1
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Białas K, Spiechowicz J. Mechanism for giant enhancement of transport induced by active fluctuations. Phys Rev E 2023; 107:064120. [PMID: 37464690 DOI: 10.1103/physreve.107.064120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 05/15/2023] [Indexed: 07/20/2023]
Abstract
Understanding the role of active fluctuations in physics is a problem in statu nascendi appearing both as a hot topic and a major challenge. The reason for this is the fact that they are inherently nonequilibrium. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone. Recently a paradoxical effect has been briefly communicated in which a free-particle transport induced by active fluctuations in the form white Poisson shot noise can be enormously boosted when the particle is additionally subjected to a periodic potential. In this work we considerably extend the original predictions and investigate the impact of statistics of active noise on the occurrence of this effect. We construct a toy model of the jump-relaxation process that allow us to identify different regimes of the free-particle transport boost and explain their corresponding mechanisms. Moreover, we formulate and interpret the conditions for statistics of active fluctuations that are necessary for the emergence of giant enhancement of the free-particle transport induced by the periodic potential. Our results are relevant not only for microscopic physical systems but also for biological ones such as, e.g., living cells where fluctuations generated by metabolic activities are active by default.
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Affiliation(s)
- K Białas
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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2
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Abstract
Granular particles exhibit rich collective behaviors on vibration beds, but the motion of an isolated particle is not well understood even for uniform particles with a simple shape such as disks or spheres. Here we measured the motion of a single disk confined to a quasi-two-dimensional horizontal box on a vertically vibrating stage. The translational displacements obey compressed exponential distributions whose exponent [Formula: see text] increases with the frequency, while the rotational displacements exhibit unimodal distributions at low frequencies and bimodal distributions at high frequencies. During short time intervals, the translational displacements are subdiffusive and negatively correlated, while the rotational displacements are superdiffusive and positively correlated. After prolonged periods, the rotational displacements become diffusive and their correlations decay to zero. Both the rotational and the translational displacements exhibit white noise at low frequencies, and blue noise for translational motions and Brownian noise for rotational motions at high frequencies. The translational kinetic energy obeys Boltzmann distribution while the rotational kinetic energy deviates from it. Most energy is distributed in translational motions at low frequencies and in rotational motions at high frequencies, which violates the equipartition theorem. Translational and rotational motions are not correlated. These experimental results show that the random diffusion of such driven particles is distinct from thermal motion in both the translational and rotational degrees of freedom, which poses new challenges to theory. The results cast new light on the motion of individual particles and the collective motion of driven granular particles.
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3
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Cheng K, Dong JQ, Han WH, Liu F, Huang L. Infima statistics of entropy production in an underdamped Brownian motor. Phys Rev E 2020; 102:062127. [PMID: 33466062 DOI: 10.1103/physreve.102.062127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 11/15/2020] [Indexed: 06/12/2023]
Abstract
The second law of thermodynamics states that the entropy never decreases for isolated macroscopical systems, which defines the arrow of time. For small systems, although the entropy increases on average, due to strong fluctuation, it may encounter a temporary decrease. The probability of negative entropy production follows the fluctuation theorem. Recently, it has been demonstrated theoretically the infima law that there exists a lower bound for the average values of the minima of the negative entropy production, which is -k_{B}. In this paper, we have constructed a horizontal Brownian motor immersed in a granular gas, whose dynamics is governed by the underdamped stochastic process. By recording the angular motion of the motor and measuring the key parameters of the system, we experimentally demonstrate that, despite the nonideal elements in the experiments and that the complex underlying dynamics, the average value of the minima of the negative entropy production is still bounded by -k_{B}, which may invoke further theoretical investigations of the applicability of the infima law in nonideal realistic small systems.
