1
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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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Braun F, Wagner MFP, Toimil-Molares ME, von Klitzing R. Comparison of Different Preparation Techniques of Thermophoretic Swimmers and Their Propulsion Velocity. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:5606-5616. [PMID: 38501265 DOI: 10.1021/acs.langmuir.3c01776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/20/2024]
Abstract
The motion of partly gold (Au)-coated Janus particles under laser irradiation is caused by self-thermophoresis. Despite numerous studies addressing this topic, the impact of the preparation method and the degree of coverage of the particle with Au on the resulting thermophoretic velocity has not yet been fully understood. A detailed understanding of the most important tuning parameters during the preparation process is crucial to design Janus particles that are optimized for Au coverage to receive a high thermophoretic velocity. In this study, we explore the influence of the fabrication process, which changes the Au cap size, on the resulting self-propulsion behavior of partly Au-coated polystyrene particles (Au-PS). Additionally, the impact of an underlying adhesion chromium layer is investigated. In addition to the most commonly used qualitative SEM and EDX measurements, we propose a novel and fast technique utilizing AFM studies to quantify the cap size. This non-invasive technique can be used to determine both the size and the maximum thickness of the Au cap. The Au cap size was systematically varied in a range between about 36 and 74% by different preparation strategies. Nevertheless, we showed that the differing Au cap sizes of the Janus particles in this range have no obvious effect on the thermophoretic velocity. This is a surprising result since one would expect an effect of the Au cap size due to different solvent flows around the Janus particles and is attributed to an additional torque near the surface of the measuring cell.
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Affiliation(s)
- Franziska Braun
- Soft Matter at Interfaces, Institute for Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
| | | | | | - Regine von Klitzing
- Soft Matter at Interfaces, Institute for Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
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3
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Nizama M, Cáceres MO. Intermittent Kac's flights and the generalized telegrapher's equation. Phys Rev E 2024; 109:024116. [PMID: 38491600 DOI: 10.1103/physreve.109.024116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
A generalized one-dimensional telegrapher equation associated with an intermittent change of sign in the velocity of a Kac's flight has been proposed. To solve this random differential equation, we used the enlarged master equation approach to obtain the exact differential equation for the evolution of a normalized positive distribution. This distribution is associated with a generalized finite-velocity diffusionlike process. We studied the robustness of the ballistic regime, the cutoff of its domain, and the time-dependent Gaussian convergence. The second moment for the evolution of the profile has been studied as a function of non-Poisson statistics (possibly intermittent) for the time intervals Δ_{ij} in the Kac's flight. Numerical results for the evolution of sharp and wide initial profiles have also been presented. In addition, for comparison with a non-Gaussian process at all times, we have revisited the non-Markov Poisson's flight with exponential pulses. A theory for generalized random flights with intermittent stochastic velocity and in the presence of a force is also presented, and the stationary distribution for two classes of potential has been obtained.
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Affiliation(s)
- Marco Nizama
- Departamento de Fisica, Facultad de Ingenieria and CONICET, Universidad Nacional del Comahue, CP 8300, Neuquen, Argentina
| | - Manuel O Cáceres
- Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
- CONICET, Centro Atomico Bariloche, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
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4
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Angelani L. Optimal escapes in active matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:9. [PMID: 38281233 DOI: 10.1140/epje/s10189-023-00402-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 12/20/2023] [Indexed: 01/30/2024]
Abstract
The out-of-equilibrium character of active particles, responsible for accumulation at boundaries in confining domains, determines not-trivial effects when considering escape processes. Non-monotonous behavior of exit times with respect to tumbling rate (inverse of mean persistent time) appears, as a consequence of the competing processes of exploring the bulk and accumulate at boundaries. By using both 1D analytical results and 2D numerical simulations of run-and-tumble particles with different behaviours at boundaries, we scrutinize this very general phenomenon of active matter, evidencing the role of accumulation at walls for the existence of optimal tumbling rates for fast escapes.
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Affiliation(s)
- Luca Angelani
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale A. Moro 2, I-00185, Roma, Italy.
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185, Roma, Italy.
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5
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Zhao Y, Kurzthaler C, Zhou N, Schwarz-Linek J, Devailly C, Arlt J, Huang JD, Poon WCK, Franosch T, Martinez VA, Tailleur J. Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions. Phys Rev E 2024; 109:014612. [PMID: 38366485 DOI: 10.1103/physreve.109.014612] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 12/04/2023] [Indexed: 02/18/2024]
Abstract
We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.
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Affiliation(s)
- Yongfeng Zhao
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, Suzhou 215006, China
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- School of Biomedical Sciences, Li Ka Shing Faculty of Medicine, University of Hong Kong, Pok Fu Lam, Hong Kong, People's Republic of China
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
| | - 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
| | - 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, People's Republic of 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
| | - Vincent A Martinez
- School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Julien Tailleur
- Université de Paris, MSC, UMR 7057 CNRS, 75205 Paris, France
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6
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Jose S, Rosso A, Ramola K. Generalized disorder averages and current fluctuations in run and tumble particles. Phys Rev E 2023; 108:L052601. [PMID: 38115454 DOI: 10.1103/physreve.108.l052601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
We present exact results for the fluctuations in the number of particles crossing the origin up to time t in a collection of noninteracting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom, positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance σ^{2} of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times, σ^{2}∼t vs σ^{2}∼t^{2}, respectively, with a sqrt[t] behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.
