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Schiltz-Rouse E, Row H, Mallory SA. Kinetic temperature and pressure of an active Tonks gas. Phys Rev E 2023; 108:064601. [PMID: 38243499 DOI: 10.1103/physreve.108.064601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 11/06/2023] [Indexed: 01/21/2024]
Abstract
Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.
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Affiliation(s)
- Elijah Schiltz-Rouse
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hyeongjoo Row
- Department of Chemical and Biomolecular Engineering, UC Berkeley, Berkeley, California 94720, USA
| | - Stewart A Mallory
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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2
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Schweers S, Antonov AP, Ryabov A, Maass P. Scaling laws for single-file diffusion of adhesive particles. Phys Rev E 2023; 107:L042102. [PMID: 37198860 DOI: 10.1103/physreve.107.l042102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 03/29/2023] [Indexed: 05/19/2023]
Abstract
Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.
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Affiliation(s)
- Sören Schweers
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Alexander P Antonov
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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3
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Dessup T, Coste C, Saint Jean M. Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation. Phys Rev E 2018; 97:052134. [PMID: 29906851 DOI: 10.1103/physreve.97.052134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2018] [Indexed: 06/08/2023]
Abstract
A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [h_{C1},h_{C2}]. We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits h_{C1} and h_{C2}, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.
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Affiliation(s)
- Tommy Dessup
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
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4
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Dessup T, Coste C, Saint Jean M. Enhancement of Brownian motion for a chain of particles in a periodic potential. Phys Rev E 2018; 97:022103. [PMID: 29548165 DOI: 10.1103/physreve.97.022103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 11/07/2022]
Abstract
The transport of particles in very confined channels in which single file diffusion occurs has been largely studied in systems where the transverse confining potential is smooth. However, in actual physical systems, this potential may exhibit both static corrugations and time fluctuations. Some recent results suggest the important role played by this nonsmoothness of the confining potential. In particular, quite surprisingly, an enhancement of the Brownian motion of the particles has been evidenced in these kinds of systems. We show that this enhancement results from the commensurate effects induced by the underlying potential on the vibrational spectra of the chain of particles, and from the effective temperature associated with its time fluctuations. We will restrict our derivation to the case of low temperatures for which the mean squared displacement of the particles remains smaller than the potential period.
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Affiliation(s)
- Tommy Dessup
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris-Diderot (Paris 7), 75205 Paris Cedex 13, France
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5
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Taloni A, Flomenbom O, Castañeda-Priego R, Marchesoni F. Single file dynamics in soft materials. SOFT MATTER 2017; 13:1096-1106. [PMID: 28119987 DOI: 10.1039/c6sm02570f] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.
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Affiliation(s)
- Alessandro Taloni
- Center for Complexity & Biosystems, Physics Department, University of Milan "La Statale", Via Giovanni Celoria 16, 20133 Milano, Italy and CNR-ISC - Center for Complex Systems, Via dei Taurini 19, 00185, Roma, Italy.
| | | | - Ramón Castañeda-Priego
- Division of Science and Engineering, University of Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150, Leon, Gto., Mexico
| | - Fabio Marchesoni
- Dipartimento di Fisica, Universitá di Camerino, I-62032 Camerino, Italy.
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6
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Dessup T, Coste C, Saint Jean M. Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system. Phys Rev E 2016; 94:012217. [PMID: 27575133 DOI: 10.1103/physreve.94.012217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Indexed: 06/06/2023]
Abstract
We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.
