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Farago O, Smith NR. Confined run-and-tumble particles with non-Markovian tumbling statistics. Phys Rev E 2024; 109:044121. [PMID: 38755884 DOI: 10.1103/physreve.109.044121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2024] [Accepted: 03/20/2024] [Indexed: 05/18/2024]
Abstract
Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution g(t) of waiting times between tumbling events whose mean value is equal to τ. Unless g(t) is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviation and/or small-τ regime, where the SSD can be related to the the large-deviation function, s(x), via the scaling relation P_{st}(x)∼e^{-s(x)/τ}.
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Affiliation(s)
- Oded Farago
- Department of Biomedical Engineering, Ben-Gurion University of the Negev, Marcus Family Campus, Be'er Sheva 8410501, Israel
| | - Naftali R Smith
- Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Be'er Sheva 8499000, Israel
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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] [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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Kurzthaler C, Zhao Y, Zhou N, Schwarz-Linek J, Devailly C, Arlt J, Huang JD, Poon WCK, Franosch T, Tailleur J, Martinez VA. Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli. PHYSICAL REVIEW LETTERS 2024; 132:038302. [PMID: 38307047 DOI: 10.1103/physrevlett.132.038302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 11/29/2023] [Accepted: 12/01/2023] [Indexed: 02/04/2024]
Abstract
We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.
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Affiliation(s)
- Christina Kurzthaler
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Center for Systems Biology Dresden, 01307 Dresden, Germany
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Yongfeng Zhao
- Center for Soft Condensed Matter Physics and Interdisciplinary Research and School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- School of Biomedical Sciences, Li Ka Shing Faculty of Medicine, University of Hong Kong, Pok Fu Lam, Hong Kong, China
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Nan Zhou
- ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 311200, China
| | - Jana Schwarz-Linek
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Clemence Devailly
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Jochen Arlt
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Jian-Dong Huang
- School of Biomedical Sciences, Li Ka Shing Faculty of Medicine, University of Hong Kong, Pok Fu Lam, Hong Kong, China
- CAS Key Laboratory of Quantitative Engineering Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Wilson C K Poon
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Julien Tailleur
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
| | - Vincent A Martinez
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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4
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Smith NR. Nonequilibrium steady state of trapped active particles. Phys Rev E 2023; 108:L022602. [PMID: 37723780 DOI: 10.1103/physreve.108.l022602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 07/26/2023] [Indexed: 09/20/2023]
Abstract
We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle, etc.), that is confined by an external potential. Focusing on the limit in which the correlation time τ of the active noise is small, we find the nonequilibrium steady-state distribution P_{st}(X) of the particle's position X. While typical fluctuations of X follow a Boltzmann distribution with an effective temperature that is not difficult to find, the tails of P_{st}(X) deviate from a Boltzmann behavior: In the limit τ→0, they scale as P_{st}(X)∼e^{-s(X)/τ}. We calculate the large-deviation function s(X) exactly for arbitrary trapping potential and active noise in dimension d=1, by relating it to the rate function that describes large deviations of the position of the same active particle in absence of an external potential at long times. We then extend our results to d>1 assuming rotational symmetry.
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Affiliation(s)
- Naftali R Smith
- Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel
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5
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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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Liu W, Zhu Y, Li Y, Han J, Ngai T. Unveiling the structural relaxation of microgel suspensions at hydrophilic and hydrophobic interfaces. J Colloid Interface Sci 2023; 633:948-958. [PMID: 36509038 DOI: 10.1016/j.jcis.2022.11.150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Revised: 11/24/2022] [Accepted: 11/29/2022] [Indexed: 12/12/2022]
Abstract
HYPOTHESIS Poly(N-isopropylacrylamide) (PNIPAM) microgel particles show considerable hydrophilicity below the lower critical solution temperature (LCST) while they become hydrophobic above LCST. We hypothesize that interfacial wettability could tune particle-surface interaction and subsequent structural relaxation of microgel suspensions at interfaces during the volume phase transition. EXPERIMENTS The evanescent-wave scattering images of microgels at hydrophilic and hydrophobic interfaces are analyzed by a density-fluctuation autocorrelation function (δACF) over a wide range of particle volume fraction ϕ. The structural relaxation is characterized by the decay behavior of δACF. The scattering images in bulk are also processed as a comparison. FINDINGS A two-step relaxation decay is observed at both hydrophilic and hydrophobic interfaces. Relative to fast decay, the rate of structural relaxation in slow decay is reduced by a factor of ∼ 500 and ∼ 50 at hydrophilic and hydrophobic interfaces, respectively. The relaxation times obey divergent power-law dependences on intermediate regime of observing length scales at the two interfaces. Besides, the distribution of fluctuation for relaxation time at different local regions reveals that the structural relaxation is much more homogenous at hydrophilic interfaces than that at hydrophobic interfaces, especially at high ϕ.
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Affiliation(s)
- Wei Liu
- The Key Laboratory of Synthetic and Biological Colloids, Ministry of Education & School of Chemical and Material Engineering, Jiangnan University, Wuxi 214122, China
| | - Yuwei Zhu
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Yinan Li
- Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Jie Han
- School of Science and Technology, Hong Kong Metropolitan University, Homantin, Kowloon, Hong Kong, China.
| | - To Ngai
- The Key Laboratory of Synthetic and Biological Colloids, Ministry of Education & School of Chemical and Material Engineering, Jiangnan University, Wuxi 214122, China; Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China.