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Affiliation(s)
- Stephy Jose
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India
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7
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Di Bello C, Hartmann AK, Majumdar SN, Mori F, Rosso A, Schehr G. Current fluctuations in stochastically resetting particle systems. Phys Rev E 2023; 108:014112. [PMID: 37583217 DOI: 10.1103/physreve.108.014112] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 04/28/2023] [Indexed: 08/17/2023]
Abstract
We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density ρ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with stochastic resetting to its initial position with rate r and (ii) each particle performs run-and-tumble motion, and with rate r its position gets reset to its initial value and simultaneously its velocity gets randomized. We study the effects of resetting on the distribution P(Q,t) of the integrated particle current Q up to time t through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution P_{an}(Q,t) approaches its stationary limit uniformly for all Q. In contrast, the quenched distribution P_{qu}(Q,t) attains its stationary form for QQ_{crit}(t). We show that Q_{crit}(t) increases linearly with t for large t. On the scale where Q∼Q_{crit}(t), we show that P_{qu}(Q,t) has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as 10^{-14000}, we were able to compute numerically this nonanalytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.
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Affiliation(s)
- Costantino Di Bello
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | | | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Francesco Mori
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 75252 Paris Cedex 05, France
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8
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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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9
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Yan R, Tan F, Wang J, Zhao N. Conformation and dynamics of an active filament in crowded media. J Chem Phys 2023; 158:114905. [PMID: 36948796 DOI: 10.1063/5.0142559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/04/2023] Open
Abstract
The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.
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Affiliation(s)
- Ran Yan
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Fei Tan
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Jingli Wang
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China
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10
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Ledesma-Motolinía M, Carrillo-Estrada JL, Escobar A, Donado F, Castro-Villarreal P. Magnetized granular particles running and tumbling on the circle S^{1}. Phys Rev E 2023; 107:024902. [PMID: 36932580 DOI: 10.1103/physreve.107.024902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
It has been shown that a nonvibrating magnetic granular system, when fed by an alternating magnetic field, behaves with most of the distinctive physical features of active matter systems. In this work, we focus on the simplest granular system composed of a single magnetized spherical particle allocated in a quasi-one-dimensional circular channel that receives energy from a magnetic field reservoir and transduces it into a running and tumbling motion. The theoretical analysis, based on the run-and-tumble model for a circle of radius R, forecasts the existence of a dynamical phase transition between an erratic motion (disordered phase) when the characteristic persistence length of the run-and-tumble motion, ℓ_{c}<R/2, to a persistent motion (ordered phase) when ℓ_{c}>R/2. It is found that the limiting behaviors of these phases correspond to Brownian motion on the circle and a simple uniform circular motion, respectively. Furthermore, it is qualitatively shown that the smaller the magnetization of a particle, the larger the persistence length. It is so at least within the experimental limit of validity of our experiments. Our results show a very good agreement between theory and experiment.
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Affiliation(s)
- M Ledesma-Motolinía
- Instituto de Física "Luis Rivera Terrazas", Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico
| | - J L Carrillo-Estrada
- Instituto de Física "Luis Rivera Terrazas", Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico
| | - A Escobar
- Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca, 42184, Hgo., México
| | - F Donado
- Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca, 42184, Hgo., 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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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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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: 1] [Impact Index Per Article: 0.5] [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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14
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Frydel D. Positing the problem of stationary distributions of active particles as third-order differential equation. Phys Rev E 2022; 106:024121. [PMID: 36109956 DOI: 10.1103/physreve.106.024121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition j=0, where j is a flux. Since an analogous equation for passive Brownian particles is first-order, a second- and third-order term are features of active motion. In all cases, the solution has a form of a convolution of two distributions: the Gaussian distribution representing the Boltzmann distribution of passive particles, and the beta distribution representing active motion at zero temperature.
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Affiliation(s)
- Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 8320000 Santiago, Chile
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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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Jose S, Mandal D, Barma M, Ramola K. Active random walks in one and two dimensions. Phys Rev E 2022; 105:064103. [PMID: 35854533 DOI: 10.1103/physreve.105.064103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the lattice in one and two dimensions and derive exact results in the continuum limit. Next, we compute the large deviation free-energy function in both one and two dimensions, which we use to compute the moments and the cumulants of the displacements exactly at late times. Our exact results demonstrate that the cross-correlations between the motion in the x and y directions in two dimensions persist in the large deviation function. We also demonstrate that the large deviation function of an active particle with diffusion displays two regimes, with differing diffusive behaviors. We verify our analytic results with kinetic Monte Carlo simulations of an active lattice walker in one and two dimensions.
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Affiliation(s)
- Stephy Jose
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Dipanjan Mandal
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Mustansir Barma
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Kabir Ramola
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500046, India
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17
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Chen Y, Yan R, Zhao N. Passive and active tracer dynamics in polymer solutions with isotropic-to-nematic phase transition. Phys Chem Chem Phys 2022; 24:7415-7429. [PMID: 35266498 DOI: 10.1039/d2cp00323f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Macromolecular crowding plays a crucial role in determining the dynamics in a living cell. We adopt Langevin dynamics simulations to investigate the anomalous diffusion dynamics of passive and active particles in a solution of polymer chains with tunable stiffness. The solution's anisotropic feature is modulated by changing both the polymer stiffness and volume fraction, where isotropic-to-nematic phase transition is involved. Our results demonstrate the significant impact of polymer flexibility on the dynamics of both passive and active probes. The distinct diffusion mechanism for an active particle is clarified by the interplay between polymer stiffness, crowdedness and activity. Polymer stiffness leads to a global inhibition effect on passive particle diffusion. The diffusion coefficient exhibits an intriguing non-monotonic variation at increasing polymer stiffness, which is due to the fact that the alignment of polymer chains is beneficial for diffusion along the nematic direction but unfavorable for that in the direction perpendicular to it. In sharp contrast, polymer stiffness plays a dominant role in facilitating active particle diffusion. Self-propulsion of the particle can utilize stiffness-induced elastic interactions more efficiently, which promotes its mobility in both directions. Meanwhile, an active particle might have a stronger ability to take advantage of the polymer alignment, contributing substantially enhanced diffusivity. In addition, the diffusion coefficient of an active particle is subject to a tendency of degeneration against varying volume fraction. This counter-intuitive behavior is due to the contrasting factors that increasing crowdedness induces a lower particle speed but a longer persistent motion time.