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Affiliation(s)
- Tommy Dessup
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire Matière et Systèmes Complexes, UMR No. 7057, CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
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7
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Dessup T, Maimbourg T, Coste C, Saint Jean M. Linear instability of a zigzag pattern. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022908. [PMID: 25768570 DOI: 10.1103/physreve.91.022908] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 06/04/2023]
Abstract
Interacting particles confined in a quasi-one-dimensional channel are physical systems which display various equilibrium patterns according to the interparticle interaction and the transverse confinement potential. Depending on the confinement, the particles may be distributed along a straight line, in a staggered row (zigzag), or in a configuration in which the linear and zigzag phases coexist (distorted zigzag). In order to clarify the conditions of existence of each configuration, we have studied the linear stability of the zigzag pattern. We find an acoustic transverse mode that destabilizes the zigzag configuration for short-range interaction potentials, and we calculate the interaction range above which this instability disappears. In particular, we recover the unconditional stability of zigzag patterns for Coulomb interactions. We show that the domain of existence for the distorted zigzag patterns is accurately described by our linear stability analysis. We also emphasize the complexity of finite size effects. Last, we provide a criterion for the onset of instability in the thermodynamic limit and propose a biphasic model that explains some characteristics of the distorted zigzag patterns.
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Affiliation(s)
- Tommy Dessup
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Thibaud Maimbourg
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
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8
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Coste C, Delfau JB, Saint Jean M. Longitudinal and Transverse Single File Diffusion in Quasi-1D Systems. ACTA ACUST UNITED AC 2014. [DOI: 10.1142/s1793048014400025] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review our recent results on Single File Diffusion (SFD) of a chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We exhibit new behaviors specifically associated to small systems and to small damping. The fluctuation dynamics is explained by the decomposition of the particles' motion in the normal modes of the chain. For longitudinal fluctuations, we emphasize the relevance of the soft mode linked to the translational invariance of the system to the long time SFD behavior. We show that close to the zigzag threshold, the transverse fluctuations also exhibit the SFD behavior, characterized by a mean square displacement that increases as the square root of time. This cannot be explained by the single file ordering, and the SFD behavior results from the strong correlation of the transverse displacements of neighbouring particles near the bifurcation. Extending our analytical modelization, we demonstrate the existence of this subdiffusive regime near the zigzag transition, in the thermodynamic limit. The zigzag transition is a supercritical pitchfork bifurcation, and we show that the transverse SFD behavior is closely linked to the vanishing of the frequency of the zigzag transverse mode at the bifurcation threshold. [Formula: see text] Special Issue Comments: This article presents mathematical results on the dynamics in files with longitudinal movements. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics,28 expanding files,63 and files with force and advanced formulations.29
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Affiliation(s)
- Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Jean-Baptiste Delfau
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
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9
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Herrera-Velarde S, Euán-Díaz EC, Córdoba-Valdés F, Castañeda-Priego R. Hydrodynamic correlations in three-particle colloidal systems in harmonic traps. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:325102. [PMID: 23838468 DOI: 10.1088/0953-8984/25/32/325102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report on the hydrodynamic correlations between colloids immersed in a low Reynolds number fluid. We consider colloidal arrays composed of three particles; each colloid is trapped in a single harmonic potential and interacts with the other colloids only via hydrodynamic forces. We focus on the role of a third body in the two-body correlation functions. We give special attention to a collinear configuration of particles, although the salient features of an equilateral triangle configuration are outlined. The correlation functions are computed both by means of Brownian dynamics simulations, and by solving analytically and numerically the Langevin equation under the assumption of constant diffusion tensor; this approximation is validated through computer simulations. We explicitly show that the presence of a third body affects the auto- and cross-correlation functions and that their behaviour, in some specific conditions, can be different from that commonly seen in a two-particle system. In particular, we have found that the auto-correlation functions show a slower decay, while the cross-correlation ones exhibit a temporal shift and a weaker amplitude. Moreover, an unexpected behaviour related to a positive correlation and associated with the appearance of new dynamical modes is observed in the case of the collinear array of three particles. This interesting effect might be used to tune the degree of hydrodynamic correlation in few-body colloidal systems.
