1
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Montero AM, Santos A. Equation of state of hard-disk fluids under single-file confinement. J Chem Phys 2023; 158:2882841. [PMID: 37094005 DOI: 10.1063/5.0139116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2022] [Accepted: 03/27/2023] [Indexed: 04/26/2023] Open
Abstract
The exact transfer-matrix solution for the longitudinal equilibrium properties of the single-file hard-disk fluid is used to study the limiting low- and high-pressure behaviors analytically as functions of the pore width. In the low-pressure regime, the exact third and fourth virial coefficients are obtained, which involve single and double integrals, respectively. Moreover, we show that the standard irreducible diagrams do not provide a complete account of the virial coefficients in confined geometries. The asymptotic equation of state in the high-pressure limit is seen to present a simple pole at the close-packing linear density, as in the hard-rod fluid, but, in contrast to the latter case, the residue is 2. Since, for an arbitrary pressure, the exact transfer-matrix treatment requires the numerical solution of an eigenvalue integral equation, we propose here two simple approximations to the equation of state, with different complexity levels, and carry out an extensive assessment of their validity and practical convenience vs the exact solution and available computer simulations.
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Affiliation(s)
- Ana M Montero
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Andrés Santos
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
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2
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Schweers S, Antonov AP, Ryabov A, Maass P. Scaling laws for single-file diffusion of adhesive particles. Phys Rev E 2023; 107:L042102. [PMID: 37198860 DOI: 10.1103/physreve.107.l042102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 03/29/2023] [Indexed: 05/19/2023]
Abstract
Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.
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Affiliation(s)
- Sören Schweers
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Alexander P Antonov
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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3
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Banerjee T, Jack RL, Cates ME. Role of initial conditions in one-dimensional diffusive systems: Compressibility, hyperuniformity, and long-term memory. Phys Rev E 2022; 106:L062101. [PMID: 36671167 DOI: 10.1103/physreve.106.l062101] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 11/04/2022] [Indexed: 06/17/2023]
Abstract
We analyze the long-lasting effects of initial conditions on dynamical fluctuations in one-dimensional diffusive systems. We consider the mean-squared displacement of tracers in homogeneous systems with single-file diffusion, and current fluctuations for noninteracting diffusive particles. In each case we show analytically that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched cases studied previously, alongside a continuous family of other classes among which equilibrated (or annealed) initial conditions are but one member. We verify our predictions through extensive Monte Carlo simulations.
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Affiliation(s)
- Tirthankar Banerjee
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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4
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Benenti G, Casati G, Marchesoni F, Wang J. Autonomous circular heat engine. Phys Rev E 2022; 106:044104. [PMID: 36397467 DOI: 10.1103/physreve.106.044104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows against the applied thermodynamic forces. Numerical simulations and linear-response analysis suggest that, in the absence of frictional losses, the Carnot efficiency can be achieved in the thermodynamic limit.
