska
- Department of Plant Anatomy and Cytology, Faculty of Biology, University of Warsaw, 02-096, Warsaw, Poland
| | - Nicholas A Kurniawan
- Department of Biomedical Engineering and Institute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
| | - Ioannis Papantoniou
- Prometheus Division of Skeletal Tissue Engineering, KU Leuven, O&N1, Herestraat 49, PB 813, 3000, Leuven, Belgium
- Skeletal Biology and Engineering Research Center, Department of Development and Regeneration, KU Leuven, O&N1, Herestraat 49, PB 813, 3000, Leuven, Belgium
- Institute of Chemical Engineering Sciences, Foundation for Research and Technology (FORTH), Stadiou Str., 26504, Patras, Greece
| | - Laurent Pieuchot
- IS2M (CNRS - UMR 7361), Université de Haute-Alsace, F-68100, Mulhouse, France
- Université de Strasbourg, F-67081, Strasbourg, France
| | - Tiago H V Pires
- IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
| | - Lars D Renner
- Leibniz Institute of Polymer Research and the Max Bergmann Center of Biomaterials, 01069, Dresden, Germany
| | | | - Gerd E Schröder-Turk
- School of Physics, Chemistry and Mathematics, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia
- Department of Materials Physics, Research School of Physics, The Australian National University, Canberra, ACT, 2600, Australia
| | - Anupam Sengupta
- Physics of Living Matter, Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Grand Duchy of Luxembourg
| | - Vikas R Sharma
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Antonio Tagua
- Instituto de Biomedicina de Sevilla (IBiS), Hospital Universitario Virgen del Rocío/CSIC/Universidad de Sevilla and Departamento de Biología Celular, Universidad de Sevilla, 41013, Seville, Spain
- Biomedical Network Research Centre on Neurodegenerative Diseases (CIBERNED), 28031, Madrid, Spain
| | - Caterina Tomba
- Univ Lyon, CNRS, INSA Lyon, Ecole Centrale de Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, 69622, Villeurbanne, France
| | - Xavier Trepat
- ICREA at the Institute for Bioengineering of Catalonia, The Barcelona Institute for Science and Technology, 08028, Barcelona, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 08028, Barcelona, Spain
| | - Sarah L Waters
- Mathematical Institute, University of Oxford, OX2 6GG, Oxford, UK
| | - Edwina F Yeo
- Mathematical Institute, University of Oxford, OX2 6GG, Oxford, UK
| | - Andreas Roschger
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
| | - Cécile M Bidan
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14476, Potsdam, Germany
| | - John W C Dunlop
- Department of the Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, 5020, Salzburg, Austria
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5
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Rajendra D, Mandal J, Hatwalne Y, Maiti PK. Packing and emergence of the ordering of rods in a spherical monolayer. SOFT MATTER 2022; 19:137-146. [PMID: 36477473 DOI: 10.1039/d2sm00799a] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational and translational order. The study of these structures is important for investigating the interplay between the geometry, topology, and elasticity, and for their potential applications in materials science, such as engineering directionally binding particles. In this work, we numerically simulate a spherical monolayer of soft repulsive spherocylinders (SRSs) and study the packing of rods and their ordering transition as a function of the packing fraction. In the model that we study, the centers of mass of the spherocylinders (situated at their geometric centers) are constrained to move on a spherical surface. The spherocylinders are free to rotate about any axis that passes through their respective centers of mass. We show that, up to moderate packing fractions, a two dimensional liquid crystalline phase is formed whose orientational ordering increases continuously with increasing density. This monolayer of orientationally ordered SRS particles at medium densities resembles a hedgehog-long axes of the SRS particles are aligned along the local normal to the sphere. At higher packing fractions, the system undergoes a transition to the solid phase, which is riddled with topological point defects (disclinations) and grain boundaries that divide the whole surface into several domains.
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Affiliation(s)
- Dharanish Rajendra
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
| | - Jaydeep Mandal
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
| | | | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bengaluru 560012, India.