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7
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Alexandre A, Lavaud M, Fares N, Millan E, Louyer Y, Salez T, Amarouchene Y, Guérin T, Dean DS. Non-Gaussian Diffusion Near Surfaces. PHYSICAL REVIEW LETTERS 2023; 130:077101. [PMID: 36867824 DOI: 10.1103/physrevlett.130.077101] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.
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Affiliation(s)
- Arthur Alexandre
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Maxime Lavaud
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Nicolas Fares
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Department of Physics, Ecole Normale Supérieure de Lyon, 69364 Lyon, France
| | - Elodie Millan
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Yann Louyer
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Thomas Salez
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | | | - Thomas Guérin
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - David S Dean
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Université de Bordeaux, F-33400 Talence, France
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8
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Yadav RS, Das C, Chakrabarti R. Dynamics of a spherical self-propelled tracer in a polymeric medium: interplay of self-propulsion, stickiness, and crowding. SOFT MATTER 2023; 19:689-700. [PMID: 36598025 DOI: 10.1039/d2sm01626e] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity (self-propulsion) brings additional complexity to the tracer dynamics. Our simulations show that on increasing the stickiness of the tracer particle to the polymer beads, the dynamics of the tracer particle slows down as it gets stuck to the polymer chain and moves along with it. But with increasing self-propulsion velocity, the dynamics gets enhanced. In the case of increasing stickiness as well as activity, the non-Gaussian parameter (NGP) exhibits non-monotonic behavior, which also shows up in the re-scaled self part of the van-Hove function. Non-Gaussianity results owing to the enhanced binding events and the sticky motion of the tracer along with the chain with increasing stickiness. On the other hand, with increasing activity, initially non-Gaussianity increases as the tracer moves through the heterogeneous polymeric environment but for higher activity, the tracer escapes resulting in a negative NGP. For higher values of stickiness, the trapping time distributions of the passive tracer particle broaden and have long tails. On the other hand, for a given stickiness with increasing self-propulsion force, the trapping time distributions become narrower and have short tails. We believe that our current simulation study will be helpful in elucidating the complex motion of activity-driven probes in viscoelastic media.
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Affiliation(s)
- Ramanand Singh Yadav
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Chintu Das
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
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9
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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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10
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Chepizhko O, Franosch T. Resonant Diffusion of a Gravitactic Circle Swimmer. PHYSICAL REVIEW LETTERS 2022; 129:228003. [PMID: 36493425 DOI: 10.1103/physrevlett.129.228003] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Revised: 08/16/2022] [Accepted: 10/07/2022] [Indexed: 06/17/2023]
Abstract
We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.
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Affiliation(s)
- Oleksandr Chepizhko
- 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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11
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Smith NR, Le Doussal P, Majumdar SN, Schehr G. Exact position distribution of a harmonically confined run-and-tumble particle in two dimensions. Phys Rev E 2022; 106:054133. [PMID: 36559430 DOI: 10.1103/physreve.106.054133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2022] [Accepted: 10/21/2022] [Indexed: 11/16/2022]
Abstract
We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion in an orientation that stochastically rotates by 90^{∘} at a constant rate, clockwise or counterclockwise with equal probabilities. In addition, the particle is confined by an external harmonic potential of stiffness μ, and possibly diffuses. We find the exact time-dependent distribution P(x,y,t) of the particle's position, and in particular, the steady-state distribution P_{st}(x,y) that is reached in the long-time limit. We also find P(x,y,t) for a "free" particle, μ=0. We achieve this by showing that, under a proper change of coordinates, the problem decomposes into two statistically independent one-dimensional problems, whose exact solution has recently been obtained. We then extend these results in several directions, to two such run-and-tumble particles with a harmonic interaction, to analogous systems of dimension three or higher, and by allowing stochastic resetting.
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Affiliation(s)
- Naftali R Smith
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel
| | - Pierre Le Doussal
- Laboratoire de Physique de l'Ecole Normale Supérieure, CNRS, ENS and Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
| | | | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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12
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Gomez-Solano JR, Rodríguez RF, Salinas-Rodríguez E. Nonequilibrium dynamical structure factor of a dilute suspension of active particles in a viscoelastic fluid. Phys Rev E 2022; 106:054602. [PMID: 36559383 DOI: 10.1103/physreve.106.054602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 10/11/2022] [Indexed: 11/06/2022]
Abstract
In this work we investigate the dynamics of the number-density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equations for the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function. For a Maxwell-type rheological model, we find an intricate dependence of these functions on the parameters that characterize the viscoelasticity of the solvent and the activity of the particles, which can significantly deviate from those of an inert suspension of passive particles and of an active suspension in a Newtonian solvent. In particular, in some regions of the parameter space we uncover the emergence of oscillations in the intermediate scattering function at certain wave numbers which represent the hallmark of the nonequilibrium particle activity in the dynamical structure of the suspension and also encode the viscoelastic properties of the medium.
