1
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Gerry M, Segal D. Random walks on modular chains: Detecting structure through statistics. Phys Rev E 2023; 108:024135. [PMID: 37723810 DOI: 10.1103/physreve.108.024135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 08/04/2023] [Indexed: 09/20/2023]
Abstract
We study kinetic transport through one-dimensional modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it depends only on global, structural-averaged properties. However, by examining high-order cumulants characterizing the kinetics, we reveal information on the degree of inhomogeneity of blocks and the size of repeating units in the network. Specifically, in unbiased diffusion, the kurtosis is the first transport coefficient that exposes structural information, whereas in biased chains, the diffusion coefficient already reveals structural motifs. Nevertheless, this latter dependence is weak, and it disappears at both low and high biasing. Our study demonstrates that high-order moments of the population distribution over sites provide information about the network structure that is not captured by the first moment (mean velocity) alone. These results are useful towards deciphering mechanisms and determining architectures underlying long-range charge transport in biomolecules and biological and chemical reaction networks.
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Affiliation(s)
- Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
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2
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Melkani A, Patapoff A, Paulose J. Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra. Phys Rev E 2023; 107:014501. [PMID: 36797938 DOI: 10.1103/physreve.107.014501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/06/2022] [Indexed: 01/09/2023]
Abstract
We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer conformations are described by a mapping to a quantum system with a non-Hermitian Hamiltonian and with fermionic statistics generated by noncrossing interactions among polymers. Using molecular dynamics simulations and analytical calculations, we identify a localized and a delocalized phase of the polymer conformations, separated by a delocalization transition which corresponds (in the quantum description) to the breakdown of a band insulator when driven by an imaginary vector potential. We calculate the average tilt of the many-body system, at arbitrary shear values and filling density of polymer chains, in terms of the complex-valued non-Hermitian band structure. We find the critical shear value, the localization length, and the critical exponent by which the shear modulus diverges in terms of the branch points (exceptional points) in the band structure at which the bandgap closes. We also investigate the combined effects of non-Hermitian delocalization and localization due to both periodicity and disorder, uncovering preliminary evidence that while disorder favors localization at high values, it encourages delocalization at lower values.
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Affiliation(s)
- Abhijeet Melkani
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA.,Institute for Fundamental Science and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | | | - Jayson Paulose
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA.,Institute for Fundamental Science and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
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3
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Barakat JM, Takatori SC. Enhanced dispersion in an oscillating array of harmonic traps. Phys Rev E 2023; 107:014601. [PMID: 36797955 DOI: 10.1103/physreve.107.014601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 12/13/2022] [Indexed: 06/18/2023]
Abstract
Experiment, theory, and simulation are employed to understand the dispersion of colloidal particles in a periodic array of oscillating harmonic traps generated by optical tweezers. In the presence of trap oscillation, a nonmonotonic and anisotropic dispersion is observed. Surprisingly, the stiffest traps produce the largest dispersion at a critical frequency, and the particles diffuse significantly faster in the direction of oscillation than those undergoing passive Stokes-Einstein-Sutherland diffusion. Theoretical predictions for the effective diffusivity of the particles as a function of trap stiffness and oscillation frequency are developed using generalized Taylor dispersion theory and Brownian dynamics simulations. Both theory and simulation demonstrate excellent agreement with the experiments, and reveal a "slingshot" mechanism that predicts a significant enhancement of colloidal diffusion in dynamic external fields.
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Affiliation(s)
- Joseph M Barakat
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA
| | - Sho C Takatori
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA
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4
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Spiechowicz J, Marchenko IG, Hänggi P, Łuczka J. Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond. ENTROPY (BASEL, SWITZERLAND) 2022; 25:42. [PMID: 36673183 PMCID: PMC9857877 DOI: 10.3390/e25010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/21/2022] [Accepted: 12/21/2022] [Indexed: 06/17/2023]
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Ivan G. Marchenko
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
- Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine
- Education and Research Institute of Computer Physics and Energy, Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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5
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Breoni D, Blossey R, Löwen H. Brownian particles driven by spatially periodic noise. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:18. [PMID: 35230521 PMCID: PMC8888531 DOI: 10.1140/epje/s10189-022-00176-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 02/18/2022] [Indexed: 05/07/2023]
Abstract
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.