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Affiliation(s)
- Ying Chen
- College of Chemistry, Sichuan University, Chengdu 610064, China.
| | - Ran Yan
- College of Chemistry, Sichuan University, Chengdu 610064, China.
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China.
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18
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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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19
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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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20
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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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21
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Persch C, Müller MJ, Yadav A, Pries J, Honné N, Kerres P, Wei S, Tanaka H, Fantini P, Varesi E, Pellizzer F, Wuttig M. The potential of chemical bonding to design crystallization and vitrification kinetics. Nat Commun 2021; 12:4978. [PMID: 34404800 PMCID: PMC8371141 DOI: 10.1038/s41467-021-25258-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 07/29/2021] [Indexed: 11/05/2022] Open
Abstract
Controlling a state of material between its crystalline and glassy phase has fostered many real-world applications. Nevertheless, design rules for crystallization and vitrification kinetics still lack predictive power. Here, we identify stoichiometry trends for these processes in phase change materials, i.e. along the GeTe-GeSe, GeTe-SnTe, and GeTe-Sb2Te3 pseudo-binary lines employing a pump-probe laser setup and calorimetry. We discover a clear stoichiometry dependence of crystallization speed along a line connecting regions characterized by two fundamental bonding types, metallic and covalent bonding. Increasing covalency slows down crystallization by six orders of magnitude and promotes vitrification. The stoichiometry dependence is correlated with material properties, such as the optical properties of the crystalline phase and a bond indicator, the number of electrons shared between adjacent atoms. A quantum-chemical map explains these trends and provides a blueprint to design crystallization kinetics. Tailoring the crystallization kinetics of materials is important for targeting applications. Here the authors observe a remarkable dependence of crystallization and vitrification kinetics and attribute it to systematic bonding changes for a class of materials between metallic and covalent bonding.
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Affiliation(s)
- Christoph Persch
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Maximilian J Müller
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Aakash Yadav
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Julian Pries
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Natalie Honné
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Peter Kerres
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany
| | - Shuai Wei
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany.,Department of Chemistry, Aarhus University, Aarhus C, Denmark
| | - Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo, Japan.,Research Center for Advanced Science and Technology, University of Tokyo, Meguro-ku, Tokyo, Japan
| | | | | | | | - Matthias Wuttig
- I. Institute of Physics, Physics of Novel Materials, RWTH Aachen University, Aachen, Germany. .,Jülich-Aachen Research Alliance (JARA FIT and JARA HPC), RWTH Aachen University, Aachen, Germany. .,PGI 10 (Green IT), Forschungszentrum Jülich GmbH, Jülich, Germany.
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22
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Mori F, Le Doussal P, Majumdar SN, Schehr G. Condensation transition in the late-time position of a run-and-tumble particle. Phys Rev E 2021; 103:062134. [PMID: 34271704 DOI: 10.1103/physreve.103.062134] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
We study the position distribution P(R[over ⃗],N) of a run-and-tumble particle (RTP) in arbitrary dimension d, after N runs. We assume that the constant speed v>0 of the particle during each running phase is independently drawn from a probability distribution W(v) and that the direction of the particle is chosen isotropically after each tumbling. The position distribution is clearly isotropic, P(R[over ⃗],N)→P(R,N) where R=|R[over ⃗]|. We show that, under certain conditions on d and W(v) and for large N, a condensation transition occurs at some critical value of R=R_{c}∼O(N) located in the large-deviation regime of P(R,N). For R<R_{c} (subcritical fluid phase), all runs are roughly of the same size in a typical trajectory. In contrast, an RTP trajectory with R>R_{c} is typically dominated by a "condensate," i.e., a large single run that subsumes a finite fraction of the total displacement (supercritical condensed phase). Focusing on the family of speed distributions W(v)=α(1-v/v_{0})^{α-1}/v_{0}, parametrized by α>0, we show that, for large N, P(R,N)∼exp[-Nψ_{d,α}(R/N)], and we compute exactly the rate function ψ_{d,α}(z) for any d and α. We show that the transition manifests itself as a singularity of this rate function at R=R_{c} and that its order depends continuously on d and α. We also compute the distribution of the condensate size for R>R_{c}. Finally, we study the model when the total duration T of the RTP, instead of the total number of runs, is fixed. Our analytical predictions are confirmed by numerical simulations, performed using a constrained Markov chain Monte Carlo technique, with precision ∼10^{-100}.