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Affiliation(s)
- Juan Ruben Gomez-Solano
- Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México, Código Postal 04510, Mexico
| | - Rosalío F Rodríguez
- Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México, Código Postal 04510, Mexico.,FENOMEC, Universidad Nacional Autónoma de México, Apdo. Postal 20-726, 01000 Ciudad de México, Mexico
| | - Elizabeth Salinas-Rodríguez
- Departamento I. P. H., Universidad Autónoma Metropolitana, Iztapalapa, Apdo. Postal 55-534, 09340 Ciudad de México, Mexico
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13
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Breoni D, Schwarzendahl FJ, Blossey R, Löwen H. A one-dimensional three-state run-and-tumble model with a 'cell cycle'. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:83. [PMID: 36258055 PMCID: PMC9579107 DOI: 10.1140/epje/s10189-022-00238-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 10/10/2022] [Indexed: 06/16/2023]
Abstract
We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling [Formula: see text] at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.
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Affiliation(s)
- Davide Breoni
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany.
| | - Fabian Jan Schwarzendahl
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
| | - Ralf Blossey
- Unité de Glycobiologie Structurale et Fonctionnelle (UGSF), CNRS UMR8576, University of Lille, 59000, Lille, France
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
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14
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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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15
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Thiffeault JL, Guo J. Anisotropic active Brownian particle with a fluctuating propulsion force. Phys Rev E 2022; 106:L012603. [PMID: 35974529 DOI: 10.1103/physreve.106.l012603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
The active Brownian particle (ABP) model describes a swimmer, synthetic or living, whose direction of swimming is a Brownian motion. The swimming is due to a propulsion force, and the fluctuations are typically thermal in origin. We present a two-dimensional model where the fluctuations arise from nonthermal noise in a propelling force acting at a single point, such as that due to a flagellum. We take the overdamped limit and find several modifications to the traditional ABP model. Since the fluctuating force causes a fluctuating torque, the diffusion tensor describing the process has a coupling between translational and rotational degrees of freedom. An anisotropic particle also exhibits a mass-dependent noise-induced drift, which does not disappear in the overdamped limit. We show that these effects have measurable consequences for the long-time diffusivity of active particles, in particular adding a contribution that is independent of where the force acts.
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Affiliation(s)
- Jean-Luc Thiffeault
- Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Jiajia Guo
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
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16
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Shee A, Chaudhuri D. Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement. Phys Rev E 2022; 105:054148. [PMID: 35706212 DOI: 10.1103/physreve.105.054148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 05/02/2022] [Indexed: 06/15/2023]
Abstract
We consider the influence of active speed fluctuations on the dynamics of a d-dimensional active Brownian particle performing a persistent stochastic motion. The speed fluctuation brings about a dynamical anisotropy even in the absence of shape anisotropy. We use the Laplace transform of the Fokker-Planck equation to obtain exact expressions for time-dependent dynamical moments. Our results agree with direct numerical simulations and show several dynamical crossovers determined by the activity, persistence, and speed fluctuation. The dynamical anisotropy leads to a subdiffusive scaling in the parallel component of displacement fluctuation at intermediate times. The kurtosis remains positive at short times determined by the speed fluctuation, crossing over to a negative minimum at intermediate times governed by the persistence before vanishing asymptotically. The probability distribution of particle displacement obtained from numerical simulations in two dimensions shows two crossovers between compact and extended trajectories via two bimodal distributions at intervening times. While the speed fluctuation dominates the first crossover, the second crossover is controlled by persistence like in the wormlike chain model of semiflexible polymers.
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Affiliation(s)
- Amir Shee
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India and Homi Bhaba National Institute, Anushaktinagar, Mumbai 400094, India
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India and Homi Bhaba National Institute, Anushaktinagar, Mumbai 400094, India
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17
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Mondal S, Ghanta KP, Bandyopadhyay S. Dynamic Heterogeneity at the Interface of an Intrinsically Disordered Peptide. J Chem Inf Model 2022; 62:1942-1955. [PMID: 35384652 DOI: 10.1021/acs.jcim.2c00019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
It is believed that water around an intrinsically disordered protein or peptide (IDP) in an aqueous environment plays an important role in guiding its conformational properties and aggregation behavior. However, despite its importance, only a handful of studies exploring the correlation between the conformational motions of an IDP and the microscopic properties of water at its surface are reported. Attempts have been made in this work to study the dynamic properties of water present in the vicinity of α-synuclein, an IDP associated with Parkinson's disease (PD). Room temperature molecular dynamics (MD) simulations of eight α-synuclein1-95 peptides with a wide range of initial conformations have been carried out in aqueous media. The calculations revealed that due to solid-like caging motions, the translational and rotational mobility of water molecules near the surfaces of the peptide repeat unit segments R1 to R7 are significantly restricted. A small degree of dynamic heterogeneity in the hydration environment around the repeat units has been observed with water near the hydrophobic R6 unit exhibiting relatively more restricted diffusivity. The time scales involving the overall structural relaxations of peptide-water and water-water hydrogen bonds near the peptide have been found to be correlated with the time scale of diffusion of the interfacial water molecules. We believe that the relatively more hindered dynamic environment near R6 can help create water-mediated contacts centered around R6 between peptide monomers at a higher concentration, thereby enhancing the early stages of peptide aggregation.