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Affiliation(s)
- Ke Cheng
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jia-Qi Dong
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
- Institute of Theoretical Physics, CAS, Beijing 100190, China
| | - Wen-Hui Han
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
| | - Liang Huang
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
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4
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Pan JX, Wei H, Qi MJ, Wang HF, Zhang JJ, Tian WD, Chen K. Vortex formation of spherical self-propelled particles around a circular obstacle. SOFT MATTER 2020; 16:5545-5551. [PMID: 32510067 DOI: 10.1039/d0sm00277a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A vortex is a common ratchet phenomenon in active systems. The spatial symmetry is usually broken by introducing asymmetric shapes or spontaneously by collective motion in the presence of hydrodynamic interactions or other alignment effects. Unexpectedly, we observe, by simulations, the formation of a vortex in the simplest model of a circular obstacle immersed in a bath of spherical self-propelled particles. No symmetry-breaking factors mentioned above are included in this model. The vortex forms only when the particle activity is high, i.e. large persistence. The obstacle size is also a key factor and the vortex only forms in a limited range of obstacle sizes. The sustainment of the vortex originates from the bias of the rotating particle cluster around the obstacle in accepting the incoming particles based on their propelling directions. Our results provide new understanding of and insights into the spontaneous symmetry-breaking and ratchet phenomena in active matter.
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Affiliation(s)
- Jun-Xing Pan
- School of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China.
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5
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Rozenbaum VM, Shapochkina IV, Teranishi Y, Trakhtenberg LI. High-temperature ratchets driven by deterministic and stochastic fluctuations. Phys Rev E 2019; 99:012103. [PMID: 30780357 DOI: 10.1103/physreve.99.012103] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Indexed: 11/07/2022]
Abstract
We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.
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Affiliation(s)
- V M Rozenbaum
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan.,Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.,Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev 03164, Ukraine
| | - I V Shapochkina
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan.,Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.,Department of Physics, Belarusian State University, Prospekt Nezavisimosti 4, Minsk 220050, Belarus
| | - Y Teranishi
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan
| | - L I Trakhtenberg
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street 4, Moscow 119991, Russia; Moscow Institute of Physics and Technology, Institutsky Lane 9, Dolgoprudny 141700, Moscow Region, Russia; and Lomonosov Moscow State University, 1-3 Leninskie Gory, Moscow 119991, Russia
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6
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Berezin S, Zayats O. Energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation. Phys Rev E 2018; 97:012144. [PMID: 29448408 DOI: 10.1103/physreve.97.012144] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2016] [Indexed: 11/07/2022]
Abstract
We study a friction-controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in such quantities as displacement, traveled distance, and energy loss due to friction. We assume that the random excitation is switched off at some time (possibly infinite) and show that the problem can be treated in an analytic, explicit, manner. Particularly, we derive formulas for the moments of the displacement and distance, and also for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process given by a system of SDEs. This equation is solved by reduction to a parametric Riemann boundary value problem of complex analysis.
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Affiliation(s)
- Sergey Berezin
- Applied Mathematics Department, Peter the Great Saint Petersburg Polytechnic University, St. Petersburg, Polytechnicheskaya, 29, 195251, Russia
| | - Oleg Zayats
- Applied Mathematics Department, Peter the Great Saint Petersburg Polytechnic University, St. Petersburg, Polytechnicheskaya, 29, 195251, Russia
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7
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Vega Reyes F, Lasanta A, Santos A, Garzó V. Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit. Phys Rev E 2017; 96:052901. [PMID: 29347772 DOI: 10.1103/physreve.96.052901] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2017] [Indexed: 06/07/2023]
Abstract
The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann-Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions. This allows us to obtain explicit analytical expressions for the temperature ratios. On the computational side, two different techniques are used. First, the kinetic equations are numerically solved by the direct simulation Monte Carlo (DSMC) method. Second, molecular dynamics simulations for dilute gases are performed. Comparison between theory and simulations shows a general good agreement. This means that (i) the impact of the molecular chaos ansatz on the temperature ratios is not significant (except at high inelasticities and/or big impurities) and (ii) the simple Maxwellian approximation yields quite reliable predictions.