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Affiliation(s)
- Francesco Mori
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Pierre Le Doussal
- Laboratoire de Physique de l'Ecole Normale Supérieure, PSL University, CNRS, Sorbonne Universités, 24 rue Lhomond, 75231 Paris, France
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, 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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23
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Mercado-Vásquez G, Boyer D. First hitting times between a run-and-tumble particle and a stochastically gated target. Phys Rev E 2021; 103:042139. [PMID: 34005900 DOI: 10.1103/physreve.103.042139] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 04/12/2021] [Indexed: 11/07/2022]
Abstract
We study the statistics of the first hitting time between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting time. However, the relative fluctuations of the first hitting time are large and exhibit nonmonotonous behaviors with respect to the turning rate or the target transition rates. Paradoxically, these fluctuations can be the largest for targets that are visible most of the time, and not for those that are mostly invisible or rapidly transiting between the two states. On the infinite line, the classical asymptotic behavior ∝t^{-3/2} of the first hitting time distribution is typically preceded, due to target intermittency, by an intermediate scaling regime varying as t^{-1/2}. The extent of this transient regime becomes very long when the target is most of the time invisible, especially at low turning rates. In both finite and infinite geometries, we draw analogies with partial absorption problems.
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Affiliation(s)
| | - Denis Boyer
- Instituto de Física, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
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24
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Dean DS, Majumdar SN, Schawe H. Position distribution in a generalized run-and-tumble process. Phys Rev E 2021; 103:012130. [PMID: 33601582 DOI: 10.1103/physreve.103.012130] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 12/02/2020] [Indexed: 06/12/2023]
Abstract
We study a class of stochastic processes of the type d^{n}x/dt^{n}=v_{0}σ(t) where n>0 is a positive integer and σ(t)=±1 represents an active telegraphic noise that flips from one state to the other with a constant rate γ. For n=1, it reduces to the standard run-and-tumble process for active particles in one dimension. This process can be analytically continued to any n>0, including noninteger values. We compute exactly the mean-squared displacement at time t for all n>0 and show that at late times while it grows as ∼t^{2n-1} for n>1/2, it approaches a constant for n<1/2. In the marginal case n=1/2, it grows very slowly with time as ∼lnt. Thus, the process undergoes a localization transition at n=1/2. We also show that the position distribution p_{n}(x,t) remains time-dependent even at late times for n≥1/2, but approaches a stationary time-independent form for n<1/2. The tails of the position distribution at late times exhibit a large deviation form, p_{n}(x,t)∼exp[-γtΦ_{n}(x/x^{*}(t))], where x^{*}(t)=v_{0}t^{n}/Γ(n+1). We compute the rate function Φ_{n}(z) analytically for all n>0 and also numerically using importance sampling methods, finding excellent agreement between them. For three special values n=1, n=2, and n=1/2 we compute the exact cumulant-generating function of the position distribution at all times t.
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Affiliation(s)
- David S Dean
- Univ. Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33400 Talence, France
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Hendrik Schawe
- LPTM, UMR 8089, CY Cergy Paris Université, CNRS, 95000 Cergy, France
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25
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Prakash P, Abdulla AZ, Singh V, Varma M. Swimming statistics of cargo-loaded single bacteria. SOFT MATTER 2020; 16:9499-9505. [PMID: 32966524 DOI: 10.1039/d0sm01066a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Burgeoning interest in the area of bacteria-powered micro robotic systems prompted us to study the dynamics of cargo transport by single bacteria. In this paper, we have studied the swimming behaviour of oil-droplets attached as cargo to the cell bodies of single bacteria. The oil-droplet loaded bacteria exhibit super-diffusive motion which is characterised by a high degree of directional persistence. Interestingly, bacteria could navigate with cargo size as large as 8 μm resulting in an increased rotational drag of more than 2 orders when compared to the free bacteria. The directional change of cargo loaded bacterial trajectories seems to be enhanced by steric hindrance from other oil-droplets present in the environment.
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Affiliation(s)
- P Prakash
- Centre for Nanoscience and Engineering, Indian Institute of Science, Bangalore, 560012, India.
| | - A Z Abdulla
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - V Singh
- Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore, 560012, India
| | - M Varma
- Centre for Nanoscience and Engineering, Indian Institute of Science, Bangalore, 560012, India. and Robert Bosch Centre for Cyber Physical Systems, Indian Institute of Science, Bangalore, 560012, India
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26
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Bressloff PC. Occupation time of a run-and-tumble particle with resetting. Phys Rev E 2020; 102:042135. [PMID: 33212628 DOI: 10.1103/physreve.102.042135] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 10/14/2020] [Indexed: 06/11/2023]
Abstract
We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times generated by a Poisson process with rate r. The velocity state is reset to ±v with fixed probabilities ρ_{1} and ρ_{-1}=1-ρ_{1}, where v is the speed. We exploit the fact that the moment-generating functions with and without resetting are related by a renewal equation, and the latter generating function can be calculated by solving a corresponding Feynman-Kac equation. This allows us to numerically locate in Laplace space the largest real pole of the moment-generating function with resetting, and thus derive a large deviation principle (LDP) for the occupation time probability density using the Gartner-Ellis theorem. We explore how the LDP depends on the switching rate α of the velocity state, the resetting rate r, and the probability ρ_{1}. First, we show that the corresponding LDP for a Brownian particle with resetting is recovered in the fast switching limit α→∞. We then consider the case of a finite switching rate. In particular, we investigate how a directional bias in the resetting protocol (ρ_{1}≠0.5) skews the LDP rate function so that its minimum is shifted away from the expected fractional occupation time of one-half. The degree of shift increases with r and decreases with α.