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Affiliation(s)
- Souvik Mondal
- Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
| | - Krishna Prasad Ghanta
- Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
| | - Sanjoy Bandyopadhyay
- Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
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18
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Ryabov A, Tasinkevych M. Enhanced diffusivity in microscopically reversible active matter. SOFT MATTER 2022; 18:3234-3240. [PMID: 35388861 DOI: 10.1039/d2sm00054g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments have focused on the motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of the possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns the origins of the reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering self-propulsion and demonstrate that MR can lead to an increase of the particle mobility and of the short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Furthermore, the derived diffusion coefficients are enhanced due to the action of an external force. These results can shed new light on interpretations of the measured diffusivities and help to test the relevance of MR for the active motion of individual nanoswimmers.
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Affiliation(s)
- Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic.
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
| | - Mykola Tasinkevych
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK.
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19
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Rizkallah P, Sarracino A, Bénichou O, Illien P. Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment. PHYSICAL REVIEW LETTERS 2022; 128:038001. [PMID: 35119883 DOI: 10.1103/physrevlett.128.038001] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.
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Affiliation(s)
- Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Dipartimento di Ingegneria, Università della Campania "Luigi Vanvitelli", 81031 Aversa (CE), Italy
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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20
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Klett K, Cherstvy AG, Shin J, Sokolov IM, Metzler R. Non-Gaussian, transiently anomalous, and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: Coupled translational and rotational motions. Phys Rev E 2022; 104:064603. [PMID: 35030844 DOI: 10.1103/physreve.104.064603] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 11/18/2021] [Indexed: 12/22/2022]
Abstract
We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction ϕ and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on ϕ, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing ϕ. We also analyze the relative motion in the dimers, finding that larger ϕ suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(ϕ) of translational and rotational motion of the dumbbells an exponential decay with ϕ for weak and a power-law variation D(ϕ)∝(ϕ-ϕ^{★})^{2.4} for strong crowding is found. A comparison of simulation results with theoretical predictions for D(ϕ) is discussed and some relevant experimental systems are overviewed.
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Affiliation(s)
- Kolja Klett
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Andrey G Cherstvy
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.,IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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21
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Ma Z, Ni R. Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles. J Chem Phys 2022; 156:021102. [PMID: 35032980 DOI: 10.1063/5.0077389] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
One of the most intriguing phenomena in active matter has been the gas-liquid-like motility-induced phase separation (MIPS) observed in repulsive active particles. However, experimentally, no particle can be a perfect sphere, and the asymmetric shape, mass distribution, or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The nonvanishing current in non-equilibrium steady states microscopically originates from the motility "relieved" by automatic rotation, which breaks the detailed balance at the continuum level. This suggests that no equilibrium-like phase separation theory can be constructed for chiral active colloids even with tiny active torque, in which no visible collective motion exists. This mechanism also sheds light on the understanding of dynamic clusters observed in a variety of active matter systems.
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Affiliation(s)
- Zhan Ma
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459, Singapore
| | - Ran Ni
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459, Singapore
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22
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Clopés Llahí J, Martín-Gómez A, Gompper G, Winkler RG. Simulating wet active polymers by multiparticle collision dynamics. Phys Rev E 2022; 105:015310. [PMID: 35193189 DOI: 10.1103/physreve.105.015310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
The conformational and dynamical properties of active Brownian polymers embedded in a fluid depend on the nature of the driving mechanism, e.g., self-propulsion or external actuation of the monomers. Implementations of self-propelled and actuated active Brownian polymers in a multiparticle collision (MPC) dynamics fluid are presented, which capture the distinct differences between the two driving mechanisms. The active force-free nature of self-propelled monomers requires adaptations of the MPC simulation scheme, with its streaming and collision steps, where the monomer self-propulsion velocity has to be omitted in the collision step. Comparison of MPC simulation results for active polymers in dilute solution with results of Brownian dynamics simulations accounting for hydrodynamics via the Rotne-Prager-Yamakawa tensor confirm the suitability of the implementation. The polymer conformational and dynamical properties are analyzed by the static and dynamic structure factor, and the scaling behavior of the latter with respect to the wave number and time dependence are discussed. The dynamic structure factor displays various activity-induced temporal regimes, depending on the considered wave number, which reflect the persistent diffusive motion of the whole polymer at small wave numbers, and the activity-enhanced internal dynamics at large wave numbers. The obtained simulation results are compared with theoretical predictions.
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Affiliation(s)
- Judit Clopés Llahí
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Aitor Martín-Gómez
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gerhard Gompper
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Roland G Winkler
- Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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23
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Sevilla FJ, Castro-Villarreal P. Generalized persistence dynamics for active motion. Phys Rev E 2021; 104:064601. [PMID: 35030873 DOI: 10.1103/physreve.104.064601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Accepted: 11/18/2021] [Indexed: 06/14/2023]
Abstract
We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, persistence, in arbitrary spatial dimensions. Such a framework allows the development of a Smoluchowski-like equation for the probability density of finding a particle at a given position and time, without assuming an explicit orientational dynamics of the self-propelling velocity as Langevin-like equation-based models do. Also, the Brownian motion due to thermal fluctuations and the active one due to a general intrinsic persistent motion of the particle are taken into consideration on an equal footing. The persistence of motion is introduced in our formalism in the form of a two-time memory function, K(t,t^{'}). We focus on the consequences when K(t,t^{'})∼(t/t^{'})^{-η}exp[-Γ(t-t^{'})], Γ being the characteristic persistence time, and show that it precisely describes a variety of active motion patterns characterized by η. We find analytical expressions for the experimentally obtainable intermediate scattering function, the time dependence of the mean-squared displacement, and the kurtosis.
