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Knippenberg T, Jayaram A, Speck T, Bechinger C. Motility-Induced Clustering of Active Particles under Soft Confinement. PHYSICAL REVIEW LETTERS 2024; 133:048301. [PMID: 39121427 DOI: 10.1103/physrevlett.133.048301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 06/26/2024] [Indexed: 08/11/2024]
Abstract
We investigate the structural and dynamic properties of active Brownian particles (APs) confined within a soft annulus-shaped channel. Depending on the strength of the confinement and the Péclet number, we observe a novel reentrant behavior that is not present in unconfined systems. Our findings are substantiated by numerical simulations and analytical considerations, revealing that this behavior arises from the strong coupling between the Péclet number and the effective confining dimensionality of the APs. Our work highlights the peculiarities of soft boundaries for APs and how clogging can be avoided under such conditions.
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2
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Mangeat M, Chakraborty S, Wysocki A, Rieger H. Stationary particle currents in sedimenting active matter wetting a wall. Phys Rev E 2024; 109:014616. [PMID: 38366426 DOI: 10.1103/physreve.109.014616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
Recently it was predicted, on the basis of a lattice gas model, that scalar active matter in a gravitational field would rise against gravity up a confining wall or inside a thin capillary-in spite of repulsive particle-wall interactions [Phys. Rev. Lett. 124, 048001 (2020)0031-900710.1103/PhysRevLett.124.048001]. In this paper we confirm this prediction with sedimenting active Brownian particles (ABPs) in a box numerically and elucidate the mechanism leading to the formation of a meniscus rising above the bulk of the sedimentation region. The height of the meniscus increases with the activity of the system, algebraically with the Péclet number. The formation of the meniscus is determined by a stationary circular particle current, a vortex, centered at the base of the meniscus, whose size and strength increase with the ABP activity. The origin of these vortices can be traced back to the confinement of the ABPs in a box: already the stationary state of ideal (noninteracting) ABPs without gravitation displays circular currents that arrange in a highly symmetric way in the eight octants of the box. Gravitation distorts this vortex configuration downward, leaving two major vortices at the two side walls, with a strong downward flow along the walls. Repulsive interactions between the ABPs change this situation only as soon as motility induced phase separation (MIPS) sets in and forms a dense, sedimented liquid region at the bottom, which pushes the center of the vortex upwards towards the liquid-gas interface. Self-propelled particles therefore represent an impressive realization of scalar active matter that forms stationary particle currents being able to perform visible work against gravity or any other external field, which we predict to be observable experimentally in active colloids under gravitation.
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Affiliation(s)
- Matthieu Mangeat
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
| | - Shauri Chakraborty
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
| | - Adam Wysocki
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
| | - Heiko Rieger
- Center for Biophysics & Department for Theoretical Physics, Saarland University, D-66123 Saarbrücken, Germany
- INM - Leibniz Institute for New Materials, Campus D2 2, D-66123 Saarbrücken, Germany
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3
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Bickmann J, Bröker S, Te Vrugt M, Wittkowski R. Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns. Phys Rev E 2023; 108:044601. [PMID: 37978644 DOI: 10.1103/physreve.108.044601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 08/24/2023] [Indexed: 11/19/2023]
Abstract
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.
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Affiliation(s)
- Jens Bickmann
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Stephan Bröker
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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Di Trapani F, Franosch T, Caraglio M. Active Brownian particles in a circular disk with an absorbing boundary. Phys Rev E 2023; 107:064123. [PMID: 37464643 DOI: 10.1103/physreve.107.064123] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 04/27/2023] [Indexed: 07/20/2023]
Abstract
We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a circular region with an absorbing boundary. Using the passive Brownian particle as basis states and dealing with the activity as a perturbation, we provide a matrix representation of the Fokker-Planck operator and we express the propagator in terms of the perturbed eigenvalues and eigenfunctions. Alternatively, we show that the propagator can be expressed as a combination of the equilibrium eigenstates with weights depending only on time and on the initial conditions, and obeying exact iterative relations. Our solution allows also obtaining the survival probability and the first-passage time distribution. These latter quantities exhibit peculiarities induced by the nonequilibrium character of the dynamics; in particular, they display a strong dependence on the activity of the particle and, to a less extent, also on its rotational diffusivity.