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Affiliation(s)
- Paul C Bressloff
- Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA
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27
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Villa-Torrealba A, Chávez-Raby C, de Castro P, Soto R. Run-and-tumble bacteria slowly approaching the diffusive regime. Phys Rev E 2020; 101:062607. [PMID: 32688514 DOI: 10.1103/physreve.101.062607] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacements. Moreover, the excess kurtosis can assume large positive values. In model (ii) it is possible for some distributions of tumbling angles that the MSD reaches a linear time dependence but, still, the dynamics remains non-Gaussian for long times. This is also the case in model (iii) for small rotational diffusivity. For all models, the long-time diffusion coefficients are also obtained. The theoretical approach, which relies on eigenvalue and angular Fourier expansions of the van Hove function, is in excellent agreement with the simulations.
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Affiliation(s)
- Andrea Villa-Torrealba
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Cristóbal Chávez-Raby
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Pablo de Castro
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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28
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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: 6] [Impact Index Per Article: 1.5] [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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29
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Banerjee T, Majumdar SN, Rosso A, Schehr G. Current fluctuations in noninteracting run-and-tumble particles in one dimension. Phys Rev E 2020; 101:052101. [PMID: 32575200 DOI: 10.1103/physreve.101.052101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 03/30/2020] [Indexed: 06/11/2023]
Abstract
We present a general framework to study the distribution of the flux through the origin up to time t, in a noninteracting one-dimensional system of particles with a step initial condition with a fixed density ρ of particles to the left of the origin. We focus principally on two cases: (i) particles undergoing diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution for both the annealed and the quenched initial conditions, for passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean μ(t) that we compute exactly in terms of the Green's function of the single-particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large-deviation form at large times, P_{qu}(Q,t)∼exp[-ρv_{0}γt^{2}ψ_{RTP}(Q/ρv_{0}t)], where γ is the rate of tumbling and v_{0} is the ballistic speed between two successive tumblings. In this paper, we compute the rate function ψ_{RTP}(q) and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time t, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, ∼exp(-csqrt[t]), where the constant c can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte Carlo method.
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Affiliation(s)
- Tirthankar Banerjee
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
- Instituut voor Theoretische Fysica, KU Leuven, 3001 Heverlee, Belgium
| | - Satya N Majumdar
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Alberto Rosso
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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Abstract
We confine a dense suspension of motile Escherichia coli inside a spherical droplet in a water-in-oil emulsion, creating a "bacterially" propelled droplet. We show that droplets move in a persistent random walk, with a persistence time τ∼ 0.3 s, a long-time diffusion coefficient D∼ 0.5 μm2 s-1, and an average instantaneous speed V∼ 1.5 μm s-1 when the bacterial suspension is at the maximum studied concentration. Several droplets are analyzed, varying the drop radius and bacterial concentration. We show that the persistence time, diffusion coefficient and average speed increase with the bacterial concentration inside the drop, but are largely independent of the droplet size. By measuring the turbulent-like motion of the bacteria inside the drop, we demonstrate that the mean velocity of the bacteria near the bottom of the drop, which is separated from a glass substrate by a thin lubrication oil film, is antiparallel to the instantaneous velocity of the drop. This suggests that the driving mechanism is a slippery rolling of the drop over the substrate, caused by the collective motion of the bacteria. Our results show that microscopic organisms can transfer useful mechanical energy to their confining environment, opening the way to the assembly of mesoscopic motors composed of microswimmers.
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Affiliation(s)
- Gabriel Ramos
- Departamento de Física, FCFM, Universidad de Chile, Av. Blanco Encalada 2008, Santiago, Chile.
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31
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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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Angelani L, Garra R. Run-and-tumble motion in one dimension with space-dependent speed. Phys Rev E 2019; 100:052147. [PMID: 31869950 DOI: 10.1103/physreve.100.052147] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Indexed: 11/07/2022]
Abstract
We consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case.
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Affiliation(s)
- L Angelani
- ISC-CNR, Institute for Complex Systems, Piazzale Aldo Moro 2, 00185 Rome, Italy.,Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - R Garra
- Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
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Basu U, Majumdar SN, Rosso A, Schehr G. Long-time position distribution of an active Brownian particle in two dimensions. Phys Rev E 2019; 100:062116. [PMID: 31962395 DOI: 10.1103/physreve.100.062116] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Indexed: 06/10/2023]
Abstract
We study the late-time dynamics of a single active Brownian particle in two dimensions with speed v_{0} and rotation diffusion constant D_{R}. We show that at late times t≫D_{R}^{-1}, while the position probability distribution P(x,y,t) in the x-y plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when sqrt[x^{2}+y^{2}]∼v_{0}t. In this regime, the distribution admits a large deviation form, P(x,y,t)∼exp{-tD_{R}Φ[sqrt[x^{2}+y^{2}]/(v_{0}t)]}, where we compute the rate function Φ(z) analytically and also numerically using an importance sampling method. We show that the rate function Φ(z), encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution P_{stat}(x,y) depends explicitly on the activity parameter D_{R}^{-1} and undergoes a crossover, as D_{R} increases, from a ring shape in the strongly active limit (D_{R}→0) to a Gaussian shape in the strongly passive limit (D_{R}→∞).