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Affiliation(s)
- Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
| | - Pavel Castro-Villarreal
- Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, 29050 Tuxtla Gutiérrez, Chiapas, México
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24
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Reichert J, Voigtmann T. Tracer dynamics in crowded active-particle suspensions. SOFT MATTER 2021; 17:10492-10504. [PMID: 34751290 DOI: 10.1039/d1sm01092a] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We discuss the dynamics of active Brownian particles (ABPs) in crowded environments through the mean-squared displacement (MSD) of active and passive tracer particles in both active and passive host systems. Exact equations for the MSD are derived using a projection operator technique, extending to dense systems the known solution for a single ABP. The interaction of the tracer particle with the host particles gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for active Brownian particles (ABP-MCT), we discuss the various dynamical regimes that emerge: While self-propelled motion gives rise to super-diffusive MSD, at high densities, this competes with an interaction-induced sub-diffusive regime. The predictions of the theory are shown to be in good agreement with results obtained from an event-driven Brownian dynamics (ED-BD) simulation scheme for the dynamics of two-dimensional active Brownian hard disks.
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Affiliation(s)
- Julian Reichert
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.
- Department of Physics, Heinrich-Heine Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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25
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Reichert J, Mandal S, Voigtmann T. Mode-coupling theory for tagged-particle motion of active Brownian particles. Phys Rev E 2021; 104:044608. [PMID: 34781467 DOI: 10.1103/physreve.104.044608] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 10/05/2021] [Indexed: 11/07/2022]
Abstract
We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.
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Affiliation(s)
- Julian Reichert
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
| | - Suvendu Mandal
- Department of Physics, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.,Department of Physics, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
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26
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Santra I, Basu U, Sabhapandit S. Direction reversing active Brownian particle in a harmonic potential. SOFT MATTER 2021; 17:10108-10119. [PMID: 34726222 DOI: 10.1039/d1sm01118a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study the two-dimensional motion of an active Brownian particle of speed v0, with intermittent directional reversals in the presence of a harmonic trap of strength μ. The presence of the trap ensures that the position of the particle eventually reaches a steady state where it is bounded within a circular region of radius v0/μ, centered at the minimum of the trap. Due to the interplay between the rotational diffusion constant DR, reversal rate γ, and the trap strength μ, the steady state distribution shows four different types of shapes, which we refer to as active-I & II, and passive-I & II phases. In the active-I phase, the weight of the distribution is concentrated along an annular region close to the circular boundary, whereas in active-II, an additional central diverging peak appears giving rise to a Mexican hat-like shape of the distribution. The passive-I is marked by a single Boltzmann-like centrally peaked distribution in the large DR limit. On the other hand, while the passive-II phase also shows a single central peak, it is distinguished from passive-I by a non-Boltzmann like divergence near the origin. We characterize these phases by calculating the exact analytical forms of the distributions in various limiting cases. In particular, we show that for DR ≪ γ, the shape transition of the two-dimensional position distribution from active-II to passive-II occurs at μ = γ. We compliment these analytical results with numerical simulations beyond the limiting cases and obtain a qualitative phase diagram in the (DR, γ, μ-1) space.
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Affiliation(s)
- Ion Santra
- Raman Research Institute, Bengaluru 560080, India
| | - Urna Basu
- Raman Research Institute, Bengaluru 560080, India
- S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India
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27
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Mayer DB, Sarmiento-Gómez E, Escobedo-Sánchez MA, Segovia-Gutiérrez JP, Kurzthaler C, Egelhaaf SU, Franosch T. Two-dimensional Brownian motion of anisotropic dimers. Phys Rev E 2021; 104:014605. [PMID: 34412330 DOI: 10.1103/physreve.104.014605] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 05/04/2021] [Indexed: 11/07/2022]
Abstract
We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.
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Affiliation(s)
- Daniel B Mayer
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25/2, A-6020 Innsbruck, Austria
| | - Erick Sarmiento-Gómez
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, D-40225 Düsseldorf, Germany.,División de Ciencias e Ingenierias, Departamento de Ingenieria Física, Universidad de Guanajuato, León, Mexico
| | - Manuel A Escobedo-Sánchez
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Juan Pablo Segovia-Gutiérrez
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Christina Kurzthaler
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25/2, A-6020 Innsbruck, Austria
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28
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Santra I, Basu U, Sabhapandit S. Active Brownian motion with directional reversals. Phys Rev E 2021; 104:L012601. [PMID: 34412243 DOI: 10.1103/physreve.104.l012601] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a motion in two dimensions, the presence of the two timescales set by the rotational diffusion constant D_{R} and the reversal rate γ gives rise to four distinct dynamical regimes: (I) t≪min(γ^{-1},D_{R}^{-1}), (II) γ^{-1}≪t≪D_{R}^{-1}, (III) D_{R}^{-1}≪t≪γ^{-1}, and (IV) t≫max(γ^{-1}, D_{R}^{-1}), showing distinct behaviors. We characterize these behaviors by analytically computing the position distribution and persistence exponents. The position distribution shows a crossover from a strongly nondiffusive and anisotropic behavior at short times to a diffusive isotropic behavior via an intermediate regime, II or III. In regime II, we show that, the position distribution along the direction orthogonal to the initial orientation is a function of the scaled variable z∝x_{⊥}/t with a nontrivial scaling function, f(z)=(2π^{3})^{-1/2}Γ(1/4+iz)Γ(1/4-iz). Furthermore, by computing the exact first-passage time distribution, we show that a persistence exponent α=1 emerges due to the direction reversal in this regime.