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6
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Debets VE, Janssen LMC. Active glassy dynamics is unaffected by the microscopic details of self-propulsion. J Chem Phys 2022; 157:224902. [DOI: 10.1063/5.0127569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Recent years have seen a rapid increase of interest in dense active materials, which, in the disordered state, share striking similarities with the conventional passive glass-forming matter. For such passive glassy materials, it is well established (at least in three dimensions) that the details of the microscopic dynamics, e.g., Newtonian or Brownian, do not influence the long-time glassy behavior. Here, we investigate whether this still holds true in the non-equilibrium active case by considering two simple and widely used active particle models, i.e., active Ornstein-Uhlenbeck particles (AOUPs) and active Brownian particles (ABPs). In particular, we seek to gain more insight into the role of the self-propulsion mechanism on the glassy dynamics by deriving a mode-coupling theory (MCT) for thermal AOUPs, which can be directly compared to a recently developed MCT for ABPs. Both theories explicitly take into account the active degrees of freedom. We solve the AOUP- and ABP-MCT equations in two dimensions and demonstrate that both models give almost identical results for the intermediate scattering function over a large variety of control parameters (packing fractions, active speeds, and persistence times). We also confirm this theoretical equivalence between the different self-propulsion mechanisms numerically via simulations of a polydisperse mixture of active quasi-hard spheres, thereby establishing that, at least for these model systems, the microscopic details of self-propulsion do not alter the active glassy behavior.
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Affiliation(s)
- Vincent E. Debets
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Liesbeth M. C. Janssen
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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7
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Schönhöfer PWA, Glotzer SC. Curvature-controlled geometrical lensing behavior in self-propelled colloidal particle systems. SOFT MATTER 2022; 18:8561-8571. [PMID: 36200373 DOI: 10.1039/d2sm01012g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
In many biological systems, the curvature of the surfaces cells live on influences their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) how curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, which we explain theoretically by the nature of parallel lines in spherical and hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the emergence of defect patterns disrupting the crystalline order inside the clusters. Using our findings, we engineer three confining surfaces that strategically combine regions of different curvature to produce a host of novel dynamical behaviors, including cyclic MIPS on spherocylinders, directionally biased cyclic MIPS on spherocones, and position dependent cluster fluctuations on metaballs.
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Affiliation(s)
| | - Sharon C Glotzer
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
- Biointerfaces Institute, University of Michigan, Ann Arbor, MI 48109, USA
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8
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Activity-induced polar patterns of filaments gliding on a sphere. Nat Commun 2022; 13:2579. [PMID: 35546549 PMCID: PMC9095588 DOI: 10.1038/s41467-022-30128-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 04/19/2022] [Indexed: 11/16/2022] Open
Abstract
Active matter systems feature the ability to form collective patterns as observed in a plethora of living systems, from schools of fish to swimming bacteria. While many of these systems move in a wide, three-dimensional environment, several biological systems are confined by a curved topology. The role played by a non-Euclidean geometry on the self-organization of active systems is not yet fully understood, and few experimental systems are available to study it. Here, we introduce an experimental setup in which actin filaments glide on the inner surface of a spherical lipid vesicle, thus embedding them in a curved geometry. We show that filaments self-assemble into polar, elongated structures and that, when these match the size of the spherical geometry, both confinement and topological constraints become relevant for the emergent patterns, leading to the formation of polar vortices and jammed states. These results experimentally demonstrate that activity-induced complex patterns can be shaped by spherical confinement and topology. Active matter exhibits a range of collective behaviors offering insights into how complex patterns can emerge at different length scales. Here, Hsu et al. confine active filaments on the spherical surface of a lipid vesicle and observe the formation of off-equator polar vortices and jammed patterns.
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9
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Klongvessa N, Ybert C, Cottin-Bizonne C, Kawasaki T, Leocmach M. Aging or DEAD: Origin of the non-monotonic response to weak self-propulsion in active glasses. J Chem Phys 2022; 156:154509. [PMID: 35459302 DOI: 10.1063/5.0087578] [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
Among amorphous states, glass is defined by relaxation times longer than the observation time. This nonergodic nature makes the understanding of glassy systems an involved topic, with complex aging effects or responses to further out-of-equilibrium external drivings. In this respect, active glasses made of self-propelled particles have recently emerged as a stimulating systems, which broadens and challenges our current understanding of glasses by considering novel internal out-of-equilibrium degrees of freedom. In previous experimental studies we have shown that in the ergodicity broken phase, the dynamics of dense passive particles first slows down as particles are made slightly active, before speeding up at larger activity. Here, we show that this nonmonotonic behavior also emerges in simulations of soft active Brownian particles and explore its cause. We refute that the deadlock by emergence of active directionality model we proposed earlier describes our data. However, we demonstrate that the nonmonotonic response is due to activity enhanced aging and thus confirm the link with ergodicity breaking. Beyond self-propelled systems, our results suggest that aging in active glasses is not fully understood.
