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Khali SS, Peruani F, Chaudhuri D. When an active bath behaves as an equilibrium one. Phys Rev E 2024; 109:024120. [PMID: 38491633 DOI: 10.1103/physreve.109.024120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 01/22/2024] [Indexed: 03/18/2024]
Abstract
Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.
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Affiliation(s)
| | - Fernando Peruani
- LPTM, CY Cergy Paris Université, 2 Avenue A. Chauvin, 95302 Cergy-Pontoise Cedex, France
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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2
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Loewe B, Kozhukhov T, Shendruk TN. Anisotropic run-and-tumble-turn dynamics. Soft Matter 2024; 20:1133-1150. [PMID: 38226730 PMCID: PMC10828927 DOI: 10.1039/d3sm00589e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 12/12/2023] [Indexed: 01/17/2024]
Abstract
Run-and-tumble processes successfully model several living systems. While studies have typically focused on particles with isotropic tumbles, recent examples exhibit "tumble-turns", in which particles undergo 90° tumbles and so possess explicitly anisotropic dynamics. We study the consequences of such tumble-turn anisotropicity at both short and long-time scales. We model run-and-tumble-turn particles as self-propelled particles subjected to an angular potential that favors directions of movement parallel to Cartesian axes. Using agent-based simulations, we study the effects of the interplay between rotational diffusion and an aligning potential on the particles' trajectories, which leads to the right-angled turns. We demonstrate that the long-time effect is to alter the tumble-turn time, which governs the long-time dynamics. In particular, when normalized by this timescale, trajectories become independent of the underlying details of the potential. As such, we develop a simplified continuum theory, which quantitatively agrees with agent-based simulations. We find that the purely diffusive hydrodynamic limit still exhibits anisotropic features at intermediate times and conclude that the transition to diffusive dynamics precedes the transition to isotropic dynamics. By considering short-range repulsive and alignment particle-particle interactions, we show how the anisotropic features of a single particle are inherited by the global order of the system. We hope this work will shed light on how active systems can extend local anisotropic properties to macroscopic scales, which might be important in biological processes occurring in anisotropic environments.
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Affiliation(s)
- Benjamin Loewe
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Timofey Kozhukhov
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Tyler N Shendruk
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
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3
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Bröker S, Te Vrugt M, Jeggle J, Stenhammar J, Wittkowski R. Pair-distribution function of active Brownian spheres in three spatial dimensions: simulation results and analytical representation. Soft Matter 2023; 20:224-244. [PMID: 38078539 DOI: 10.1039/d3sm00987d] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
The pair-distribution function, which provides information about correlations in a system of interacting particles, is one of the key objects of theoretical soft matter physics. In particular, it allows for microscopic insights into the phase behavior of active particles. While this function is by now well studied for two-dimensional active matter systems, the more complex and more realistic case of three-dimensional systems is not well understood by now. In this work, we analyze the full pair-distribution function of spherical active Brownian particles interacting via a Weeks-Chandler-Andersen potential in three spatial dimensions using Brownian dynamics simulations. Besides extracting the structure of the pair-distribution function from the simulations, we obtain an analytical representation for this function, parametrized by activity and concentration, which takes into account the symmetries of a homogeneous stationary state. Our results are useful as input to quantitative models of active Brownian particles and advance our understanding of the microstructure in dense active fluids.
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Affiliation(s)
- Stephan Bröker
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany.
| | - Michael Te Vrugt
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany.
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK
| | - Julian Jeggle
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany.
| | - Joakim Stenhammar
- Division of Physical Chemistry, Lund University, 221 00 Lund, Sweden
| | - Raphael Wittkowski
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany.
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Bröker S, Bickmann J, Te Vrugt M, Cates ME, Wittkowski R. Orientation-Dependent Propulsion of Active Brownian Spheres: From Self-Advection to Programmable Cluster Shapes. Phys Rev Lett 2023; 131:168203. [PMID: 37925724 DOI: 10.1103/physrevlett.131.168203] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 08/25/2023] [Indexed: 11/07/2023]
Abstract
Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the particles, become increasingly popular. In this Letter, we investigate systems of interacting active Brownian spheres in two spatial dimensions with orientation-dependent propulsion using analytical modeling and Brownian dynamics simulations. It is found that the orientation dependence leads to self-advection, circulating currents, and programmable cluster shapes.