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Affiliation(s)
- Ion Santra
- Raman Research Institute, Bengaluru 560080, India
| | - Urna Basu
- Raman Research Institute, Bengaluru 560080, India
- S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India
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29
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Locatelli E, Bianco V, Malgaretti P. Activity-Induced Collapse and Arrest of Active Polymer Rings. PHYSICAL REVIEW LETTERS 2021; 126:097801. [PMID: 33750170 DOI: 10.1103/physrevlett.126.097801] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 01/24/2021] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that their behavior depends crucially on their size: Short rings (N≲100) swell, whereas longer rings (N≳200) collapse, at sufficiently high activity. By investigating the nonequilibrium process leading to the steady state, we find a universal route driving both outcomes; we highlight the central role of steric interactions, at variance with linear chains, and of topology conservation. We further show that the collapsed rings are arrested by looking at different observables, all underlining the presence of an extremely long timescales at the steady state, associated with the internal dynamics of the collapsed section. Finally, we found that in some circumstances the collapsed state spins about its axis.
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Affiliation(s)
| | - Valentino Bianco
- Faculty of Chemistry, Chemical Physics Department, Complutense University of Madrid, Plaza de las Ciencias, Ciudad Universitaria, Madrid 28040, Spain
| | - Paolo Malgaretti
- Max Planck Institute for Intelligent Systems, Heisenbergstrasse 3, 70569 Stuttgart, Germany
- IV Institute for Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Helmholtz Institut Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Strasse 248, 90429 Nürnberg, Germany
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30
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Zanovello L, Caraglio M, Franosch T, Faccioli P. Target Search of Active Agents Crossing High Energy Barriers. PHYSICAL REVIEW LETTERS 2021; 126:018001. [PMID: 33480788 DOI: 10.1103/physrevlett.126.018001] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Revised: 10/26/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this nonequilibrium rare-event problem by developing an algorithm generalizing transition-path sampling to active Brownian dynamics. This method is exemplified and benchmarked for a paradigmatic two-dimensional potential with a high barrier. We find that even in such a simple landscape the structure and kinetics of the ensemble of transition paths changes drastically in the presence of activity. Indeed, active Brownian particles reach the target more frequently than passive Brownian particles, following longer and counterintuitive search patterns.
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Affiliation(s)
- Luigi Zanovello
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
- Dipartimento di Fisica, Università degli studi di Trento, Via Sommarive 14, 38123 Trento, Italy
| | - 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
| | - Pietro Faccioli
- Dipartimento di Fisica, Università degli studi di Trento, Via Sommarive 14, 38123 Trento, Italy
- Istituto Nazionale di Fisica Nucleare - Trento Institute for Fundamental Physics and Applications, Via Sommarive 14, 38123 Trento, Italy
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31
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Mandal S, Kurzthaler C, Franosch T, Löwen H. Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments. PHYSICAL REVIEW LETTERS 2020; 125:138002. [PMID: 33034497 DOI: 10.1103/physrevlett.125.138002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Revised: 07/14/2020] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counterintuitive "crowded is faster" behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled, crowded, passive to active systems. We predict a scaling theory for the effective diffusivity as a function of the Péclet number and the filament number density. Subsequently, we show that an exact expression derived for a single self-propelled filament with motility parameters as input can predict the nontrivial spatiotemporal dynamics over the entire range of length and timescales. In particular, our theory captures short-time diffusion, directed swimming motion at intermediate times, and the transition to complete orientational relaxation at long times.
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Affiliation(s)
- Suvendu Mandal
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Christina Kurzthaler
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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32
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Dulaney AR, Brady JF. Waves in active matter: The transition from ballistic to diffusive behavior. Phys Rev E 2020; 101:052609. [PMID: 32575299 DOI: 10.1103/physreve.101.052609] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 04/23/2020] [Indexed: 01/19/2023]
Abstract
We highlight the unique wavelike character observed in the relaxation dynamics of active systems via a Smoluchowski based theoretical framework and Brownian dynamic simulations. Persistent swimming motion results in wavelike dynamics until the advective swim displacements become sufficiently uncorrelated, at which point the motion becomes a random walk process characterized by a swim diffusivity, D^{swim}=U_{0}^{2}τ_{R}/[d(d-1)], dependent on the speed of swimming U_{0}, reorientation time τ_{R}, and reorientation dimension d. This change in behavior is described by a telegraph equation, which governs the transition from ballistic wavelike motion to long-time diffusive motion. We study the relaxation of active Brownian particles from an instantaneous source, and provide an explanation for the nonmonotonicity observed in the intermediate scattering function. Using our simple kinetic model we provide the density distribution for the diffusion of active particles released from a line source as a function of time, position, and the ratio of the activity to thermal energy. We extend our analysis to include the effects of an external field on particle spreading to further understand how reorientation events in the active force vector affect relaxation. The strength of the applied external field is shown to be inversely proportional to the decay of the wavelike structure. Our theoretical description for the evolution of the number density agrees with Brownian dynamic simulation data.