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Affiliation(s)
- Davide Breoni
- Institut für Theoretische Physik II: Weiche Materie, Heinrich, Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany.
| | - Ralf Blossey
- University of Lille, UGSF CNRS UMR8576, 59000, Lille, France
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich, Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
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6
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López-Alamilla NJ, Jack MW, Challis KJ. Enhanced diffusion and the eigenvalue band structure of Brownian motion in tilted periodic potentials. Phys Rev E 2020; 102:042405. [PMID: 33212597 DOI: 10.1103/physreve.102.042405] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 09/22/2020] [Indexed: 11/07/2022]
Abstract
We consider enhanced diffusion for Brownian motion on a tilted periodic potential. Expressing the effective diffusion in terms of the eigenvalue band structure, we establish a connection between band gaps in the eigenspectrum and enhanced diffusion. We explain this connection for a simple cosine potential with a linear force and then generalize to more complicated potentials including one-dimensional potentials with multiple frequency components and nonseparable multidimensional potentials. We find that potentials with multiple band gaps in the eigenspectrum can lead to multiple maxima or broadening of the force-diffusion curve. These features are likely to be observable in experiments.
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Affiliation(s)
- N J López-Alamilla
- Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
| | | | - K J Challis
- Scion, Private Bag 3020, Rotorua 3046, New Zealand
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7
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Seyler SL, Pressé S. Surmounting potential barriers: Hydrodynamic memory hedges against thermal fluctuations in particle transport. J Chem Phys 2020; 153:041102. [PMID: 32752686 DOI: 10.1063/5.0013722] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Recently, trapped-particle experiments have probed the instantaneous velocity of Brownian motion revealing that, at early times, hydrodynamic history forces dominate Stokes damping. In these experiments, nonuniform particle motion is well described by the Basset-Boussinesq-Oseen (BBO) equation, which captures the unsteady Basset history force at a low Reynolds number. Building off of these results, earlier we showed that, at low temperature, BBO particles could exploit fluid inertia in order to overcome potential barriers (generically modeled as a tilted washboard), while its Langevin counter-part could not. Here, we explore the behavior of neutrally buoyant BBO particles at finite temperature for moderate Stokes damping. Remarkably, we find that the transport of particles injected into a bumpy potential with sufficiently high barriers can be completely quenched at intermediate temperatures, whereas itinerancy may be possible above and below that temperature window. This effect is present for both Langevin and BBO dynamics, though these occur over drastically different temperature ranges. Furthermore, hydrodynamic memory mitigates these effects by sustaining initial particle momentum, even in the difficult intermediate temperature regime.
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Affiliation(s)
- Sean L Seyler
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Steve Pressé
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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8
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Bao JD. Generalization of the Kubo relation for confined motion and ergodicity breakdown. Phys Rev E 2020; 101:062131. [PMID: 32688488 DOI: 10.1103/physreve.101.062131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
A time-dependent generalized Kubo relation is derived by introducing the notion of a diffusion function for a particle confined in a harmonic potential. The relation reduces to the standard Kubo relation as a special case but holds for anomalous diffusion, nonergodic processes, and bounded motion. We analyze in detail the behaviors of the diffusion and memory functions and report a generalized Stokes-Einstein relation concerning anomalous diffusion. Furthermore, we demonstrate that when a high finite-frequency cutoff is imposed on the noise spectral density, a breakdown in ergodicity accompanied by the appearance of nonstationarity in the velocity autocorrelation function occurs in forced systems. This breakdown is taken as explicit evidence for either decay-spring-memory or recovering-force effects leading to nonexponential relaxation kinematics.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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9
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Goychuk I. Fractional Hydrodynamic Memory and Superdiffusion in Tilted Washboard Potentials. PHYSICAL REVIEW LETTERS 2019; 123:180603. [PMID: 31763886 DOI: 10.1103/physrevlett.123.180603] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Indexed: 06/10/2023]
Abstract
Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effect becomes much stronger in the underdamped case due to inertial effects. What happens upon inclusion of usually neglected fractional hydrodynamics memory effects (Basset-Boussinesq frictional force), which result in a heavy algebraic tail of the velocity autocorrelation function of the potential-free diffusion making it transiently superdiffusive? Will a giant enhancement of diffusion become even stronger, and the transient superdiffusion last even longer? These are the questions that we answer in this Letter based on an accurate numerical investigation. We show that a resonancelike enhancement of normal diffusion becomes indeed much stronger and sharper. Moreover, a long-lasting transient regime of superdiffusion, including Richardson-like diffusion, ⟨δx^{2}(t)⟩∝t^{3} and ballistic supertransport, ⟨δx(t)⟩∝t^{2}, is revealed.