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Affiliation(s)
- Francisco Vega Reyes
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
| | - Antonio Lasanta
- Gregorio Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
| | - Vicente Garzó
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
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8
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Cândido MM, Morgado WAM, Duarte Queirós SM. Macroscopic violation of the law of heat conduction. Phys Rev E 2017; 96:032143. [PMID: 29347020 DOI: 10.1103/physreve.96.032143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2017] [Indexed: 06/07/2023]
Abstract
We analyze a model describing an anharmonic macroscopic chain in contact with general reservoirs that follow the Lévy-Itô theorem on the Gaussian-Poissonian decomposition of the measure. We do so by considering a perturbative approach to compute the heat flux and the (canonical) temperature profile when the system reaches the steady state. This approach allows observing a macroscopic violation of the law of the heat conduction equivalent to that found for small (N=2) systems in contact with general reservoirs, which conveys the ascendency of the nature of the reservoirs over the size of the system.
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Affiliation(s)
- Michael M Cândido
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro-RJ, Brazil
| | - Welles A M Morgado
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro-RJ, Brazil
| | - Sílvio M Duarte Queirós
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazil
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9
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Geffert PM, Just W. Nonequilibrium dynamics of a pure dry friction model subjected to colored noise. Phys Rev E 2017; 95:062111. [PMID: 28709275 DOI: 10.1103/physreve.95.062111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Indexed: 06/07/2023]
Abstract
We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose, we consider the motion of a particle subjected to dry friction and colored noise. The finite correlation time of the noise provides an additional dimension in phase space, causes a nontrivial probability current, and establishes a proper nonequilibrium regime. Furthermore, the setup allows for the study of stick-slip phenomena, which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified colored noise approximation, developed by Jung and Hänggi [Phys. Rev. A 35, 4464(R) (1987)0556-279110.1103/PhysRevA.35.4464]. The analysis of probability currents and of power spectral densities underpins the observed stick-slip transition, which is related with a critical value of the noise correlation time.
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Affiliation(s)
- Paul M Geffert
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Wolfram Just
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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10
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Tutu H, Ouchi K, Horita T. Performance optimization in two-dimensional Brownian rotary ratchet models. Phys Rev E 2017; 95:062103. [PMID: 28709182 DOI: 10.1103/physreve.95.062103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
With a model for two-dimensional (2D) Brownian rotary ratchets being capable of producing a net torque under athermal random forces, its optimization for mean angular momentum (L), mean angular velocity (ω), and efficiency (η) is considered. In the model, supposing that such a small ratchet system is placed in a thermal bath, the motion of the rotor in the stator is described by the Langevin dynamics of a particle in a 2D ratchet potential, which consists of a static and a time-dependent interaction between rotor and stator; for the latter, we examine a force [randomly directed dc field (RDDF)] for which only the direction is instantaneously updated in a sequence of events in a Poisson process. Because of the chirality of the static part of the potential, it is found that the RDDF causes net rotation while coupling with the thermal fluctuations. Then, to maximize the efficiency of the power consumption of the net rotation, we consider optimizing the static part of the ratchet potential. A crucial point is that the proposed form of ratchet potential enables us to capture the essential feature of 2D ratchet potentials with two closed curves and allows us to systematically construct an optimization strategy. In this paper, we show a method for maximizing L, ω, and η, its outcome in 2D two-tooth ratchet systems, and a direction of optimization for a three-tooth ratchet system.
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Affiliation(s)
- Hiroki Tutu
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | | | - Takehiko Horita
- Department of Mathematical Sciences, Osaka Prefecture University, Sakai 599-8531, Japan
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11
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Das P, Puri S, Schwartz M. Single particle Brownian motion with solid friction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:60. [PMID: 28589413 DOI: 10.1140/epje/i2017-11549-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Accepted: 05/19/2017] [Indexed: 06/07/2023]
Abstract
We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.
