1
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Schweers S, Locher DF, Schütz GM, Maass P. Weak Pinning and Long-Range Anticorrelated Motion of Phase Boundaries in Driven Diffusive Systems. PHYSICAL REVIEW LETTERS 2024; 132:167101. [PMID: 38701467 DOI: 10.1103/physrevlett.132.167101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 03/19/2024] [Indexed: 05/05/2024]
Abstract
We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) has a scaling behavior w(t,L)=L^{3/4}f(t/L^{9/4}), with f(u) constant for u≫1 and f(u)∼u^{1/3} for u≪1. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent 9/4 is a new dynamical exponent for relaxation processes in driven diffusive systems.
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Affiliation(s)
- Sören Schweers
- Universität Osnabrück, Fachbereich Mathematik/Informatik/Physik, Institut für Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - David F Locher
- Universität Osnabrück, Fachbereich Mathematik/Informatik/Physik, Institut für Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
- Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany
| | - Gunter M Schütz
- Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Mathematik/Informatik/Physik, Institut für Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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2
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Terai K, Yuly JL, Zhang P, Beratan DN. Correlated particle transport enables biological free energy transduction. Biophys J 2023; 122:1762-1771. [PMID: 37056051 PMCID: PMC10209040 DOI: 10.1016/j.bpj.2023.04.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 02/17/2023] [Accepted: 04/07/2023] [Indexed: 04/15/2023] Open
Abstract
Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. We show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).
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Affiliation(s)
- Kiriko Terai
- Department of Chemistry, Duke University, Durham, North Carolina
| | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersy
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina
| | - David N Beratan
- Department of Chemistry, Duke University, Durham, North Carolina; Department of Physics, Duke University, Durham, North Carolina; Department of Biochemistry, Duke University, Durham, North Carolina.
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3
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Cereceda-López E, Lips D, Ortiz-Ambriz A, Ryabov A, Maass P, Tierno P. Hydrodynamic Interactions Can Induce Jamming in Flow-Driven Systems. PHYSICAL REVIEW LETTERS 2021; 127:214501. [PMID: 34860099 DOI: 10.1103/physrevlett.127.214501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
Hydrodynamic interactions between fluid-dispersed particles are ubiquitous in soft matter and biological systems and they give rise to intriguing collective phenomena. While it was reported that these interactions can facilitate force-driven particle motion over energetic barriers, here we show the opposite effect in a flow-driven system, i.e., that hydrodynamic interactions hinder transport across barriers. We demonstrate this result by combining experiments and theory. In the experiments, we drive colloidal particles using rotating optical traps, thus creating a vortex flow in the corotating reference frame. We observe a jamminglike decrease of particle currents with density for large barriers between traps. The theoretical model shows that this jamming arises from hydrodynamic interactions between the particles. The impact of hydrodynamic interactions is reversed compared to force-driven motion, suggesting that our findings are a generic feature of flow-driven transport.
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Affiliation(s)
- Eric Cereceda-López
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona (IN2UB), Barcelona 08028, Spain
| | - Dominik Lips
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona (IN2UB), Barcelona 08028, Spain
- University of Barcelona Institute of Complex Systems (UBICS), 08028 Barcelona, Spain
| | - Artem Ryabov
- Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona (IN2UB), Barcelona 08028, Spain
- University of Barcelona Institute of Complex Systems (UBICS), 08028 Barcelona, Spain
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4
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Lips D, Ryabov A, Maass P. Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process. Phys Rev E 2019; 100:052121. [PMID: 31869987 DOI: 10.1103/physreve.100.052121] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Indexed: 06/10/2023]
Abstract
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
- Centro de Física Teórica e Computacional, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande P-1749-016 Lisboa, Portugal
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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5
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Abstract
Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model.