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Affiliation(s)
- Igor Goychuk
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
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10
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Berezhkovskii AM, Dagdug L. Biased diffusion in periodic potentials: Three types of force dependence of effective diffusivity and generalized Lifson-Jackson formula. J Chem Phys 2019; 151:131102. [PMID: 31594338 DOI: 10.1063/1.5120279] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Diffusive transport of particles in a biased periodic potential is characterized by the effective drift velocity and diffusivity, which are functions of the biasing force. We derive a simple exact expression for the effective diffusivity and use it to show that the force dependence of this quantity may be a nonmonotonic function with a maximum [as shown in the work of Reimann et al. Phys. Rev. Lett. 87, 010602 (2001) for periodic sinusoidal potential] or with a minimum, or a monotonic function. The shape of the dependence is determined by the shape of the periodic potential.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Leonardo Dagdug
- Physics Department, Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico City, Mexico
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11
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Li Y, Xu Y, Kurths J, Duan J. The influences of correlated spatially random perturbations on first passage time in a linear-cubic potential. CHAOS (WOODBURY, N.Y.) 2019; 29:101102. [PMID: 31675827 DOI: 10.1063/1.5116626] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Accepted: 09/17/2019] [Indexed: 06/10/2023]
Abstract
The influences of correlated spatially random perturbations (SRPs) on the first passage problem are studied in a linear-cubic potential with a time-changing external force driven by a Gaussian white noise. First, the escape rate in the absence of SRPs is obtained by Kramers' theory. For the random potential case, we simplify the escape rate by multiplying the escape rate of smooth potentials with a specific coefficient, which is to evaluate the influences of randomness. Based on this assumption, the escape rates are derived in two scenarios, i.e., small/large correlation lengths. Consequently, the first passage time distributions (FPTDs) are generated for both smooth and random potential cases. We find that the position of the maximal FPTD has a very good agreement with that of numerical results, which verifies the validity of the proposed approximations. Besides, with increasing the correlation length, the FPTD shifts to the left gradually and tends to the smooth potential case. Second, we investigate the most probable passage time (MPPT) and mean first passage time (MFPT), which decrease with increasing the correlation length. We also find that the variation ranges of both MPPT and MFPT increase nonlinearly with increasing the intensity. Besides, we briefly give constraint conditions to guarantee the validity of our approximations. This work enables us to approximately evaluate the influences of the correlation length of SRPs in detail, which was always ignored previously.
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Affiliation(s)
- Yongge Li
- Center for Mathematical Sciences & School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yong Xu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Jürgen Kurths
- Center for Mathematical Sciences & School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jinqiao Duan
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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12
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Akimoto T, Saito K. Exact results for first-passage-time statistics in biased quenched trap models. Phys Rev E 2019; 99:052127. [PMID: 31212478 DOI: 10.1103/physreve.99.052127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Indexed: 11/07/2022]
Abstract
We provide exact results for the mean and variance of first-passage times (FPTs) of making a directed revolution in the presence of a bias in heterogeneous quenched environments where the disorder is expressed by random traps on a ring with period L. FPT statistics are crucially affected by the disorder realization. In the large-L limit, we obtain exact formulas for the FPT statistics, which are described by the sample mean and variance for waiting times of periodically arranged traps. Furthermore, we find that these formulas are still useful for nonperiodic heterogeneous environments; i.e., the results are valid for almost all disorder realizations. Our findings are fundamentally important for the application of FPT to estimate diffusivity of a heterogeneous environment under a bias.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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13
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Akimoto T, Cherstvy AG, Metzler R. Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks. Phys Rev E 2018; 98:022105. [PMID: 30253516 DOI: 10.1103/physreve.98.022105] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2018] [Indexed: 06/08/2023]
Abstract
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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14
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Liao JJ, Zhu WJ, Ai BQ. Transport and diffusion of paramagnetic ellipsoidal particles in a rotating magnetic field. Phys Rev E 2018; 97:062151. [PMID: 30011563 DOI: 10.1103/physreve.97.062151] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2018] [Indexed: 06/08/2023]
Abstract
Transport and diffusion of paramagnetic ellipsoidal particles under the action of a rotating magnetic field are numerically investigated in a two-dimensional channel. It is found that paramagnetic ellipsoidal particles in a rotating magnetic field can be rectified in the upper-lower asymmetric channel. The transport and the effective diffusion coefficient are much more different and complicated for active particles, while they have similar behaviors and change a little when applying rotating magnetic fields of different frequencies for passive particles. For active particles, the back-and-forth rotational motion facilitates the effective diffusion coefficient and reduces the rectification, whereas the rotational motion synchronous with the magnetic field suppresses the effective diffusion coefficient and enhances the rectification. There exist optimized values of the parameters (the anisotropic degree, the amplitude and frequency of magnetic field, the self-propelled velocity, and the rotational diffusion rate) at which the average velocity and diffusion take their maximal values. Particles with different shapes, self-propelled speeds, or rotational diffusion rates will move to the opposite directions and can be separated by applying rotating magnetic fields of suitable strength and frequency. Our results can be used to separate particles, orient the particles along any direction at will during motion, and control the particle diffusion.