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Affiliation(s)
- Prasenjit Das
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | - Moshe Schwartz
- Beverly and Raymond Sackler School of Physics and Astronomy, Tel Aviv University, 69934, Ramat Aviv, Israel.
- Faculty of Engineering, Holon Institute of Technology, Golomb 52, 5810201, Holon, Israel.
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12
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Chastaing JY, Géminard JC, Naert A. Experimental study of energy exchanges between two coupled granular gases. Phys Rev E 2016; 94:062110. [PMID: 28085409 DOI: 10.1103/physreve.94.062110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2016] [Indexed: 06/06/2023]
Abstract
We report on the energy exchanges between two granular gases of different densities coupled electromechanically by immersed blades attached to dc motors. Zeroing the energy flux between the two subsystems, we demonstrate that an immersed blade is a convenient way to assess the properties of the granular gases, provided that the dissipation in the motor is properly taken into account. In addition, when the two gases have different densities, the fluctuations of the energy flux are asymmetric, very intermittent, and with most probable zero flux. We show that, for weak coupling, the main features of the energy exchanges can be explained considering the fluctuations of the two subsystems.
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Affiliation(s)
- J-Y Chastaing
- Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - J-C Géminard
- Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - A Naert
- Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
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13
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Sano TG, Kanazawa K, Hayakawa H. Granular rotor as a probe for a nonequilibrium bath. Phys Rev E 2016; 94:032910. [PMID: 27739823 DOI: 10.1103/physreve.94.032910] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Indexed: 11/07/2022]
Abstract
This study numerically and analytically investigates the dynamics of a rotor under viscous or dry friction as a nonequilibrium probe of a granular gas. In order to demonstrate the role of the rotor as a probe for a nonequilibrium bath, the molecular dynamics (MD) simulation of the rotor is performed under viscous or dry friction surrounded by a steady granular gas under gravity. A one-to-one map between the velocity distribution function (VDF) of the granular gas and the angular distribution function for the rotor is theoretically derived. The MD simulation demonstrates that the one-to-one map accurately infers the local VDF of the granular gas from the angular VDF of the rotor, and vice versa.
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Affiliation(s)
- Tomohiko G Sano
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kiyoshi Kanazawa
- Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259-G3-52 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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14
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Joyce M, Morand J, Viot P. Attractor nonequilibrium stationary states in perturbed long-range interacting systems. Phys Rev E 2016; 93:052129. [PMID: 27300851 DOI: 10.1103/physreve.93.052129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2016] [Indexed: 11/07/2022]
Abstract
Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one-dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSSs we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique nonequilibrium stationary state, completely different from its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g., spatial density or velocity distribution) of the system itself.
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Affiliation(s)
- Michael Joyce
- Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, Sorbonne Universités, 4, place Jussieu, 75252 Paris Cedex 05, France
| | - Jules Morand
- Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, Sorbonne Universités, 4, place Jussieu, 75252 Paris Cedex 05, France.,National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.,Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch 7600, South Africa.,Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Pascal Viot
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France
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15
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Suzuki K, Hayakawa H. Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach. PHYSICAL REVIEW LETTERS 2015; 115:098001. [PMID: 26371683 DOI: 10.1103/physrevlett.115.098001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.
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Affiliation(s)
- Koshiro Suzuki
- Analysis Technology Development Center, Canon Inc., 30-2 Shimomaruko 3-chome, Ohta-ku, Tokyo 146-8501, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
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16
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Kanazawa K, Sano TG, Sagawa T, Hayakawa H. Minimal model of stochastic athermal systems: origin of non-Gaussian noise. PHYSICAL REVIEW LETTERS 2015; 114:090601. [PMID: 25793791 DOI: 10.1103/physrevlett.114.090601] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2014] [Indexed: 06/04/2023]
Abstract
For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.