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Lips D, Ryabov A, Maass P. Brownian Asymmetric Simple Exclusion Process. PHYSICAL REVIEW LETTERS 2018; 121:160601. [PMID: 30387631 DOI: 10.1103/physrevlett.121.160601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Indexed: 06/08/2023]
Abstract
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking, and exchange symmetry effect. The latter leads to a current equal to that of noninteracting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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7
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Tian B, Jiang R, Hu MB, Jia B. Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances. CHINESE PHYSICS B 2017; 26:020503. [DOI: 10.1088/1674-1056/26/2/020503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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8
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Foulaadvand ME, Maass P. Phase transitions and optimal transport in stochastic roundabout traffic. Phys Rev E 2016; 94:012304. [PMID: 27575145 DOI: 10.1103/physreve.94.012304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Indexed: 11/07/2022]
Abstract
We study traffic in a roundabout model, where the dynamics along the interior lane of the roundabout are described by the totally asymmetric simple exclusion process (TASEP). Vehicles can enter the interior lane or exit from it via S intersecting streets with given rates, and locally modified dynamics at the junctions take into account that collisions of entering vehicles with vehicles approaching the entrance point from the interior lane should be avoided. A route matrix specifies the probabilities for vehicles to arrive from and to exit to certain intersecting streets. By subdividing the interior lane into segments between consecutive intersecting streets with effective entrance and exit rates, a classification of the stationary roundabout traffic in terms of TASEP multiphases is given, where each segment can be in either the low-density, high-density, or maximum current TASEP phase. A general methodology is developed, which allows one to calculate the multiphases and optimal throughput conditions based on a mean-field treatment. Explicit analytical results from this treatment are derived for equivalent interesting streets. The results are shown to be in good agreement with kinetic Monte Carlo simulations.
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Affiliation(s)
- M Ebrahim Foulaadvand
- Department of Physics, University of Zanjan, P.O. Box 45196-313, Zanjan, Iran.,School of Nanosciences, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
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9
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Hao QY, Chen Z, Sun XY, Liu BB, Wu CY. Theoretical analysis and simulation for a facilitated asymmetric exclusion process. Phys Rev E 2016; 94:022113. [PMID: 27627252 DOI: 10.1103/physreve.94.022113] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Indexed: 06/06/2023]
Abstract
Driven diffusive systems are important models in nonequilibrium state statistical mechanics. This paper studies an asymmetric exclusion process model with nearest rear neighbor interactions associated with energy. The exact flux expression of the model is obtained by a cluster mean-field method. Based on the flux expression, the properties of the fundamental diagram have been investigated in detail. To probe the energy's influence on the coarsening process of the system, Monte Carlo simulations are carried out to acquire the monotonic phase boundary in energy-density space. Above the phase boundary, the system is inhomogeneous and the normalized residence distribution p(s) is nonmonotonically decreasing. Under the phase boundary, the system is homogeneous and p(s) is monotonically decreasing. Further study comparatively shows that the system has turned into a microscopic inhomogeneous state from a homogeneous state before the system current arrives at maximum, if nearest rear neighbor interactions are strong. Our findings offer insights to deeply understand the dynamic features of nonequilibrium state systems.
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Affiliation(s)
- Qing-Yi Hao
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, China
| | - Zhe Chen
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, China
| | - Xiao-Yan Sun
- College of Physics and Electronic Engineering, Guangxi Teachers Education University, Nanning 530023, China
| | - Bing-Bing Liu
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, China
- School of Management, University of Science and Technology of China, Hefei 230026, China
| | - Chao-Yun Wu
- School of Mathematics and Computational Science, Anqing Normal University, Anqing 246133, China
- School of Engineering Science, University of Science and Technology of China, Hefei 230026, China
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10
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Einax M, Nitzan A. Maximum efficiency of state-space models of nanoscale energy conversion devices. J Chem Phys 2016; 145:014108. [DOI: 10.1063/1.4955160] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state. Sci Rep 2016; 6:19652. [PMID: 26804770 PMCID: PMC4726421 DOI: 10.1038/srep19652] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2015] [Accepted: 10/21/2015] [Indexed: 11/08/2022] Open
Abstract
Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.
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Einax M, Nitzan A. Network Analysis of Photovoltaic Energy Conversion. THE JOURNAL OF PHYSICAL CHEMISTRY C 2014; 118:27226-27234. [DOI: 10.1021/jp5084373] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Affiliation(s)
- Mario Einax
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - Abraham Nitzan
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
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13
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Dierl M, Dieterich W, Einax M, Maass P. Phase transitions in Brownian pumps. PHYSICAL REVIEW LETTERS 2014; 112:150601. [PMID: 24785016 DOI: 10.1103/physrevlett.112.150601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2014] [Indexed: 06/03/2023]
Abstract
We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur inside the channel when exclusion interactions between the particles are taken into account. These transitions reflect those known for the asymmetric simple exclusion process. We argue that their occurrence is a generic feature of Brownian motors operating in open systems.