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Affiliation(s)
- Natsuda Klongvessa
- School of Physics, Center of Excellence in Advanced Functional Materials, Institute of Science, Suranaree University of Technology, 3000 Nakhon Ratchasima, Thailand
| | - Christophe Ybert
- Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Cécile Cottin-Bizonne
- Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Takeshi Kawasaki
- Department of Physics, Nagoya University, 464-8602 Nagoya, Japan
| | - Mathieu Leocmach
- Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
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10
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Khelfa B, Korbmacher R, Schadschneider A, Tordeux A. Heterogeneity-induced lane and band formation in self-driven particle systems. Sci Rep 2022; 12:4768. [PMID: 35306506 PMCID: PMC8934355 DOI: 10.1038/s41598-022-08649-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 03/08/2022] [Indexed: 01/23/2023] Open
Abstract
The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and nonuniform patterns. In this article, we investigate the effects of different types of heterogeneity in a two-species self-driven particle system. We show that heterogeneity can generically initiate segregation in the motion and identify two heterogeneity mechanisms. Longitudinal lanes parallel to the direction of motion emerge when the heterogeneity statically lies in the agent characteristics (quenched disorder). While transverse bands orthogonal to the motion direction arise from dynamic heterogeneity in the interactions (annealed disorder). In both cases, non-linear transitions occur as the heterogeneity increases, from disorder to ordered states with lane or band patterns. These generic features are observed for a first and a second order motion model and different characteristic parameters related to particle speed and size. Simulation results show that the collective dynamics occur in relatively short time intervals, persist stationary, and are partly robust against random perturbations.
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11
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Debets VE, de Wit XM, Janssen LMC. Cage Length Controls the Nonmonotonic Dynamics of Active Glassy Matter. PHYSICAL REVIEW LETTERS 2021; 127:278002. [PMID: 35061437 DOI: 10.1103/physrevlett.127.278002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 10/18/2021] [Accepted: 11/23/2021] [Indexed: 06/14/2023]
Abstract
Dense active matter is gaining widespread interest due to its remarkable similarity with conventional glass-forming materials. However, active matter is inherently out of equilibrium and even simple models such as active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs) behave markedly differently from their passive counterparts. Controversially, this difference has been shown to manifest itself via either a speedup, slowdown, or nonmonotonic change of the glassy relaxation dynamics. Here we rationalize these seemingly contrasting views on the departure from equilibrium by identifying the ratio of the short-time length scale to the cage length, i.e., the length scale of local particle caging, as a vital and unifying control parameter for active glassy matter. In particular, we explore the glassy dynamics of both thermal and athermal ABPs and AOUPs upon increasing the persistence time. We find that for all studied systems there is an optimum of the dynamics; this optimum occurs when the cage length coincides with the corresponding short-time length scale of the system, which is either the persistence length for athermal systems or a combination of the persistence length and a diffusive length scale for thermal systems. This new insight, for which we also provide a simple physical argument, allows us to reconcile and explain the manifestly disparate departures from equilibrium reported in many previous studies of dense active materials.
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Affiliation(s)
- Vincent E Debets
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Xander M de Wit
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
| | - Liesbeth M C Janssen
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
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12
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Militaru A, Lasanta A, Frimmer M, Bonilla LL, Novotny L, Rica RA. Kovacs Memory Effect with an Optically Levitated Nanoparticle. PHYSICAL REVIEW LETTERS 2021; 127:130603. [PMID: 34623831 DOI: 10.1103/physrevlett.127.130603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
The understanding of the dynamics of nonequilibrium cooling and heating processes at the nanoscale is still an open problem. These processes can follow surprising relaxation paths due to, e.g., memory effects, which significantly alter the expected equilibration routes. The Kovacs effect can take place when a thermalization process is suddenly interrupted by a change of the bath temperature, leading to a nonmonotonic evolution of the energy of the system. Here, we demonstrate that the Kovacs effect can be observed in the thermalization of the center of mass motion of a levitated nanoparticle. The temperature is controlled during the experiment through an external source of white Gaussian noise that mimics an effective thermal bath at a temperature that can be changed faster than any relaxation time of the system. We describe our experiments in terms of the dynamics of a Brownian particle in a harmonic trap without any fitting parameter, suggesting that the Kovacs effect can appear in a large variety of systems.