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Affiliation(s)
- Jing-Jing Liao
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- College of Applied Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Wei-Jing Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
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15
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Hu M, Bao JD. Diffusion crossing over a barrier in a random rough metastable potential. Phys Rev E 2018; 97:062143. [PMID: 30011451 DOI: 10.1103/physreve.97.062143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Indexed: 06/08/2023]
Abstract
We carry out a detailed study of escape dynamics of a particle driven by a white noise over a metastable potential corrugated by spatial disorder in the form of zero-mean random correlated potential. The approach of double-averaging over test particles and statistic ensemble is proposed to calculate the escape rate in a finite-size random rough metastable potential, moreover, the interference mechanism of test particles multi-passing over the saddle point is considered. Through analyzing the dependence of the steady escape rate on various modelled potentials and parameters, we demonstrate that the obstruction induced by roughness leads to a decrease in the steady escape rate with the increase of rough intensity. We also add the random correlated potential into the vicinity of the saddle-point of metastable potentials of three kinds and show an enhancement phenomenon of escape rate similar to the previous study of a surmounting fluctuating sharp barrier.
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Affiliation(s)
- Meng Hu
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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16
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Illien P, Bénichou O, Oshanin G, Sarracino A, Voituriez R. Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment. PHYSICAL REVIEW LETTERS 2018; 120:200606. [PMID: 29864325 DOI: 10.1103/physrevlett.120.200606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Revised: 01/02/2018] [Indexed: 06/08/2023]
Abstract
We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.
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Affiliation(s)
- Pierre Illien
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
| | - Gleb Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185 Rome, Italy
- Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
| | - Raphaël Voituriez
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
- Laboratoire Jean Perrin, CNRS UMR 8237, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
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17
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Guérin T, Dean DS. Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential. Phys Rev E 2017; 95:012109. [PMID: 28208337 DOI: 10.1103/physreve.95.012109] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Indexed: 11/07/2022]
Abstract
We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F<F_{c} the late-time and intermediate-time diffusive regimes are indistinguishable. Explicit asymptotic regimes for the MSD curves are identified at all time scales.
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Affiliation(s)
- T Guérin
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
| | - D S Dean
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
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18
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Guérin T, Dean DS. Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062103. [PMID: 26764628 DOI: 10.1103/physreve.92.062103] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Indexed: 06/05/2023]
Abstract
We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.
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Affiliation(s)
- T Guérin
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
| | - D S Dean
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), CNRS, UMR 5798/Université de Bordeaux, F-33400 Talence, France
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Wu JC, Chen Q, Wang R, Ai BQ. Diffusion and mobility of anisotropic particles in tilted periodic structures. CHAOS (WOODBURY, N.Y.) 2015; 25:023114. [PMID: 25725650 DOI: 10.1063/1.4913491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We numerically investigated the transport of anisotropic particles in tilted periodic structures. The diffusion and mobility of the particles demonstrate distinct behaviors dependence on the shape of the particles. In two-dimensional (2D) periodic potentials, we find that the mobility is influenced a little by the anisotropy of the particle, while the diffusion increases monotonically with the increasing of the particle anisotropy for large enough biased force. However, due to the sensitivity of the channels for the particle anisotropy, the transport in smooth channels is obviously different from that in energy potentials. The mobility decreases monotonically with the increasing of the particle anisotropy, while the diffusion can be a non-monotonic function of the particle anisotropy with a peak under appropriate biased force.
