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Liao JJ, Huang XQ, Ai BQ. Current reversals of active particles in time-oscillating potentials. SOFT MATTER 2018; 14:7850-7858. [PMID: 30209474 DOI: 10.1039/c8sm01291a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.
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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.
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Ramírez-Piscina L. Fixed-density boundary conditions in overdamped Langevin simulations of diffusion in channels. Phys Rev E 2018; 98:013302. [PMID: 30110749 DOI: 10.1103/physreve.98.013302] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2018] [Indexed: 11/07/2022]
Abstract
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears, for instance, when considering the diffusion of ions in molecular channels, between the different concentrations at both sides of the cellular membrane. For this application the overdamped limit of Brownian motion (leading to a first order Langevin equation) is most convenient, but in previous works some difficulties associated with this limit were found for the implementation of the boundary conditions. We derive here an algorithm that, unlike previous attempts, does not require the simulation of particle reservoirs or the consideration of velocity variables or adjustable parameters. Simulations of Brownian particles in simple cases show that results agree perfectly with theory, both for the local concentration values and for the resulting particle flux in nonequilibrium situations. The algorithm is appropriate for the modeling of more complex ionic channels and, in general, for the treatment of analogous boundary conditions in other physical models using first order Langevin equations.
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Affiliation(s)
- L Ramírez-Piscina
- Departament de Física, Universitat Politècnica de Catalunya, Avinguda Doctor Marañón 44, 08028 Barcelona, Spain
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Rozenbaum VM, Makhnovskii YA, Shapochkina IV, Sheu SY, Yang DY, Lin SH. Adiabatically driven Brownian pumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012104. [PMID: 23944411 DOI: 10.1103/physreve.88.012104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2012] [Indexed: 06/02/2023]
Abstract
We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.
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Affiliation(s)
- Viktor M Rozenbaum
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
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4
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Ai BQ, He YF, Li FG, Zhong WR. Hydrodynamically enforced entropic Brownian pump. J Chem Phys 2013; 138:154107. [DOI: 10.1063/1.4801661] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Chew LY. Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:016212. [PMID: 22400648 DOI: 10.1103/physreve.85.016212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2011] [Revised: 11/23/2011] [Indexed: 05/31/2023]
Abstract
We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from thermodynamic equilibrium, as exemplified by the constant flashing, the state-dependent, and the tilted deterministic Smoluchowski-Feynman ratchets, with the consequence of an enhancement in the directed current.
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Affiliation(s)
- Lock Yue Chew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371.
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Fa KS. Solution of Fokker-Planck equation for a broad class of drift and diffusion coefficients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:012102. [PMID: 21867236 DOI: 10.1103/physreve.84.012102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2011] [Revised: 06/14/2011] [Indexed: 05/31/2023]
Abstract
A Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach are considered. From this Fokker-Planck equation a class of exact solutions with the same spatial drift and diffusion coefficients is obtained. Furthermore, some details of this system are analyzed by using the spatial diffusion coefficient D(x) = sqrt[D]|x|(-θ/2).
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Affiliation(s)
- Kwok Sau Fa
- Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná 87020-900, Brazil.
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Liu J, He J. Diode system rectifying thermal fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:022101. [PMID: 20866857 DOI: 10.1103/physreve.82.022101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2010] [Indexed: 05/29/2023]
Abstract
We present an approach to the energetics of a diode based on the Langevin equation for an ideal RC circuit and establish a simple model consisting of two diodes switched in the same directions located in two heat reservoirs with different temperatures. We calculate the thermoelectric voltage and the efficiency of the diode system as a fluctuation rectifier and show the efficiency is always smaller than the Carnot value, thus, indicating the irreversible mode of operation. The Carnot efficiency is achieved only when the diode works as the normal resistor.
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Affiliation(s)
- Jiuliang Liu
- Department of Physics, Nanchang University, People's Republic of China
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Ai BQ, He D, Hu B. Heat conduction in driven Frenkel-Kontorova lattices: thermal pumping and resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031124. [PMID: 20365714 DOI: 10.1103/physreve.81.031124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2009] [Revised: 03/07/2010] [Indexed: 05/29/2023]
Abstract
Heat conduction through the Frenkel-Kontorova chain under the influence of an ac driving force applied locally at one boundary is studied by nonequilibrium molecular dynamics simulations. We observe the occurrence of thermal resonance, namely, there exists a value of the driving frequency at which the heat flux takes its maximum value. The resonance frequency is determined by the dynamical parameters of the model, which has been numerically explored. Remarkably, the heat can be pumped from the low-temperature heat bath to the high temperature one by suitably adjusting the frequency of the ac driving force. By examining effects of the driving amplitude on heat conduction, we show that the amplitude threshold for nonlinear supratransmission is absent when the system is in contact with heat baths, namely, the heat flux smoothly increases with the increasing of amplitude.
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Affiliation(s)
- Bao-quan Ai
- Department of Physics, Centre for Nonlinear Studies, and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems Hong Kong, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
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Orlandi JG, Sancho JM. Theoretical study of a membrane channel gated by ATP. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2009; 29:329-336. [PMID: 19575251 DOI: 10.1140/epje/i2009-10483-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Revised: 05/27/2009] [Accepted: 06/02/2009] [Indexed: 05/28/2023]
Abstract
We study channel transport across biomembranes. We propose a model that couples the diffusive dynamics with the gating process via a two-state ratchet mechanism. This gating process is governed by ATP binding and hydrolysis, and the process exhibits Michaelis-Menten enzymatic kinetics. The particle flow and permeability of the channel are studied both analytically and numerically in the steady-state regime, while working between fixed concentrations. The results are compared with simpler models and with experimental data. Also, a simulation framework, that allows high flexibility in parameter exploration, is introduced.
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Affiliation(s)
- J G Orlandi
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, E-08028 Barcelona, Spain.
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