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Affiliation(s)
- Andrei Militaru
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n, 51001 Ceuta, Spain
- Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
- Grupo de Matemática Aplicada a la Física de la Materia Condensada, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Ciencias de Materiales de Madrid, CSIC, Spain
- Nanoparticles Trapping Laboratory, Universidad de Granada, 18071 Granada, Spain
| | - Martin Frimmer
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Luis L Bonilla
- Grupo de Matemática Aplicada a la Física de la Materia Condensada, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Ciencias de Materiales de Madrid, CSIC, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Instituto Gregorio Millán, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Raúl A Rica
- Nanoparticles Trapping Laboratory, Universidad de Granada, 18071 Granada, Spain
- Universidad de Granada, Department of Applied Physics and Research Unit "Modeling Nature" (MNat), 18071 Granada, Spain
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13
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Mandal R, Sollich P. Multiple Types of Aging in Active Glasses. PHYSICAL REVIEW LETTERS 2020; 125:218001. [PMID: 33274976 DOI: 10.1103/physrevlett.125.218001] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 10/20/2020] [Indexed: 06/12/2023]
Abstract
Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids. This leads to a fundamental question: how do these nonequilibrium (active) amorphous materials differ from conventional passive glasses, created by lowering temperature or increasing density? To address this we investigate the aging after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behavior of this dense active matter system: short persistence times of the active forcing give effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times and activity-driven aging at late times. We develop a dedicated simulation method that gives access to this longtime scaling regime for highly persistent active forces.
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Affiliation(s)
- Rituparno Mandal
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
- Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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14
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Heckel S, Grauer J, Semmler M, Gemming T, Löwen H, Liebchen B, Simmchen J. Active Assembly of Spheroidal Photocatalytic BiVO 4 Microswimmers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:12473-12480. [PMID: 32825804 DOI: 10.1021/acs.langmuir.0c01568] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We create single-component photocatalytic bismuth vanadate (BiVO4) microswimmers with a spheroidal shape that move individually upon irradiation without any asymmetrization step. These particles form active assemblies which we investigate combining an experimental approach with numerical simulations and analytical calculations. We systematically explore the speed and assembly of the swimmers into clusters of up to four particles and find excellent agreement between experiment and theory, which helps us to understand motion patterns and speed trends. Moreover, different batches of particles can be functionalized separately, making them ideal candidates to fulfill a multitude of tasks, such as sensing or environmental remediation. To exemplify this, we coat our swimmers with silica (SiO2) and selectively couple some of their modules to fluorophores in a way which does not inhibit self-propulsion. The present work establishes spheroidal BiVO4 microswimmers as a versatile platform to design multifunctional microswimmers.