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Affiliation(s)
- Salvador Herrera-Velarde
- Subdirección de Postgrado e Investigación, Instituto Tecnológico Superior de Xalapa, Sección 5A Reserva Territorial s/n, 91096, Xalapa, Veracruz, Mexico
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10
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Lucena D, Ferreira WP, Munarin FF, Farias GA, Peeters FM. Tunable diffusion of magnetic particles in a quasi-one-dimensional channel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012307. [PMID: 23410331 DOI: 10.1103/physreve.87.012307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Revised: 12/04/2012] [Indexed: 06/01/2023]
Abstract
The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.
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Affiliation(s)
- D Lucena
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil.
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11
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Saxton MJ. Wanted: a positive control for anomalous subdiffusion. Biophys J 2012; 103:2411-22. [PMID: 23260043 DOI: 10.1016/j.bpj.2012.10.038] [Citation(s) in RCA: 94] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Revised: 09/23/2012] [Accepted: 10/10/2012] [Indexed: 11/25/2022] Open
Abstract
Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion. Anomalous subdiffusion measurements would be strengthened by an experimental standard, particularly one able to cross-calibrate the different types of measurements. Criteria for a calibration standard are proposed. First, diffusion must be anomalous over the length and timescales of the different measurements. The length-scale is fundamental; the time scale can be adjusted through the viscosity of the medium. Second, the standard must be theoretically well understood, with a known anomalous subdiffusion exponent, ideally readily tunable. Third, the standard must be simple, reproducible, and independently characterizable (by, for example, electron microscopy for nanostructures). Candidate experimental standards are evaluated, including obstructed lipid bilayers; aqueous systems obstructed by nanopillars; a continuum percolation system in which a prescribed fraction of randomly chosen obstacles in a regular array is ablated; single-file diffusion in pores; transient anomalous subdiffusion due to binding of particles in arrays such as transcription factors in randomized DNA arrays; and computer-generated physical trajectories.
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Affiliation(s)
- Michael J Saxton
- Department of Biochemistry and Molecular Medicine, University of California at Davis, Davis, California, USA.
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12
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Euán-Díaz EC, Misko VR, Peeters FM, Herrera-Velarde S, Castañeda-Priego R. Single-file diffusion in periodic energy landscapes: the role of hydrodynamic interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031123. [PMID: 23030882 DOI: 10.1103/physreve.86.031123] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2012] [Indexed: 06/01/2023]
Abstract
We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.
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Affiliation(s)
- E C Euán-Díaz
- Division of Sciences and Engineering, University of Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico
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13
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Delfau JB, Coste C, Saint Jean M. Single-file diffusion of particles in a box: transient behaviors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061111. [PMID: 23005055 DOI: 10.1103/physreve.85.061111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2012] [Revised: 05/03/2012] [Indexed: 06/01/2023]
Abstract
We consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given.
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Affiliation(s)
- Jean-Baptiste Delfau
- Laboratoire Matière et Systèmes Complexes, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 7057, Université Paris Diderot, Paris, France
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14
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Carvalho JCN, Nelissen K, Ferreira WP, Farias GA, Peeters FM. Diffusion in a quasi-one-dimensional system on a periodic substrate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021136. [PMID: 22463181 DOI: 10.1103/physreve.85.021136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2011] [Revised: 12/21/2011] [Indexed: 05/31/2023]
Abstract
The diffusion of charged particles interacting through a repulsive Yukawa potential, exp(-r/λ)/r, confined by a parabolic potential in the y direction and subjected to a periodic substrate potential in the x direction is investigated. Langevin dynamic simulations are used to investigate the effect of the particle density, the amplitude of the periodic substrate, and the range of the interparticle interaction potential on the diffusive behavior of the particles. We found that in general the diffusion is suppressed with increasing the amplitude of the periodic potential, but for specific values of the strength of the substrate potential a remarkable increase of the diffusion is found with increasing the periodic potential amplitude. In addition, we found a strong dependence of the diffusion on the specific arrangement of the particles, e.g., single-chain versus multichain configuration. For certain particle configurations, a reentrant behavior of the diffusion is found as a function of the substrate strength due to structural transitions in the ordering of the particles.
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Affiliation(s)
- J C N Carvalho
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil.