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Affiliation(s)
- Giuliano Benenti
- Dipartimento di Scienza e Alta Technologia, Center for Nonlinear and Complex Systems, Universitâ degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Giulio Casati
- Dipartimento di Scienza e Alta Technologia, Center for Nonlinear and Complex Systems, Universitâ degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário - Lagoa Nova, CP. 1613, Natal, Rio Grande Do Norte 59078-970, Brazil
| | - Fabio Marchesoni
- Department of Physics, University of Camerino, 61032 Camerino, Italy
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jiao Wang
- Department of Physics and Key Laboratory of Low Dimensional Condensed Matter Physics (Department of Education of Fujian Province), Xiamen University, Xiamen 361005, Fujian, China
- Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, Gansu, China
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5
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Zhang Y, Ge J, Bian X, Kumar A. Quantitative Models of Lipid Transfer and Membrane Contact Formation. CONTACT (THOUSAND OAKS (VENTURA COUNTY, CALIF.)) 2022; 5:1-21. [PMID: 36120532 DOI: 10.1177/25152564221096024] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Lipid transfer proteins (LTPs) transfer lipids between different organelles, and thus play key roles in lipid homeostasis and organelle dynamics. The lipid transfer often occurs at the membrane contact sites (MCS) where two membranes are held within 10-30 nm. While most LTPs act as a shuttle to transfer lipids, recent experiments reveal a new category of eukaryotic LTPs that may serve as a bridge to transport lipids in bulk at MCSs. However, the molecular mechanisms underlying lipid transfer and MCS formation are not well understood. Here, we first review two recent studies of extended synaptotagmin (E-Syt)-mediated membrane binding and lipid transfer using novel approaches. Then we describe mathematical models to quantify the kinetics of lipid transfer by shuttle LTPs based on a lipid exchange mechanism. We find that simple lipid mixing among membranes of similar composition and/or lipid partitioning among membranes of distinct composition can explain lipid transfer against a concentration gradient widely observed for LTPs. We predict that selective transport of lipids, but not membrane proteins, by bridge LTPs leads to osmotic membrane tension by analogy to the osmotic pressure across a semipermeable membrane. A gradient of such tension and the conventional membrane tension may drive bulk lipid flow through bridge LTPs at a speed consistent with the fast membrane expansion observed in vivo. Finally, we discuss the implications of membrane tension and lipid transfer in organelle biogenesis. Overall, the quantitative models may help clarify the mechanisms of LTP-mediated MCS formation and lipid transfer.
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Affiliation(s)
- Yongli Zhang
- Department of Cell Biology, Yale University School of Medicine, New Haven, CT, USA.,Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA
| | - Jinghua Ge
- Department of Cell Biology, Yale University School of Medicine, New Haven, CT, USA
| | - Xin Bian
- Department of Cell Biology, Yale University School of Medicine, New Haven, CT, USA.,Department of Neuroscience, Yale University School of Medicine, New Haven, CT, USA.,Present address: State Key Laboratory of Medicinal Chemical Biology, College of Life Sciences, Nankai University, Tianjin, China
| | - Avinash Kumar
- Department of Cell Biology, Yale University School of Medicine, New Haven, CT, USA
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6
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Knowles SF, Fletcher M, Mc Hugh J, Earle M, Keyser UF, Thorneywork AL. Observing capture with a colloidal model membrane channel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:344001. [PMID: 35679844 DOI: 10.1088/1361-648x/ac7764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
We use video microscopy to study the full capture process for colloidal particles transported through microfluidic channels by a pressure-driven flow. In particular, we obtain trajectories for particles as they move from the bulk into confinement, using these to map in detail the spatial velocity and concentration fields for a range of different flow velocities. Importantly, by changing the height profiles of our microfluidic devices, we consider systems for which flow profiles in the channel are the same, but flow fields in the reservoir differ with respect to the quasi-2D monolayer of particles. We find that velocity fields and profiles show qualitative agreement with numerical computations of pressure-driven fluid flow through the systems in the absence of particles, implying that in the regimes studied here particle-particle interactions do not strongly perturb the flow. Analysis of the particle flux through the channel indicates that changing the reservoir geometry leads to a change between long-range attraction of the particles to the pore and diffusion-to-capture-like behaviour, with concentration fields that show qualitative changes based on device geometry. Our results not only provide insight into design considerations for microfluidic devices, but also a foundation for experimental elucidation of the concept of a capture radius. This long standing problem plays a key role in transport models for biological channels and nanopore sensors.
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Affiliation(s)
- Stuart F Knowles
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Marcus Fletcher
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Jeffrey Mc Hugh
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Max Earle
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Ulrich F Keyser
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
| | - Alice L Thorneywork
- Cavendish Laboratory, University of Cambridge, J J Thomson Ave, Cambridge CB3 0HE, United Kingdom
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7
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Farrell S, Rutenberg AD. Non-Fickian single-file pore transport. Phys Rev E 2021; 104:L032102. [PMID: 34654154 DOI: 10.1103/physreve.104.l032102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Accepted: 08/26/2021] [Indexed: 11/07/2022]
Abstract
Single-file diffusion exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short porelike channels using a symmetric exclusion process with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux 〈Φ〉∼1/L^{3}, where L is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with 〈Φ〉∼1/L. Longer systems are more often in a low-flux state, leading to the non-Fickian behavior.