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Affiliation(s)
- Urna Basu
- Raman Research Institute, Bengaluru 560080, India
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Grégory Schehr
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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Lavergne FA, Wendehenne H, Bäuerle T, Bechinger C. Group formation and cohesion of active particles with visual perception-dependent motility. Science 2019; 364:70-74. [PMID: 30948548 DOI: 10.1126/science.aau5347] [Citation(s) in RCA: 94] [Impact Index Per Article: 18.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2018] [Accepted: 03/12/2019] [Indexed: 12/29/2022]
Abstract
Group formation in living systems typically results from a delicate balance of repulsive, aligning, and attractive interactions. We found that a mere motility change of the individuals in response to the visual perception of their peers induces group formation and cohesion. We tested this principle in a real system of active particles whose motilities are controlled by an external feedback loop. For narrow fields of view, individuals gathered into cohesive nonpolarized groups without requiring active reorientations. For wider fields of view, cohesion could be achieved by lowering the response threshold. We expect this motility-induced cohesion mechanism to be relevant not only for the self-organization of living systems, but also for the design of robust and scalable autonomous systems.
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Affiliation(s)
| | - Hugo Wendehenne
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany
| | - Tobias Bäuerle
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany
| | - Clemens Bechinger
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany.
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Invariance properties of bacterial random walks in complex structures. Nat Commun 2019; 10:2442. [PMID: 31164651 PMCID: PMC6547659 DOI: 10.1038/s41467-019-10455-y] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Accepted: 05/09/2019] [Indexed: 11/30/2022] Open
Abstract
Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientations and speed fluctuations. This interplay of internal and external noise sources gives rise to a complex dynamical behavior that can be strongly sensitive to details and hard to model quantitatively. In striking contrast to this general picture we show that the mean residence time of swimming bacteria inside artificial complex microstructures is quantitatively predicted by a generic invariance property of random walks. We find that while external shape and internal disorder have dramatic effects on the distributions of path lengths and residence times, the corresponding mean values are constrained by the sole free surface to perimeter ratio. As a counterintuitive consequence, bacteria escape faster from structures with higher density of obstacles due to the lower accessible surface. It has been previously shown theoretically that the average path length of random walks inside a closed domain is invariant. Here the authors demonstrate that this invariance property can be used to predict the mean residence time of swimming bacteria exploring structured micro-environments.
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36
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Dhar A, Kundu A, Majumdar SN, Sabhapandit S, Schehr G. Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties. Phys Rev E 2019; 99:032132. [PMID: 30999430 DOI: 10.1103/physreve.99.032132] [Citation(s) in RCA: 60] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Indexed: 06/09/2023]
Abstract
We study the dynamics of a one-dimensional run-and-tumble particle subjected to confining potentials of the type V(x)=α|x|^{p}, with p>0. The noise that drives the particle dynamics is telegraphic and alternates between ±1 values. We show that the stationary probability density P(x) has a rich behavior in the (p,α) plane. For p>1, the distribution has a finite support in [x_{-},x_{+}] and there is a critical line α_{c}(p) that separates an activelike phase for α>α_{c}(p) where P(x) diverges at x_{±}, from a passivelike phase for α<α_{c}(p) where P(x) vanishes at x_{±}. For p<1, the stationary density P(x) collapses to a delta function at the origin, P(x)=δ(x). In the marginal case p=1, we show that, for α<α_{c}, the stationary density P(x) is a symmetric exponential, while for α>α_{c}, it again is a delta function P(x)=δ(x). For the harmonic case p=2, we obtain exactly the full time-dependent distribution P(x,t), which allows us to study how the system relaxes to its stationary state. In addition, for this p=2 case, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.
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Affiliation(s)
- Abhishek Dhar
- International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
| | - Anupam Kundu
- International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
| | - Satya N Majumdar
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | | | - Grégory Schehr
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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37
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Belan S, Kardar M. Pair dispersion in dilute suspension of active swimmers. J Chem Phys 2019; 150:064907. [PMID: 30770005 DOI: 10.1063/1.5081006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in a dramatic increase in diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. Although each tracer is subject to strong fluctuations resulting in large absolute diffusivity, the small-scale relative dispersion is suppressed due to the correlations in fluid velocity which are relevant when the inter-tracer separation is below the persistence length of the swimmer's motion. Our results suggest that the reorientation of swimming direction plays an important role in biological mixing and should be accounted in the design of potential active matter devices capable of effective fluid mixing at microscale.
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Affiliation(s)
- Sergey Belan
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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38
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Ekiel-Jeżewska M, Boniecki R, Bukowicki M, Gruca M. Stokes velocity generated by a point force in various geometries. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:120. [PMID: 30327947 DOI: 10.1140/epje/i2018-11727-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Accepted: 09/06/2018] [Indexed: 06/08/2023]
Abstract
In this short review, we visualize the fluid velocity generated by a point force close to a plane free surface or a plane rigid wall. We present separately contributions from all the multipoles which form the corresponding classical systems of images. Such graphical images might be useful in the theoretical and numerical modeling of the dynamics of micro-objects moving close to an interface.