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Affiliation(s)
- Jian-chun Wu
- Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
| | - Qun Chen
- Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
| | - Rang Wang
- Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
| | - Bao-quan Ai
- Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou, China
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Salgado-García R. Effective diffusion coefficient in tilted disordered potentials: optimal relative diffusivity at a finite temperature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032105. [PMID: 25314393 DOI: 10.1103/physreve.90.032105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2014] [Indexed: 06/04/2023]
Abstract
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case of random potentials resulting from the interaction of a particle with a "random polymer". In our model the polymer is made up, by means of some stochastic process, of monomers that can be taken from a finite or countable infinite set of possible monomer types. For the case of uncorrelated random polymers we found that the diffusion coefficient exhibits a non-monotonous behavior as a function of the noise intensity. Particularly interesting is the fact that the relative diffusivity becomes optimal at a finite temperature, a behavior which is reminiscent of stochastic resonance. We explain this effect as an interplay between the deterministic and noisy dynamics of the system. We also show that this behavior of the diffusion coefficient at a finite temperature is more pronounced for the case of weakly disordered potentials. We test our findings by means of numerical simulations of the corresponding Langevin dynamics of an ensemble of noninteracting overdamped particles diffusing on uncorrelated random potentials.
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Affiliation(s)
- R Salgado-García
- Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, Colonia Chamilpa, 62209, Cuernavaca Morelos, Mexico
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Hurowitz D, Cohen D. Nonequilibrium version of the Einstein relation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032129. [PMID: 25314417 DOI: 10.1103/physreve.90.032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Indexed: 06/04/2023]
Abstract
The celebrated Einstein relation between the diffusion coefficient D and the drift velocity v is violated in nonequilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice, taking into account the interplay between the periodicity, the randomness, and the asymmetry of the transition rates. Based on the nonequilibrium fluctuation theorem the v/D ratio is found to be a nonlinear function of the affinity. Hence it depends in a nontrivial way on the microscopics of the sample.
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Affiliation(s)
- Daniel Hurowitz
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Doron Cohen
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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Salgado-García R, Maldonado C. Normal-to-anomalous diffusion transition in disordered correlated potentials: from the central limit theorem to stable laws. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062143. [PMID: 24483421 DOI: 10.1103/physreve.88.062143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2013] [Indexed: 06/03/2023]
Abstract
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations.
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Affiliation(s)
- R Salgado-García
- Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001, Colonia Chamilpa, 62209 Cuernavaca Morelos, Mexico
| | - Cesar Maldonado
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Avenida Manuel Nava 6, Zona Universitaria, 78290 San Luis Potosí, Mexico
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Simon MS, Sancho JM, Lindenberg K. Transport and diffusion of overdamped Brownian particles in random potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062105. [PMID: 24483384 DOI: 10.1103/physreve.88.062105] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Indexed: 06/03/2023]
Abstract
We present a numerical study of the anomalies in transport and diffusion of overdamped Brownian particles in totally disordered potential landscapes in one and in two dimensions. We characterize and analyze the effects of three different disordered potentials. The anomalous regimes are characterized by the time exponents that exhibit the statistical moments of the ensemble of particle trajectories. The anomaly in the transport is always of the subtransport type, but diffusion presents a greater variety of anomalies: Both subdiffusion and superdiffusion are possible. In two dimensions we present a mixed anomaly: subdiffusion in the direction perpendicular to the force and superdiffusion in the parallel direction.
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Affiliation(s)
- Marc Suñé Simon
- Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
| | - J M Sancho
- Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
| | - Katja Lindenberg
- Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, USA
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Bao JD, Liu J. Group superballistic diffusion: bimodal velocity inducing coexistence of two states in a corrugated plane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022153. [PMID: 24032820 DOI: 10.1103/physreve.88.022153] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Revised: 07/10/2013] [Indexed: 06/02/2023]
Abstract
We consider anomalous diffusion of a particle moving in a tilted periodic potential in the presence of Lévy noise and nonlinear friction. Using Monte Carlo simulations, we have found some interesting characteristics of diffusion in such a nonlinear system: when the noise intensity is weak and the external force is close to the critical value at which local minima of the potential just vanish, the nonmonotonic behavior of the effective diffusion index and the superballistic diffusion are observed. This is due to the bimodal nature of the velocity distribution, and thus the test particles exist in either a running state or a long-tailed behind state in the spatial coordinate; the latter is disintegrated into small pieces of the probability peaks. We provide a relation between the group diffusion coefficient and the phase diffusion coefficient. It is shown that the distance between the above two-state centers increasing with time plays the definitive role in the superballistic group diffusion.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Cerbelli S. Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:060102. [PMID: 23848611 DOI: 10.1103/physreve.87.060102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2013] [Revised: 05/08/2013] [Indexed: 05/19/2023]
Abstract
Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D([perpendicular]) along the direction orthogonal to the uniform drive in the limit where Pe→∞. A simple one-dimensional model is proposed, which predicts the anomalous scaling D([perpendicular])~1/[A(1)+A(2)log(Pe)].