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Affiliation(s)
- A R Dulaney
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - J F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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33
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Santra I, Basu U, Sabhapandit S. Run-and-tumble particles in two dimensions: Marginal position distributions. Phys Rev E 2020; 101:062120. [PMID: 32688530 DOI: 10.1103/physreve.101.062120] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
We study a set of run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation θ of the particle can assume a set of n possible discrete values, while in the second case θ is a continuous variable. We calculate exactly the marginal position distributions for n=3,4 and the continuous case and show that in all cases the RTP shows a crossover from a ballistic to diffusive regime. The ballistic regime is a typical signature of the active nature of the systems and is characterized by nontrivial position distributions which depend on the specific model. We also show that the signature of activity at long times can be found in the atypical fluctuations, which we also characterize by computing the large deviation functions explicitly.
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Affiliation(s)
- Ion Santra
- Raman Research Institute, Bengaluru 560080, India
| | - Urna Basu
- Raman Research Institute, Bengaluru 560080, India
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34
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Shee A, Dhar A, Chaudhuri D. Active Brownian particles: mapping to equilibrium polymers and exact computation of moments. SOFT MATTER 2020; 16:4776-4787. [PMID: 32409794 DOI: 10.1039/d0sm00367k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
It is well known that the path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers. Here we investigate the properties of the equilibrium polymer that corresponds to the trajectories of particles acted on simultaneously by both Brownian and active noise. Through this mapping we can see interesting crossovers in the mechanical properties of the polymer with changing contour length. The polymer end-to-end distribution exhibits Gaussian behaviour for short lengths, which changes to the form of semiflexible filaments at intermediate lengths, to finally go back to a Gaussian form for long contour lengths. By performing a Laplace transform of the governing Fokker-Planck equation of the active Brownian particle, we discuss a direct method to derive exact expressions for all the moments of the relevant dynamical variables, in arbitrary dimensions. These are verified via numerical simulations and used to describe interesting qualitative features such as, for example, dynamical crossovers. Finally we discuss the kurtosis of the ABP's position, which we compute exactly, and show that it can be used to differentiate between active Brownian particles and the active Ornstein-Uhlenbeck process.
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Affiliation(s)
- Amir Shee
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India.
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35
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Kolb T, Klotsa D. Active binary mixtures of fast and slow hard spheres. SOFT MATTER 2020; 16:1967-1978. [PMID: 31859309 DOI: 10.1039/c9sm01799b] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We computationally studied the phase behavior and dynamics of binary mixtures of active particles, where each species had distinct activities leading to distinct velocities, fast and slow. We obtained phase diagrams demonstrating motility-induced phase separation (MIPS) upon varying the activity and concentration of each species, and extended current kinetic theory of active/passive mixtures to active/active mixtures. We discovered two regimes of behavior quantified through the participation of each species in the dense phase compared to their monodisperse counterparts. In regime I (active/passive and active/weakly-active), we found that the dense phase was segregated by particle type into domains of fast and slow particles. Moreover, fast particles were suppressed from entering the dense phase while slow particles were enhanced entering the dense phase, compared to monodisperse systems of all-fast or all-slow particles. These effects decayed asymptotically as the activity of the slow species increased, approaching the activity of the fast species until they were negligible (regime II). In regime II, the dense phase was homogeneously mixed and each species participated in the dense phase as if it were it a monodisperse system (i.e. not mixed at all). Finally, we showed that a weighted average of constituent particle activities, which we term the net activity, defines a binodal for the MIPS transition in active/active binary mixtures. We examined the critical point of the transition and found a critical exponent (β = 0.45) in agreement with similar studies on monodisperse systems, and distinct from equilibrium systems.
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Affiliation(s)
- Thomas Kolb
- Department of Chemistry, University of North Carolina at Chapel Hill, USA and Department of Applied Physical Sciences, University of North Carolina at Chapel Hill, USA.
| | - Daphne Klotsa
- Department of Applied Physical Sciences, University of North Carolina at Chapel Hill, USA.
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36
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Abstract
The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.
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Affiliation(s)
- Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
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37
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Löwen H. Inertial effects of self-propelled particles: From active Brownian to active Langevin motion. J Chem Phys 2020; 152:040901. [DOI: 10.1063/1.5134455] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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38
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Caprini L, Hernández-García E, López C, Marini Bettolo Marconi U. A comparative study between two models of active cluster crystals. Sci Rep 2019; 9:16687. [PMID: 31723160 PMCID: PMC6853940 DOI: 10.1038/s41598-019-52420-1] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 08/19/2019] [Indexed: 12/28/2022] Open
Abstract
We study a system of active particles with soft repulsive interactions that lead to an active cluster-crystal phase in two dimensions. We use two different modelizations of the active force - Active Brownian particles (ABP) and Ornstein-Uhlenbeck particles (AOUP) - and focus on analogies and differences between them. We study the different phases appearing in the system, in particular, the formation of ordered patterns drifting in space without being altered. We develop an effective description which captures some properties of the stable clusters for both ABP and AOUP. As an additional point, we confine such a system in a large channel, in order to study the interplay between the cluster crystal phase and the well-known accumulation near the walls, a phenomenology typical of active particles. For small activities, we find clusters attached to the walls and deformed, while for large values of the active force they collapse in stripes parallel to the walls.