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Affiliation(s)
- Marcel Dierl
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
| | | | - Mario Einax
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany and School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
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14
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Einax M. Optimal driving protocols for nano-sized devices and their dependence on couplings to reservoirs. JOURNAL OF PHYSICS: CONFERENCE SERIES 2014; 490:012185. [DOI: 10.1088/1742-6596/490/1/012185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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15
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Heuer A, Lühning L. Physical mechanisms of nonlinear conductivity: A model analysis. J Chem Phys 2014; 140:094508. [DOI: 10.1063/1.4867058] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Bakhti B, Karbach M, Maass P, Mokim M, Müller G. Statistically interacting vacancy particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012137. [PMID: 24580202 DOI: 10.1103/physreve.89.012137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2013] [Indexed: 06/03/2023]
Abstract
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits.
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Affiliation(s)
- Benaoumeur Bakhti
- Fachbereich Physik, Universität Osnabrück, D-49076 Osnabrück, Germany
| | - Michael Karbach
- Fachgruppe Physik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, D-49076 Osnabrück, Germany
| | - Mohammad Mokim
- Department of Physics, University of Rhode Island, Kingston, Rhode Island 02881, USA
| | - Gerhard Müller
- Department of Physics, University of Rhode Island, Kingston, Rhode Island 02881, USA
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17
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Arita C, Bouttier J, Krapivsky PL, Mallick K. Asymmetric exclusion process with global hopping. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042120. [PMID: 24229129 DOI: 10.1103/physreve.88.042120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Indexed: 06/02/2023]
Abstract
We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a nontrivial stationary state with a density profile varying over the spatial extent of the system. The density profile undergoes a nonequilibrium phase transition when the average density passes through the critical value 1-[4(1-ln2)](-1)=0.185277..., viz., in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.
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Affiliation(s)
- Chikashi Arita
- Institut de Physique Théorique, IPhT, CEA Saclay and URA 2306, CNRS, 91191 Gif-sur-Yvette Cedex, France and Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany
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18
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Bakhti B, Müller G, Maass P. Interacting hard rods on a lattice: distribution of microstates and density functionals. J Chem Phys 2013; 139:054113. [PMID: 23927249 DOI: 10.1063/1.4816379] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods, we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.
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Affiliation(s)
- Benaoumeur Bakhti
- Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, 49076 Osnabrück, Germany
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19
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Tian B, Jiang R, Ding ZJ, Hu MB, Wu QS. Phase diagrams of the Katz-Lebowitz-Spohn process on lattices with a junction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062124. [PMID: 23848644 DOI: 10.1103/physreve.87.062124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2012] [Revised: 03/13/2013] [Indexed: 06/02/2023]
Abstract
This paper studies the Katz-Lebowitz-Spohn (KLS) process on lattices with a junction, where particles move on parallel lattice branches that combine into a single lattice at the junction. It is shown that 11 kinds of phase diagrams could be observed, depending on the two parameters ε and δ in the KLS process. We have investigated the phase diagrams as well as bulk density analytically based on flow rate conservation and the extremal current principle. Extensive Monte Carlo computer simulations are performed, and it is found that they are in excellent agreement with theoretical prediction.
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Affiliation(s)
- Bo Tian
- School of Engineering Science, University of Science and Technology of China, Hefei 230026, China
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20
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Dierl M, Einax M, Maass P. One-dimensional transport of interacting particles: currents, density profiles, phase diagrams, and symmetries. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062126. [PMID: 23848646 DOI: 10.1103/physreve.87.062126] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2013] [Indexed: 06/02/2023]
Abstract
Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of nonequilibrium steady states. Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed, and its consequence for the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.
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Affiliation(s)
- Marcel Dierl
- Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, 49076 Osnabrück, Germany.
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21
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Bakhti B, Schott S, Maass P. Exact density functional for hard-rod mixtures derived from Markov chain approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:042107. [PMID: 22680524 DOI: 10.1103/physreve.85.042107] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2012] [Indexed: 06/01/2023]
Abstract
Using a Markov chain approach we rederive the exact density functional for hard-rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, which means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive.
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Affiliation(s)
- Benaoumeur Bakhti
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
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