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Affiliation(s)
- Stephan Bröker
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Jens Bickmann
- 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
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Abstract
In this work, the free expansion of an inertial active gas in three dimensions made of spherical non-interactive active Brownian particles with both translational and rotational inertia (IABPs) is studied. After elucidating the active particles' orientational correlation in three dimensions by employing a Fokker-Planck formalism, the diffusion, mean-square speed, persistence length, reorientation time, Swim and Reynolds pressures and total pressure of this system, are obtained theoretically and corroborated by performing Langevin dynamics simulations. Afterwards, a numerical study on particles' distribution and the mechanical pressure exerted by the active gas enclosed in a cubic box and its dependence on inertia is also carried out. This experiment highlights two important observations: first, as inertia in the system grows while fixing activity, a more uniform particle distribution within the box is achieved. In other words, the classical accumulation of active particles at the walls is seen to be suppressed by inertia. Second, an active gas with translational and rotational inertiae and made of spherical particles still has a state equation which is offered here. This is supported by the fact that both the mechanical pressure definition and the bulk pressure definition as the trace of the swim and Reynolds stress tensors, coincide in the thermodynamic limit.
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Affiliation(s)
- Mario Sandoval
- Department of Physics, Complex Systems, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico.
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Paul K, Mutneja A, Nandi SK, Karmakar S. Dynamical heterogeneity in active glasses is inherently different from its equilibrium behavior. Proc Natl Acad Sci U S A 2023; 120:e2217073120. [PMID: 37585467 PMCID: PMC10450852 DOI: 10.1073/pnas.2217073120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 07/12/2023] [Indexed: 08/18/2023] Open
Abstract
Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc., also extends the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, [Formula: see text]. Here, we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a [Formula: see text], effects of activity on the dynamic heterogeneity (DH), which is a hallmark of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows that active glasses exhibit dramatic growth of DH and systems with similar relaxation times, and thus, [Formula: see text] can have widely varying DH. To theoretically study DH, we extend active MCT and find good qualitative agreement between the theory and simulation results. Our results pave avenues for understanding the role of DH in glassy dynamics and can have fundamental significance even in equilibrium.
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Affiliation(s)
- Kallol Paul
- Tata Institute of Fundamental Research Center for Interdisciplinary Science, Hyderabad500046, Telangana, India
| | - Anoop Mutneja
- Tata Institute of Fundamental Research Center for Interdisciplinary Science, Hyderabad500046, Telangana, India
| | - Saroj Kumar Nandi
- Tata Institute of Fundamental Research Center for Interdisciplinary Science, Hyderabad500046, Telangana, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research Center for Interdisciplinary Science, Hyderabad500046, Telangana, India
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Wittmann R, Monderkamp PA, Löwen H. Statistics of carrier-cargo complexes. Phys Rev E 2023; 107:064602. [PMID: 37464670 DOI: 10.1103/physreve.107.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 05/17/2023] [Indexed: 07/20/2023]
Abstract
We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.
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Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Paul A Monderkamp
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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Schmitz GJ, te Vrugt M, Haug-Warberg T, Ellingsen L, Needham P, Wittkowski R. Thermodynamics of an Empty Box. Entropy (Basel) 2023; 25:315. [PMID: 36832681 PMCID: PMC9955345 DOI: 10.3390/e25020315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 01/15/2023] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.
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Affiliation(s)
- Georg J. Schmitz
- MICRESS Group, ACCESS e.V., Intzestr. 5, D-52072 Aachen, Germany
| | - Michael te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
| | - Tore Haug-Warberg
- Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway
| | - Lodin Ellingsen
- Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway
| | - Paul Needham
- Department of Philosophy, University of Stockholm, SE-106 91 Stockholm, Sweden
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
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