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Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100, L'Aquila, Italy.
| | - Emilio Hernández-García
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
| | - Cristóbal López
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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39
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Caprini L, Cecconi F, Marini Bettolo Marconi U. Transport of active particles in an open-wedge channel. J Chem Phys 2019; 150:144903. [DOI: 10.1063/1.5090104] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via F.Crispi 7, I-67100 L’Aquila, Italy
| | - Fabio Cecconi
- Istituto dei Sistemi Complessi (CNR), Via Taurini 19, I-00185 Roma, Italy
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40
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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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41
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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: 3] [Impact Index Per Article: 0.6] [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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42
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Kurzthaler C. Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces. SOFT MATTER 2018; 14:7634-7644. [PMID: 30168558 DOI: 10.1039/c8sm01403e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.
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Affiliation(s)
- Christina Kurzthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
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43
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Kurzthaler C, Devailly C, Arlt J, Franosch T, Poon WCK, Martinez VA, Brown AT. Probing the Spatiotemporal Dynamics of Catalytic Janus Particles with Single-Particle Tracking and Differential Dynamic Microscopy. PHYSICAL REVIEW LETTERS 2018; 121:078001. [PMID: 30169062 DOI: 10.1103/physrevlett.121.078001] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Revised: 05/01/2018] [Indexed: 05/25/2023]
Abstract
We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations resolve the crossover between directed motion to orientational relaxation and allow us to discriminate active Brownian motion from other reorientation processes, e.g., run-and-tumble motion. A direct comparison to theoretical predictions reliably yields the rotational and translational diffusion coefficients of the particles, the mean and width of their speed distribution, and the temporal evolution of these parameters.
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Affiliation(s)
- Christina Kurzthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Clémence Devailly
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Jochen Arlt
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Wilson C K Poon
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Vincent A Martinez
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Aidan T Brown
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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44
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Kurzthaler C, Franosch T. Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression. SOFT MATTER 2018; 14:2682-2693. [PMID: 29564466 DOI: 10.1039/c8sm00366a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.
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Affiliation(s)
- Christina Kurzthaler
- 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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45
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Leitmann S, Höfling F, Franosch T. Dynamically crowded solutions of infinitely thin Brownian needles. Phys Rev E 2018; 96:012118. [PMID: 29347251 DOI: 10.1103/physreve.96.012118] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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46
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Liluashvili A, Ónody J, Voigtmann T. Mode-coupling theory for active Brownian particles. Phys Rev E 2017; 96:062608. [PMID: 29347410 DOI: 10.1103/physreve.96.062608] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2017] [Indexed: 06/07/2023]
Abstract
We present a mode-coupling theory (MCT) for the slow dynamics of two-dimensional spherical active Brownian particles (ABPs). The ABPs are characterized by a self-propulsion velocity v_{0} and by their translational and rotational diffusion coefficients D_{t} and D_{r}, respectively. Based on the integration-through-transients formalism, the theory requires as input only the equilibrium static structure factors of the passive system (where v_{0}=0). It predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity, and rotational diffusivity that arise because at high densities, the persistence length of active swimming ℓ_{p}=v_{0}/D_{r} interferes with the interaction length ℓ_{c} set by the caging of particles. While the low-density dynamics of ABPs is characterized by a single Péclet number Pe=v_{0}^{2}/D_{r}D_{t}, close to the glass transition the dynamics is found to depend on Pe and ℓ_{p} separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to speed up, while decreasing the persistence length slows down the relaxation. The active-MCT glass is a nonergodic state that is qualitatively different from the passive glass. In it, correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.
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Affiliation(s)
- Alexander Liluashvili
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
| | - Jonathan Ónody
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
- Department of Physics, Heinrich-Heine Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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Kurzthaler C, Franosch T. Intermediate scattering function of an anisotropic Brownian circle swimmer. SOFT MATTER 2017; 13:6396-6406. [PMID: 28872170 DOI: 10.1039/c7sm00873b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.
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Affiliation(s)
- Christina Kurzthaler
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
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Campbell AI, Wittkowski R, ten Hagen B, Löwen H, Ebbens SJ. Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory. J Chem Phys 2017; 147:084905. [DOI: 10.1063/1.4998605] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Andrew I. Campbell
- Department of Chemical and Biological Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom
| | - 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
| | - Borge ten Hagen
- Physics of Fluids Group and Max Planck Center Twente, Department of Science and Technology, MESA+ Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Stephen J. Ebbens
- Department of Chemical and Biological Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom
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Kurzthaler C, Franosch T. Exact solution for the force-extension relation of a semiflexible polymer under compression. Phys Rev E 2017; 95:052501. [PMID: 28618478 DOI: 10.1103/physreve.95.052501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Indexed: 11/07/2022]
Abstract
Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.
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Affiliation(s)
- Christina Kurzthaler
- 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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