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Affiliation(s)
- Maria Ekiel-Jeżewska
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106, Warsaw, Poland.
| | - Robert Boniecki
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106, Warsaw, Poland
| | - Marek Bukowicki
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106, Warsaw, Poland
| | - Marta Gruca
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106, Warsaw, Poland
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39
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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: 54] [Impact Index Per Article: 9.0] [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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40
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Liang X, Lu N, Chang LC, Nguyen TH, Massoudieh A. Evaluation of bacterial run and tumble motility parameters through trajectory analysis. JOURNAL OF CONTAMINANT HYDROLOGY 2018; 211:26-38. [PMID: 29606374 DOI: 10.1016/j.jconhyd.2018.03.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2017] [Revised: 02/03/2018] [Accepted: 03/02/2018] [Indexed: 06/08/2023]
Abstract
In this paper, a method for extraction of the behavior parameters of bacterial migration based on the run and tumble conceptual model is described. The methodology is applied to the microscopic images representing the motile movement of flagellated Azotobacter vinelandii. The bacterial cells are considered to change direction during both runs and tumbles as is evident from the movement trajectories. An unsupervised cluster analysis was performed to fractionate each bacterial trajectory into run and tumble segments, and then the distribution of parameters for each mode were extracted by fitting mathematical distributions best representing the data. A Gaussian copula was used to model the autocorrelation in swimming velocity. For both run and tumble modes, Gamma distribution was found to fit the marginal velocity best, and Logistic distribution was found to represent better the deviation angle than other distributions considered. For the transition rate distribution, log-logistic distribution and log-normal distribution, respectively, was found to do a better job than the traditionally agreed exponential distribution. A model was then developed to mimic the motility behavior of bacteria at the presence of flow. The model was applied to evaluate its ability to describe observed patterns of bacterial deposition on surfaces in a micro-model experiment with an approach velocity of 200 μm/s. It was found that the model can qualitatively reproduce the attachment results of the micro-model setting.
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Affiliation(s)
- Xiaomeng Liang
- Civil Engineering, The Catholic University of America, Washington, DC, USA
| | - Nanxi Lu
- Civil and Environmental Engineering, Northwestern University, Evanston, IL, USA
| | - Lin-Ching Chang
- Department of Computer Science, The Catholic University of America, Washington, DC, USA
| | - Thanh H Nguyen
- Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Arash Massoudieh
- Civil Engineering, The Catholic University of America, Washington, DC, USA.
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41
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Memory-less response and violation of the fluctuation-dissipation theorem in colloids suspended in an active bath. Sci Rep 2017; 7:17588. [PMID: 29242505 PMCID: PMC5730581 DOI: 10.1038/s41598-017-17900-2] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 12/01/2017] [Indexed: 12/02/2022] Open
Abstract
We investigate experimentally and numerically the stochastic dynamics and the time-dependent response of colloids subject to a small external perturbation in a dense bath of motile E. coli bacteria. The external field is a magnetic field acting on a superparamagnetic microbead suspended in an active medium. The measured linear response reveals an instantaneous friction kernel despite the complexity of the bacterial bath. By comparing the mean squared displacement and the response function we detect a clear violation of the fluctuation dissipation theorem.
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42
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Guccione G, Pimponi D, Gualtieri P, Chinappi M. Diffusivity of E. coli-like microswimmers in confined geometries: The role of the tumbling rate. Phys Rev E 2017; 96:042603. [PMID: 29347505 DOI: 10.1103/physreve.96.042603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2017] [Indexed: 11/07/2022]
Abstract
We analyzed the effect of confinement on the effective diffusion of a run-and-tumble E. coli-like flagellated microswimmer. We used a simulation protocol where the run phases are obtained via a fully resolved swimming problem, i.e., Stokes equations for the fluid coupled with rigid-body dynamics for the microorganism, while tumbles and collisions with the walls are modeled as random reorientation of the microswimmer. For weak confinement, the swimmer is trapped in circular orbits close to the solid walls. In this case, optimal diffusivity is observed when the tumbling frequency is comparable with the angular velocity of the stable orbits. For strong confinement, stable circular orbits disappear and the diffusion coefficient monotonically decreases with the tumbling rate. Our findings are generic and can be potentially applied to other natural or artificial chiral microswimmers that follow circular trajectories close to an interface or in confined geometries.
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Affiliation(s)
- Giorgia Guccione
- Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italia
| | - Daniela Pimponi
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, via Eudossiana 18, 00184 Roma, Italia
| | - Paolo Gualtieri
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, via Eudossiana 18, 00184 Roma, Italia
| | - Mauro Chinappi
- Dipartimento di Ingegneria Industriale, Università di Roma Tor Vergata, via del Politecnico 1, 00133 Roma, Italia
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43
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Morin A, Lopes Cardozo D, Chikkadi V, Bartolo D. Diffusion, subdiffusion, and localization of active colloids in random post lattices. Phys Rev E 2017; 96:042611. [PMID: 29347592 DOI: 10.1103/physreve.96.042611] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2017] [Indexed: 06/07/2023]
Abstract
Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive to subdiffusive to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids. In contrast, the localization transition stems solely from excluded-volume interactions and occurs at the void-percolation threshold. Within this critical scenario, equivalent to that of the random Lorentz gas, genuine asymptotic subdiffusion is found only at the critical density where the motile particles explore a fractal maze.
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Affiliation(s)
- Alexandre Morin
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - David Lopes Cardozo
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Vijayakumar Chikkadi
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Denis Bartolo
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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44
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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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45
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Mathijssen AJTM, Doostmohammadi A, Yeomans JM, Shendruk TN. Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films. J R Soc Interface 2016; 13:20150936. [PMID: 26841796 DOI: 10.1098/rsif.2015.0936] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Biological flows over surfaces and interfaces can result in accumulation hotspots or depleted voids of microorganisms in natural environments. Apprehending the mechanisms that lead to such distributions is essential for understanding biofilm initiation. Using a systematic framework, we resolve the dynamics and statistics of swimming microbes within flowing films, considering the impact of confinement through steric and hydrodynamic interactions, flow and motility, along with Brownian and run-tumble fluctuations. Micro-swimmers can be peeled off the solid wall above a critical flow strength. However, the interplay of flow and fluctuations causes organisms to migrate back towards the wall above a secondary critical value. Hence, faster flows may not always be the most efficacious strategy to discourage biofilm initiation. Moreover, we find run-tumble dynamics commonly used by flagellated microbes to be an intrinsically more successful strategy to escape from boundaries than equivalent levels of enhanced Brownian noise in ciliated organisms.