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Affiliation(s)
- Sandra Heckel
- Physical Chemistry, TU Dresden, Zellescher Weg 19, 01069 Dresden, Germany
| | - Jens Grauer
- Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Maria Semmler
- Physical Chemistry, TU Dresden, Zellescher Weg 19, 01069 Dresden, Germany
| | - Thomas Gemming
- Institute of Complex Materials, Leibniz IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
| | - Hartmut Löwen
- Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
| | - Benno Liebchen
- Institute of Condensed Matter Physics, TU Darmstadt, 64289 Darmstadt, Germany
| | - Juliane Simmchen
- Physical Chemistry, TU Dresden, Zellescher Weg 19, 01069 Dresden, Germany
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15
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Herrera P, Apaza L, Sandoval M. One-dimensional displacement of active matter on curved substrates. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1711974] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Pedro Herrera
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
| | - Leonardo Apaza
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City, Mexico
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16
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Hindes J, Edwards V, Kamimoto S, Stantchev G, Schwartz IB. Stability of milling patterns in self-propelled swarms on surfaces. Phys Rev E 2020; 102:022212. [PMID: 32942377 DOI: 10.1103/physreve.102.022212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 07/31/2020] [Indexed: 06/11/2023]
Abstract
In some physical and biological swarms, agents effectively move and interact along curved surfaces. The associated constraints and symmetries can affect collective-motion patterns, but little is known about pattern stability in the presence of surface curvature. To make progress, we construct a general model for self-propelled swarms moving on surfaces using Lagrangian mechanics. We find that the combination of self-propulsion, friction, mutual attraction, and surface curvature produce milling patterns where each agent in a swarm oscillates on a limit cycle with different agents splayed along the cycle such that the swarm's center-of-mass remains stationary. In general, such patterns loose stability when mutual attraction is insufficient to overcome the constraint of curvature, and we uncover two broad classes of stationary milling-state bifurcations. In the first, a spatially periodic mode undergoes a Hopf bifurcation as curvature is increased, which results in unstable spatiotemporal oscillations. This generic bifurcation is analyzed for the sphere and demonstrated numerically for several surfaces. In the second, a saddle-node-of-periodic orbits occurs in which stable and unstable milling states collide and annihilate. The latter is analyzed for milling states on cylindrical surfaces. Our results contribute to the general understanding of swarm pattern formation and stability in the presence of surface curvature and may aid in designing robotic swarms that can be controlled to move over complex surfaces and terrains.
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Affiliation(s)
- Jason Hindes
- U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
| | | | - Sayomi Kamimoto
- Department of Mathematics, George Mason University, Fairfax, Virginia 22030, USA
| | | | - Ira B Schwartz
- U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
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17
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Chakraborty S, Das SK. Relaxation in a phase-separating two-dimensional active matter system with alignment interaction. J Chem Phys 2020; 153:044905. [PMID: 32752724 DOI: 10.1063/5.0010043] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Via computer simulations, we study kinetics of pattern formation in a two-dimensional active matter system. Self-propulsion in our model is incorporated via the Vicsek-like activity, i.e., particles have the tendency of aligning their velocities with the average directions of motion of their neighbors. In addition to this dynamic or active interaction, there exists passive inter-particle interaction in the model for which we have chosen the standard Lennard-Jones form. Following quenches of homogeneous configurations to a point deep inside the region of coexistence between high and low density phases, as the systems exhibit formation and evolution of particle-rich clusters, we investigate properties related to the morphology, growth, and aging. A focus of our study is on the understanding of the effects of structure on growth and aging. To quantify the latter, we use the two-time order-parameter autocorrelation function. This correlation, as well as the growth, is observed to follow power-law time dependence, qualitatively similar to the scaling behavior reported for passive systems. The values of the exponents have been estimated and discussed by comparing with the previously obtained numbers for other dimensions as well as with the new results for the passive limit of the considered model. We have also presented results on the effects of temperature on the activity mediated phase separation.
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Affiliation(s)
- Saikat Chakraborty
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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18
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Ai BQ, Zhou BY, Zhang XM. Binary mixtures of active and passive particles on a sphere. SOFT MATTER 2020; 16:4710-4717. [PMID: 32367106 DOI: 10.1039/d0sm00281j] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the cooperation and segregation dynamics of binary mixtures of active and passive particles on a sphere. According to the competition between rotational diffusion and polar alignment, we find three distinct phases: a mixed phase and two different demixed phases. When rotational diffusion dominates the dynamics, the demixing is due to the aggregation of passive particles, where active and passive particles respectively occupy two hemispheres. When polar alignment is dominated, the demixing is caused by the aggregation of active particles, where active particles occupy the equator of the sphere and passive particles occupy the two poles of the sphere. In this case, there exist a circulating band cluster and two cambered surface clusters, which is a purely curvature-driven effect with no equivalent in the planar model. When rotational diffusion and polar alignment are comparable, particles are completely mixed. Our findings are relevant to the experimental pursuit of segregation dynamics of binary mixtures on curved surfaces.
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Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China.