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15
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Mersch E, Vandewalle N. Antiphase synchronization of electrically shaken conducting beads. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061301. [PMID: 22304087 DOI: 10.1103/physreve.84.061301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2010] [Revised: 10/20/2011] [Indexed: 05/31/2023]
Abstract
When a spherical conducting bead is placed in an electrode, it experiences an electric force. In a plane capacitor, it can undergo a periodic bouncing between the electrodes. Using a fast video camera, we measured the acceleration of the bead and the period of its motion as a function of the applied voltage. A mathematical model based on the hypothesis of electrostatic equilibrium is proposed to describe the dynamics of the system. We observe a stabilization of the trajectories: A bead bouncing between two electrodes tends to oscillate on a quasivertical trajectory, whatever its initial horizontal velocity. When two identical beads are placed together in a capacitor, they oscillate at the same frequency and an antiphase synchronization effect occurs. We propose a simple mechanism based on a Kuramoto-like model to explain it.
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Affiliation(s)
- E Mersch
- Group for Research and Applications in Statistical Physics, Institut de Physique B5, Université de Liège, B-4000 Liège, Belgium
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16
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Delfau JB, Coste C, Saint Jean M. Single-file diffusion of particles with long-range interactions: damping and finite-size effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011101. [PMID: 21867107 DOI: 10.1103/physreve.84.011101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2011] [Indexed: 05/31/2023]
Abstract
We study the single file diffusion of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long-ranged interactions and arbitrary damping. We present simulations that exhibit new behaviors specifically associated with systems of small numbers of particles and with small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles' motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations and provides convincing estimates of the crossover times between those regimes.
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Affiliation(s)
- Jean-Baptiste Delfau
- Laboratoire Matiere et Systemes Complexes, UMR CNRS 7057 et Université Paris Diderot-Paris 7, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
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17
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Reichhardt C, Bairnsfather C, Reichhardt CJO. Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with Yukawa interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061404. [PMID: 21797361 DOI: 10.1103/physreve.83.061404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2010] [Revised: 04/14/2011] [Indexed: 05/31/2023]
Abstract
We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Bustingorry S, Kolton AB. Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium. PAPERS IN PHYSICS 2010. [DOI: 10.4279/pip.020008] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
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19
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Herrera-Velarde S, Zamudio-Ojeda A, Castañeda-Priego R. Ordering and single-file diffusion in colloidal systems. J Chem Phys 2010; 133:114902. [DOI: 10.1063/1.3479003] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Delfau JB, Coste C, Even C, Saint Jean M. Single-file diffusion of interacting particles in a finite-sized channel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031201. [PMID: 21230062 DOI: 10.1103/physreve.82.031201] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2010] [Revised: 07/06/2010] [Indexed: 05/30/2023]
Abstract
We study the dynamics of charged macroscopic particles (millimetric steel balls) confined in a linear channel of finite length, sufficiently narrow to avoid particles crossing. We show that their individual response to thermal fluctuations strongly depends either on their position in the channel or the local potential they experience. Three different dynamical regimes are identified. At small times, a "free regime" takes place, with the outermost particles exhibiting the highest diffusion coefficient. This effect results from an "echo" of the thermal fluctuations reflected by the channel wall. Then, forbidden crossing induces a correlated regime similar to single file diffusion. Surprisingly, the corresponding mobility increases with the local potential. Lastly, the finite length of the channel induces the saturation of fluctuations. We show that those behaviors may be described heuristically with the help of models for N hard-core interacting particles diffusing in a finite channel of length L, provided that we replace the uniform interparticle distance L/N by a characteristic distance (k(B)T/K)(1/2) built upon the temperature T and the stiffness K of the local potential. It provides a very satisfactory estimate for the fluctuations sizes, whereas they are greatly overestimated assuming hard-core interactions.
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Affiliation(s)
- J B Delfau
- Laboratoire MSC, UMR CNRS 7057 et Université Paris Diderot-Paris7 Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
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