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Affiliation(s)
- Kiyoshi Kanazawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Tomohiko G Sano
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Takahiro Sagawa
- Department of Basic Science, The University of Tokyo, Komaba, Meguro-ku 153-8902, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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17
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Kanazawa K, Sagawa T, Hayakawa H. Energy pumping in electrical circuits under avalanche noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012115. [PMID: 25122259 DOI: 10.1103/physreve.90.012115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2014] [Indexed: 06/03/2023]
Abstract
We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasistatic and finite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.
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Affiliation(s)
- Kiyoshi Kanazawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Takahiro Sagawa
- Department of Basic Science, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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Sano TG, Hayakawa H. Roles of dry friction in the fluctuating motion of an adiabatic piston. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032104. [PMID: 24730787 DOI: 10.1103/physreve.89.032104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2013] [Indexed: 06/03/2023]
Abstract
The motion of an adiabatic piston under dry friction is investigated to clarify the roles of dry friction in nonequilibrium steady states. We clarify that dry friction can reverse the direction of the piston motion and causes a discontinuity or a cusplike singularity for velocity distribution functions of the piston. We also show that the heat fluctuation relation is modified under dry friction.
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Affiliation(s)
- Tomohiko G Sano
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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19
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Joyce M, Morand J, Sicard F, Viot P. Scaling quasistationary states in long-range systems with dissipation. PHYSICAL REVIEW LETTERS 2014; 112:070602. [PMID: 24579582 DOI: 10.1103/physrevlett.112.070602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2013] [Indexed: 06/03/2023]
Abstract
Hamiltonian systems with long-range interactions give rise to long-lived out-of-equilibrium macroscopic states, so-called quasistationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasistationary states," i.e., states that are quasistationary in rescaled variables. A numerical study of one-dimensional self-gravitating systems confirms the relevance of these solutions and gives indications of their regime of validity in line with theoretical predictions. We underline that the velocity distributions never show any tendency to evolve towards a Maxwell-Boltzmann form.
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Affiliation(s)
- Michael Joyce
- Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, 4, Place Jussieu, 75252 Paris Cedex 05, France
| | - Jules Morand
- Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, 4, Place Jussieu, 75252 Paris Cedex 05, France
| | - François Sicard
- Laboratoire de Physique Théorique, IRSAMC, CNRS UMR 5152, Université Paul Sabatier, 31062 Toulouse, France
| | - Pascal Viot
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, 4, Place Jussieu, 75252 Paris Cedex 05, France
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20
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Sarracino A. Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052124. [PMID: 24329231 DOI: 10.1103/physreve.88.052124] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2013] [Indexed: 06/03/2023]
Abstract
We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by studying the generalized fluctuation-dissipation relation for this ratchet model driven by Coulomb friction.
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Affiliation(s)
- A Sarracino
- CNR-ISC and Dipartimento di Fisica, Università Sapienza, p.le A. Moro 2, 00185 Roma, Italy
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21
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Gnoli A, Sarracino A, Puglisi A, Petri A. Nonequilibrium fluctuations in a frictional granular motor: experiments and kinetic theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052209. [PMID: 23767532 DOI: 10.1103/physreve.87.052209] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2013] [Indexed: 06/02/2023]
Abstract
We report the study of an experimental granular Brownian motor, inspired by the one published in Eshuis et al. [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating blade, the surfaces of which break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main difference of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance v(0)(2). We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions, with an average angular velocity <ω>~v(0)(3), and (ii) frequent collisions (FC), with <ω>~v(0). We also study the fluctuations of the angle spanned in a large-time interval Δθ, which in the FC regime is proportional to the work done upon the motor. We observe that the fluctuation relation is satisfied with a slope which weakly depends on the relative collision frequency.
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Affiliation(s)
- Andrea Gnoli
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università Sapienza, p.le A. Moro 2, 00185 Rome, Italy.