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19
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Abstract
The glass transition in soft matter systems is generally triggered by an increase in packing fraction or a decrease in temperature. It has been conjectured that the internal topology of the constituent particles, such as polymers, can cause glassiness too. However, the conjecture relies on immobilizing a fraction of the particles and is therefore difficult to fulfill experimentally. Here we show that in dense solutions of circular polymers containing (active) segments of increased mobility, the interplay of the activity and the topology of the polymers generates an unprecedented glassy state of matter. The active isotropic driving enhances mutual ring threading to the extent that the rings can relax only in a cooperative way, which dramatically increases relaxation times. Moreover, the observed phenomena feature similarities with the conformation and dynamics of the DNA fibre in living nuclei of higher eukaryotes.
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Affiliation(s)
- Jan Smrek
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria.
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany.
| | - Iurii Chubak
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria
| | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany
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20
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Janssen LMC. Active glasses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:503002. [PMID: 31469099 DOI: 10.1088/1361-648x/ab3e90] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.
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Affiliation(s)
- Liesbeth M C Janssen
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands
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21
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Ambruş VE, Busuioc S, Wagner AJ, Paillusson F, Kusumaatmaja H. Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach. Phys Rev E 2019; 100:063306. [PMID: 31962535 DOI: 10.1103/physreve.100.063306] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Indexed: 11/07/2022]
Abstract
We develop and implement a finite difference lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. The standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focusing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of the torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our finite difference lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.
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Affiliation(s)
- Victor E Ambruş
- Department of Physics, West University of Timişoara, 300223 Timişoara, Romania
| | - Sergiu Busuioc
- Department of Physics, West University of Timişoara, 300223 Timişoara, Romania
| | - Alexander J Wagner
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108, USA
| | - Fabien Paillusson
- School of Mathematics and Physics, University of Lincoln, Lincoln LN6 7TS, United Kingdom
| | - Halim Kusumaatmaja
- Department of Physics, Durham University, Durham, DH1 3LE, United Kingdom
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22
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23
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Hoell C, Löwen H, Menzel AM. Multi-species dynamical density functional theory for microswimmers: Derivation, orientational ordering, trapping potentials, and shear cells. J Chem Phys 2019. [DOI: 10.1063/1.5099554] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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24
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Szamel G. Mode-coupling theory for the steady-state dynamics of active Brownian particles. J Chem Phys 2019; 150:124901. [PMID: 30927902 DOI: 10.1063/1.5085752] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a many-particle evolution equation for the probability distribution of the particles' positions. Second, we use the projection operator technique and a mode-coupling-like factorization approximation to derive an equation of motion for the density correlation function. The nonequilibrium character of the active system manifests itself through the presence of a steady-state correlation function that quantifies spatial correlations of microscopic steady-state currents of the particles. This function determines the dependence of the short-time dynamics on the activity. It also enters into the expression for the memory matrix and thus influences the long-time glassy dynamics.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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25
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Mathijssen AJTM, Guzmán-Lastra F, Kaiser A, Löwen H. Nutrient Transport Driven by Microbial Active Carpets. PHYSICAL REVIEW LETTERS 2018; 121:248101. [PMID: 30608743 DOI: 10.1103/physrevlett.121.248101] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Indexed: 06/09/2023]
Abstract
We demonstrate that active carpets of bacteria or self-propelled colloids generate coherent flows towards the substrate, and propose that these currents provide efficient pathways to replenish nutrients that feed back into activity. A full theory is developed in terms of gradients in the active matter density and velocity, and applied to bacterial turbulence, topological defects and clustering. Currents with complex spatiotemporal patterns are obtained, which are tunable through confinement. Our findings show that diversity in carpet architecture is essential to maintain biofunctionality.
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Affiliation(s)
- Arnold J T M Mathijssen
- Department of Bioengineering, Stanford University, 443 Via Ortega, Stanford, California 94305, USA
| | - Francisca Guzmán-Lastra
- Facultad de Ciencias, Universidad Mayor, Av. Manuel Montt 367, Providencia, Santiago 7500994, Chile
- Departamento de Física, FCFM Universidad de Chile, Beauchef 850, Santiago 8370448, Chile
| | - Andreas Kaiser
- Department of Biomedical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
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26
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Abstract
We formulate the dynamics of overdamped Brownian active particles (swimmers) moving on any Riemannian 2-manifold. To characterize such dynamics at short times, an analytical expression for the variance of swimmers diffusing on any Riemmanian 2-manifold is derived. To show the generality of the present work, we apply the latter dynamics to swimmers moving on the surface of a spheroid and a torus, and offer analytical expressions for both their long-time variances and steady angular marginal probability density functions. Finally, Brownian dynamics simulations are used to validate our theoretical findings.