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Affiliation(s)
- S Cerbelli
- Dipartimento di Ingegneria Chimica, Sapienza Università di Roma, via Eudossiana 18, 00184 Roma, Italy.
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Zeng C, Wang H, Nie L. Multiple current reversals and diffusion enhancement in a symmetrical periodic potential. CHAOS (WOODBURY, N.Y.) 2012; 22:033125. [PMID: 23020464 DOI: 10.1063/1.4745853] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Transport and diffusion of Brownian particles in a symmetrical periodic potential were investigated for both overdamped and underdamped cases, where the ratchet potential is driven by an external unbiased time periodic force and correlation between thermal and potential fluctuations. It is shown that the correlation between two noises breaks the symmetry of the potential to generate motion of the Brownian particles in particular direction, and the current can reverse its direction by changing the sign of the noise correlation. For the overdamped case, the systemic parameters only induce the directed current, and the noise correlation suppresses the diffusion of the overdamped Brownian particles. However for the underdamped case, the current reverses its direction multiple times with increasing the systemic parameters, i.e., the multiple current reversal is observed, and the noise negative correlation suppresses the diffusion of the underdamped Brownian particles, while the noise positive correlation enhances it.
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Affiliation(s)
- Chunhua Zeng
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China.
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Khoury M, Lacasta AM, Sancho JM, Lindenberg K. Weak disorder: anomalous transport and diffusion are normal yet again. PHYSICAL REVIEW LETTERS 2011; 106:090602. [PMID: 21405612 DOI: 10.1103/physrevlett.106.090602] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Indexed: 05/30/2023]
Abstract
We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.
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Affiliation(s)
- M Khoury
- Departament d'Estructura i Constituents de la Matèria, Barcelona, Spain
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Tierno P, Reimann P, Johansen TH, Sagués F. Giant transversal particle diffusion in a longitudinal magnetic ratchet. PHYSICAL REVIEW LETTERS 2010; 105:230602. [PMID: 21231443 DOI: 10.1103/physrevlett.105.230602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Indexed: 05/30/2023]
Abstract
We study the transversal motion of paramagnetic particles on a uniaxial garnet film, exhibiting a longitudinal ratchet effect in the presence of an oscillating magnetic field. Without the field, the thermal diffusion coefficient obtained by video microscopy is D(0) ≈ 3 × 10(-4) μm2/s. With the field, the transversal diffusion exhibits a giant enhancement by almost four decades and a pronounced maximum as a function of the driving frequency. We explain the experimental findings with a theoretical interpretation in terms of random disorder effects within the magnetic film.
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Affiliation(s)
- Pietro Tierno
- Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.
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Xiao K, Grier DG. Sorting colloidal particles into multiple channels with optical forces: prismatic optical fractionation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051407. [PMID: 21230479 DOI: 10.1103/physreve.82.051407] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2010] [Revised: 07/03/2010] [Indexed: 05/13/2023]
Abstract
Brownian particles drifting through a periodically structured force landscape can become entrained by the landscape's symmetries. What direction a particular particle takes can depend strongly on subtle variations in its physical properties. Consequently, a homogeneously structured force field can sort a mixture of particles into spatially separated fractions, much as an optical prism refracts light into its component wavelengths. When the force landscape is implemented with structured light fields, such continuous multichannel sorting may be termed prismatic optical fractionation. We describe experimental and numerical studies of colloidal spheres' transport through periodic arrays of optical tweezers, which reveal an important role for three-dimensional motion in determining a drifting particle's fate. These studies also demonstrate sorting on the basis of statistically locked-in transport, in which brownian fluctuations contribute to direction selection.
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Affiliation(s)
- Ke Xiao
- Department of Physics and Center for Soft Matter Research, New York University, New York, New York 10003, USA
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Denisov SI, Kantz H. Anomalous biased diffusion in a randomly layered medium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021117. [PMID: 20365540 DOI: 10.1103/physreve.81.021117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2009] [Revised: 01/07/2010] [Indexed: 05/29/2023]
Abstract
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws, and analyze their dependence on the particle mass and the distribution of the random force.
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Affiliation(s)
- S I Denisov
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
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Hennig D. Current control in a tilted washboard potential via time-delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041114. [PMID: 19518180 DOI: 10.1103/physreve.79.041114] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2008] [Revised: 01/19/2009] [Indexed: 05/27/2023]
Abstract
We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.
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Affiliation(s)
- D Hennig
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
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