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22
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Sarracino A, Gnoli A, Puglisi A. Ratchet effect driven by Coulomb friction: the asymmetric Rayleigh piston. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:040101. [PMID: 23679355 DOI: 10.1103/physreve.87.040101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2013] [Indexed: 06/02/2023]
Abstract
The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.
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Affiliation(s)
- A Sarracino
- CNR-ISC and Dipartimento di Fisica, Università Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy
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23
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Gnoli A, Petri A, Dalton F, Pontuale G, Gradenigo G, Sarracino A, Puglisi A. Brownian ratchet in a thermal bath driven by Coulomb friction. PHYSICAL REVIEW LETTERS 2013; 110:120601. [PMID: 25166785 DOI: 10.1103/physrevlett.110.120601] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2012] [Indexed: 06/03/2023]
Abstract
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well-known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the friction-induced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.
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Affiliation(s)
- Andrea Gnoli
- Istituto dei Sistemi Complessi-CNR, via del Fosso del Cavaliere 100, 00133 Rome, Italy and Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università "Sapienza", Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Alberto Petri
- Istituto dei Sistemi Complessi-CNR, via del Fosso del Cavaliere 100, 00133 Rome, Italy
| | - Fergal Dalton
- Istituto dei Sistemi Complessi-CNR, via del Fosso del Cavaliere 100, 00133 Rome, Italy
| | - Giorgio Pontuale
- Istituto dei Sistemi Complessi-CNR, via del Fosso del Cavaliere 100, 00133 Rome, Italy
| | - Giacomo Gradenigo
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università "Sapienza", Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Alessandro Sarracino
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università "Sapienza", Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università "Sapienza", Piazzale Aldo Moro 2, 00185 Rome, Italy
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Heckel M, Müller P, Pöschel T, Gallas JAC. Circular ratchets as transducers of vertical vibrations into rotations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061310. [PMID: 23367935 DOI: 10.1103/physreve.86.061310] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2012] [Indexed: 06/01/2023]
Abstract
Granular ratchets are well-known devices that when driven vertically produce a counterintuitive horizontal transport of particles. Here we report the experimental observation of a complementary effect: the striking ability of circular ratchets to convert their vertical vibration into their own rotation. The average revolution speed shows a maximum value for an optimal tooth height. With no special effort the rotation speed could be maintained steady during several hours. Unexpected random arrests and reversals of the velocity were also observed abundantly.
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Affiliation(s)
- Michael Heckel
- Institute for Multiscale Simulations, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91052 Erlangen, Germany
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25
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Joubaud S, Lohse D, van der Meer D. Fluctuation theorems for an asymmetric rotor in a granular gas. PHYSICAL REVIEW LETTERS 2012; 108:210604. [PMID: 23003232 DOI: 10.1103/physrevlett.108.210604] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2011] [Indexed: 06/01/2023]
Abstract
We investigate the validity of fluctuation theorems for an asymmetric rotor experiment in a granular gas. A first state, with a Gaussian distribution of the angular velocity, is found to be well described by a first order Langevin equation. We show that fluctuation theorems are valid for the injected work and for the total entropy production. In a second state, the angular velocity distribution is double peaked due to a spontaneous symmetry breaking: A convection roll develops in the granular gas, which strongly couples to the rotor. Surprisingly, in this case, similar symmetry relations hold, which lead to a good prediction for the height ratio of the two peaks.
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Affiliation(s)
- Sylvain Joubaud
- Physics of Fluids, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
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26
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Talbot J, Viot P. Effect of dynamic and static friction on an asymmetric granular piston. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021310. [PMID: 22463205 DOI: 10.1103/physreve.85.021310] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2011] [Revised: 12/29/2011] [Indexed: 05/31/2023]
Abstract
We investigate the influence of dry friction on an asymmetric, granular piston of mass M, composed of two materials, undergoing inelastic collisions with bath particles of mass m. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the friction strength. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio M/m, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.
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Affiliation(s)
- Julian Talbot
- Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, 4, place Jussieu, 75252 Paris Cedex 05, France.
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