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Affiliation(s)
- Leonardo Apaza
- Faculty of Pure and Natural Sciences, Universidad Mayor de San Andres, La Paz, Bolivia
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27
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Allahyarov E, Löwen H. Length segregation in mixtures of spherocylinders induced by imposed topological defects. SOFT MATTER 2018; 14:8962-8973. [PMID: 30375629 DOI: 10.1039/c8sm01790e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We explore length segregation in binary mixtures of spherocylinders of lengths L1 and L2 which are tangentially confined on a spherical surface of radius R. The orientation of the spherocylinders is constrained along an externally imposed direction field on the sphere which is either along the longitude or the latitude lines of the sphere. In both situations, integer orientational defects at the poles are imposed. Using computer simulations we show that these topological defects induce a complex segregation picture also depending on the length ratio factor γ = L2/L1 and the total packing fraction η of the spherocylinders. When the binary mixture is aligned along the longitude lines of the sphere, shorter rods tend to accumulate at the topological defects of the polar caps whereas longer rods occupy the central equatorial area of the spherical surface. In the reverse case of latitude ordering, a new state can emerge where longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. As a reference situation, we consider a defect-free situation in the flat plane and do not find any length segregation there at similar γ and η; hence, the segregation is purely induced by the imposed topological defects. We also develop an Onsager-like density functional theory which is capable of predicting length segregation in ordered mixtures. At low density, the results of this theory are in good agreement with the simulation data.
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Affiliation(s)
- Elshad Allahyarov
- Theoretische Chemie, Universität Duisburg-Essen, D-45141 Essen, Germany
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28
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Pastore R, Uttieri M, Bianco G, Ribera d'Alcalá M, Mazzocchi MG. Distinctive diffusive properties of swimming planktonic copepods in different environmental conditions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:79. [PMID: 29934856 DOI: 10.1140/epje/i2018-11688-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 06/07/2018] [Indexed: 06/08/2023]
Abstract
Suspensions of small planktonic copepods represent a special category in the realm of active matter, as their size falls within the range of colloids, while their motion is so complex that it cannot be rationalized according to basic models of self-propelled particles. Indeed, the wide range of individual variability and swimming patterns resemble the behaviour of much larger animals. By analysing hundreds of three-dimensional trajectories of the planktonic copepod Clausocalanus furcatus, we investigate the possibility of detecting how the motion of this species is affected by different external conditions, such as the presence of food and the effect of gravity. While this goal is hardly achievable by direct inspection of single organism trajectories, we show that this is possible by focussing on simple average metrics commonly used to characterize colloidal suspensions, such as the mean square displacement and the dynamic correlation functions. We find that the presence of food leads to the onset of a clear localization that separates a short-time ballistic from a long-time diffusive regime. Such a benchmark reflects the tendency of C. furcatus to remain temporally feeding in a limited space and disappears when food is absent. Localization is clearly evident in the horizontal plane, but is negligible in the vertical direction, due to the effect of gravity. Our results suggest that simple average descriptors may provide concise and useful information on the swimming properties of planktonic copepods, even though single organism behaviour is strongly heterogeneous.
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Affiliation(s)
- Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, Università di Napoli Federico II, Piazzale V. Tecchio 80, 80125, Napoli, Italy.
- CNR-SPIN, Via Cintia, 80126, Napoli, Italy.
| | - Marco Uttieri
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, 80121, Napoli, Italy
- CoNISMa (Consorzio Nazionale Interuniversitario per le Scienze del Mare), Piazzale Flaminio 9, 00196, Roma, Italy
| | - Giuseppe Bianco
- Department of Biology, Lund University, Sölvegatan 35, 223 62, Lund, Sweden
| | - Maurizio Ribera d'Alcalá
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, 80121, Napoli, Italy
| | - Maria Grazia Mazzocchi
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, 80121, Napoli, Italy
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29
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Praetorius S, Voigt A, Wittkowski R, Löwen H. Active crystals on a sphere. Phys Rev E 2018; 97:052615. [PMID: 29906962 DOI: 10.1103/physreve.97.052615] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Indexed: 06/08/2023]
Abstract
Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a phase-field-crystal-type model that involves a density and a polarization field on the sphere. Depending on the strength of the self-propulsion, three different types of crystals are found: a static crystal, a self-spinning "vortex-vortex" crystal containing two vortical poles of the local velocity, and a self-translating "source-sink" crystal with a source pole where crystallization occurs and a sink pole where the active crystal melts. These different crystalline states as well as their defects are studied theoretically here and can in principle be confirmed in experiments.