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Affiliation(s)
- Francesco Di Trapani
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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Caraglio M, Franosch T. Analytic Solution of an Active Brownian Particle in a Harmonic Well. PHYSICAL REVIEW LETTERS 2022; 129:158001. [PMID: 36269953 DOI: 10.1103/physrevlett.129.158001] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the Fokker-Planck operator becomes lower diagonal, implying that the eigenvalues are unaffected by the activity. The propagator is then expressed as a combination of the equilibrium eigenstates with weights obeying exact iterative relations. We show that for the low-order correlation functions, such as the positional autocorrelation function, the recursion terminates at finite order in the Péclet number, allowing us to generate exact compact expressions and derive the velocity autocorrelation function and the time-dependent diffusion coefficient. The nonmonotonic behavior of latter quantities serves as a fingerprint of the nonequilibrium dynamics.
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Affiliation(s)
- Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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Hermann S, Schmidt M. Why Noether's theorem applies to statistical mechanics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:213001. [PMID: 35255482 DOI: 10.1088/1361-648x/ac5b47] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
Noether's theorem is familiar to most physicists due its fundamental role in linking the existence of conservation laws to the underlying symmetries of a physical system. Typically the systems are described in the particle-based context of classical mechanics or on the basis of field theory. We have recently shown (2021Commun. Phys.4176) that Noether's reasoning also applies to thermal systems, where fluctuations are paramount and one aims for a statistical mechanical description. Here we give a pedagogical introduction based on the canonical ensemble and apply it explicitly to ideal sedimentation. The relevant mathematical objects, such as the free energy, are viewed as functionals. This vantage point allows for systematic functional differentiation and the resulting identities express properties of both macroscopic average forces and molecularly resolved correlations in many-body systems, both in and out-of-equilibrium, and for active Brownian particles. To provide further background, we briefly describe the variational principles of classical density functional theory, of power functional theory, and of classical mechanics.
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Affiliation(s)
- Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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Vachier J, Wettlaufer JS. Premelting controlled active matter in ice. Phys Rev E 2022; 105:024601. [PMID: 35291135 DOI: 10.1103/physreve.105.024601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Accepted: 01/14/2022] [Indexed: 06/14/2023]
Abstract
Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.
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Affiliation(s)
- Jérémy Vachier
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
| | - J S Wettlaufer
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
- Yale University, New Haven, Connecticut 06520-8109, USA
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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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Hermann S, de las Heras D, Schmidt M. Phase separation of active Brownian particles in two dimensions: anything for a quiet life. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1902585] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany
| | - Daniel de las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany
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10
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Abstract
AbstractUsing Brownian dynamics simulations, we investigate the response to shear of a two-dimensional system of quasi-hard disks that are confined in the velocity gradient direction by a smooth external potential. Shearing the confined system leads to a homogenization of the one-body density profile. In order to rationalize this deconfinement effect, we split the internal one-body force field into adiabatic and superadiabatic contributions. We demonstrate that the superadiabatic force field consists of viscous and of structural contributions. We give an empirical scaling law that yields results for the superadiabatic force profiles both in the flow and in the gradient direction, in excellent agreement with the simulation data.
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11
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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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12
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Krinninger P, Schmidt M. Power functional theory for active Brownian particles: General formulation and power sum rules. J Chem Phys 2019; 150:074112. [DOI: 10.1063/1.5061764] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Philip Krinninger
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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13
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Fischer A, Chatterjee A, Speck T. Aggregation and sedimentation of active Brownian particles at constant affinity. J Chem Phys 2019; 150:064910. [PMID: 30769983 DOI: 10.1063/1.5081115] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Andreas Fischer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
- Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Arkya Chatterjee
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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Vachier J, Mazza MG. Dynamics of sedimenting active Brownian particles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:11. [PMID: 30687883 DOI: 10.1140/epje/i2019-11770-6] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2018] [Accepted: 01/04/2019] [Indexed: 06/09/2023]
Abstract
We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker-Planck equation for the stochastic process which allows us to describe the dynamics of one active Brownian particle in three dimensions. We address the time evolution of the density, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collective motion. These results qualitatively agree with our model. Finally, we compare our results with experiments (J. Palacci et al., Phys. Rev. Lett. 105, 088304 (2010)) and find very good agreement.
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Affiliation(s)
- Jérémy Vachier
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany
| | - Marco G Mazza
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077, Göttingen, Germany.
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, LE11 3TU, Loughborough, Leicestershire, UK.
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Rodenburg J, Paliwal S, de Jager M, Bolhuis PG, Dijkstra M, van Roij R. Ratchet-induced variations in bulk states of an active ideal gas. J Chem Phys 2018; 149:174910. [DOI: 10.1063/1.5048698] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jeroen Rodenburg
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Siddharth Paliwal
- Soft Condensed Matter Group, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Marjolein de Jager
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Peter G. Bolhuis
- Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter Group, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - René van Roij
- Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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