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Affiliation(s)
| | - Amin Doostmohammadi
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
| | - Tyler N Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
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Intermediate scattering function of an anisotropic active Brownian particle. Sci Rep 2016; 6:36702. [PMID: 27830719 PMCID: PMC5378927 DOI: 10.1038/srep36702] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2016] [Accepted: 10/19/2016] [Indexed: 11/08/2022] Open
Abstract
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.
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47
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Rupprecht JF, Bénichou O, Voituriez R. Optimal search strategies of run-and-tumble walks. Phys Rev E 2016; 94:012117. [PMID: 27575087 DOI: 10.1103/physreve.94.012117] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Indexed: 06/06/2023]
Abstract
The run-and-tumble walk, consisting of randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a two- or three-dimensional spherical confinement. We find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions (exponential, power-law, deterministic). Our result stands in sharp contrast to the pure ballistic motion, which is predicted to be the optimal search strategy in the case of Poisson-distributed targets.
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Affiliation(s)
- Jean-François Rupprecht
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, 4 Place Jussieu, Paris, France
- Mechanobiology Institute, National University of Singapore, 5A Engineering Drive 1, 117411, Singapore
| | - Olivier Bénichou
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, 4 Place Jussieu, Paris, France
| | - Raphael Voituriez
- Sorbonne Universités, UPMC Université Paris 06, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, 4 Place Jussieu, Paris, France
- Sorbonne Universités, UPMC Université Paris 06, Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, Paris, France
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48
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Chen YF, Wei HH, Sheng YJ, Tsao HK. Superdiffusion in dispersions of active colloids driven by an external field and their sedimentation equilibrium. Phys Rev E 2016; 93:042611. [PMID: 27176356 DOI: 10.1103/physreve.93.042611] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2016] [Indexed: 11/07/2022]
Abstract
The diffusive behaviors of active colloids with run-and-tumble movement are explored by dissipative particle dynamics simulations for self-propelled particles (force dipole) and external field-driven particles (point force). The self-diffusion of tracers (solvent) is investigated as well. The influences of the active force, run time, and concentration associated with active particles are studied. For the system of self-propelled particles, the normal diffusion is observed for both active particles and tracers. The diffusivity of the former is significantly greater than that of the latter. For the system of field-driven particles, the superdiffusion is seen for both active particles and tracers. In contrast, it is found that the anomalous diffusion exponent of the former is slightly less than that of the latter. The anomalous diffusion is caused by the many-body, long-range hydrodynamic interactions. In spite of the superdiffusion, the sedimentation equilibrium of field-driven particles can be acquired and the density profile is still exponentially decayed. The sedimentation length of field-driven particles is always greater than that of self-propelled particles.
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Affiliation(s)
- Yen-Fu Chen
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China
| | - Hsien-Hung Wei
- Department of Chemical Engineering, National Cheng Kung University, Tainan, Taiwan 701, Republic of China
| | - Yu-Jane Sheng
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China
| | - Heng-Kwong Tsao
- Department of Physics, National Central University, Jhongli, Taiwan 320, Republic of China.,Department of Chemical and Materials Engineering, National Central University, Jhongli, Taiwan 320, Republic of China
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49
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Maggi C, Marconi UMB, Gnan N, Di Leonardo R. Multidimensional stationary probability distribution for interacting active particles. Sci Rep 2015; 5:10742. [PMID: 26021260 PMCID: PMC4448265 DOI: 10.1038/srep10742] [Citation(s) in RCA: 107] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2015] [Accepted: 04/29/2015] [Indexed: 11/13/2022] Open
Abstract
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the “pressure” generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.
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Affiliation(s)
- Claudio Maggi
- Dipartimento di Fisica, Universit`a di Roma "Sapienza", Roma, I-00185, Italy
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Universit`a di Camerino, Via Madonna delle Carceri, Camerino, INFN Perugia, 62032, Italy
| | - Nicoletta Gnan
- CNR-ISC, UOS Sapienza, P.le A. Moro2, Roma, I-00185, Italy
| | - Roberto Di Leonardo
- 1] Dipartimento di Fisica, Universit`a di Roma "Sapienza", Roma, I-00185, Italy [2] CNR-IMIP, UOS Roma, Dipartimento di Fisica Universit`a Sapienza, Roma, I-00185, Italy
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50
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Xiao S, Wang Z, Chen HY, Sheng YJ, Tsao HK. Diffusion and surface excess of a confined nanoswimmer dispersion. J Chem Phys 2014; 141:184902. [DOI: 10.1063/1.4901117] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Song Xiao
- Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650500, China
- Department of Chemical and Materials Engineering, National Central University, Jhongli 320, Taiwan
| | - Zhengjia Wang
- Department of Chemical and Materials Engineering, National Central University, Jhongli 320, Taiwan
| | - Hsuan-Yi Chen
- Department of Physics, National Central University, Jhongli 320, Taiwan
| | - Yu-Jane Sheng
- Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan
| | - Heng-Kwong Tsao
- Department of Chemical and Materials Engineering, National Central University, Jhongli 320, Taiwan
- Department of Physics, National Central University, Jhongli 320, Taiwan
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