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Affiliation(s)
- Simon Praetorius
- Institute for Scientific Computing, Technische Universität Dresden, D-01062 Dresden, Germany
| | - Axel Voigt
- Institute for Scientific Computing, Technische Universität Dresden, D-01062 Dresden, Germany
- Dresden Center for Computational Materials Science (DCMS), D-01062 Dresden, Germany
- Center for Systems Biology Dresden (CSBD), D-01307 Dresden, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Mickelin O, Słomka J, Burns KJ, Lecoanet D, Vasil GM, Faria LM, Dunkel J. Anomalous Chained Turbulence in Actively Driven Flows on Spheres. PHYSICAL REVIEW LETTERS 2018; 120:164503. [PMID: 29756929 DOI: 10.1103/physrevlett.120.164503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Indexed: 06/08/2023]
Abstract
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of antiferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.
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Affiliation(s)
- Oscar Mickelin
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jonasz Słomka
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Keaton J Burns
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Daniel Lecoanet
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Geoffrey M Vasil
- School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Luiz M Faria
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
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Henkes S, Marchetti MC, Sknepnek R. Dynamical patterns in nematic active matter on a sphere. Phys Rev E 2018; 97:042605. [PMID: 29758687 DOI: 10.1103/physreve.97.042605] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Indexed: 01/24/2023]
Abstract
Using simulations of self-propelled agents with short-range repulsion and nematic alignment, we explore the dynamical phases of a dense active nematic confined to the surface of a sphere. We map the nonequilibrium phase diagram as a function of curvature, alignment strength, and activity. Our model reproduces several phases seen in recent experiments on active microtubule bundles confined the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a polar band wrapping around an equator, with large empty spherical caps corresponding to two +1 defects at the poles. Upon further increasing activity, the bands fold onto themselves, and the system eventually transitions to a turbulent state marked by the proliferation of pairs of topological defects. We highlight the key role of the nematic persistence length in controlling pattern formation in these confined systems with positive Gaussian curvature.
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Affiliation(s)
- Silke Henkes
- Institute for Complex Systems and Mathematical Biology, Department of Physics, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - M Cristina Marchetti
- Department of Physics and Soft Matter Program, Syracuse University, Syracuse, New York 13244, USA
| | - Rastko Sknepnek
- School of Sciences and Engineering and School of Life Sciences, University of Dundee, Dundee DD1 4HN, United Kingdom
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Grauer J, Löwen H, Janssen LMC. Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field. Phys Rev E 2018; 97:022608. [PMID: 29548202 DOI: 10.1103/physreve.97.022608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Indexed: 06/08/2023]
Abstract
We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semipermeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation." Our results are gained by computer simulations of self-propelled rod models confined on a two-dimensional planar or spherical surface with a stepwise constant motility field, but the phenomenon should be observable in any geometry with sufficiently large spatial inhomogeneity. We also discuss possibilities to verify our predictions of active-membrane formation in experiments of self-propelled colloidal rods and vibrated granular matter.
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Affiliation(s)
- Jens Grauer
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Liesbeth M C Janssen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, P. O. Box 513, 5600MB Eindhoven, The Netherlands
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33
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Apaza L, Sandoval M. Brownian self-driven particles on the surface of a sphere. Phys Rev E 2017; 96:022606. [PMID: 28950475 DOI: 10.1103/physreve.96.022606] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2017] [Indexed: 11/07/2022]
Abstract
We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.
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Affiliation(s)
- Leonardo Apaza
- Faculty of Pure and Natural Sciences, Universidad Mayor de San Andres, La Paz, Bolivia
| | - Mario Sandoval
- Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico
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