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Affiliation(s)
- Spencer Farrell
- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
| | - Andrew D Rutenberg
- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
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8
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Poncet A, Bénichou O, Illien P. Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes. Phys Rev E 2021; 103:L040103. [PMID: 34005907 DOI: 10.1103/physreve.103.l040103] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 04/02/2021] [Indexed: 11/07/2022]
Abstract
The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions-annealed or quenched-has a quantitative impact on the long-time properties of tracer diffusion. However, so far, the cumulant generating function in the quenched case was only determined in the low-density limit and for the specific case of a half-filled system. Here, we derive it in the opposite dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.
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Affiliation(s)
- Alexis Poncet
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Olivier Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
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9
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Cho JH, Bischofberger I. Two modes of cluster dynamics govern the viscoelasticity of colloidal gels. Phys Rev E 2021; 103:032609. [PMID: 33862797 DOI: 10.1103/physreve.103.032609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 03/05/2021] [Indexed: 11/07/2022]
Abstract
Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.
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Affiliation(s)
- Jae Hyung Cho
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Irmgard Bischofberger
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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10
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Sprenger AR, Jahanshahi S, Ivlev AV, Löwen H. Time-dependent inertia of self-propelled particles: The Langevin rocket. Phys Rev E 2021; 103:042601. [PMID: 34005997 DOI: 10.1103/physreve.103.042601] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.
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Affiliation(s)
- Alexander R Sprenger
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Soudeh Jahanshahi
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Alexei V Ivlev
- Max-Planck-Institut für Extraterrestrische Physik, 85748 Garching, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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11
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Duarte-Filho GC, Santos FAN, Gaffney EA. Fock-space methods for diffusion: Capturing volume exclusion via fermionic statistics. Phys Rev E 2020; 102:052101. [PMID: 33327117 DOI: 10.1103/physreve.102.052101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 10/13/2020] [Indexed: 11/07/2022]
Abstract
Volume exclusion and single-file diffusion play an important role at very small scales, such as those associated with molecular machines, ion channels, and transport in zeolites, while introducing fundamental differences compared to Brownian motion, such as changes to the power-law relation between the mean square displacement and time. In this work we map the chemical master equation for excluded diffusion onto a Schrödinger equation via annihilation and creation ladder operators with fermionic statistics, together with linear and symbolic algebra with the resulting Fock-space representation to describe the effect of volume-exclusion processes in finite one-dimensional chains. We contrast the dynamics with the nonexclusive (bosonic) diffusion for crowded, intermediate, and dilute particle populations. Motivated by shuttling in molecular machines, we proceed to investigate differences in exit time distributions introduced by volume exclusion, incorporating the presence of transport bias. More generally, this study demonstrates how one can analyze volume-excluded transport for small stochastic systems, without the need for stochastic simulation and ensemble averaging, simply by considering anticommutation relations and fermionic statistics in a Fock-space representation of the stochastic dynamics.
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Affiliation(s)
- Gerson C Duarte-Filho
- Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristóvão, Sergipe, Brazil
| | - Fernando A N Santos
- Departamento de Matemática Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil and Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Pernambuco, Brazil
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
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12
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Lapolla A, Godec A. Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle. J Chem Phys 2020; 153:194104. [PMID: 33218229 DOI: 10.1063/5.0025785] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the "confining" (all background particles in front of the tagged-particle) and "pushing" (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.
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Affiliation(s)
- Alessio Lapolla
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany
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13
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Shin J, Berezhkovskii AM, Kolomeisky AB. Biased Random Walk in Crowded Environment: Breaking Uphill/Downhill Symmetry of Transition Times. J Phys Chem Lett 2020; 11:4530-4535. [PMID: 32433884 DOI: 10.1021/acs.jpclett.0c01113] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Various natural processes can be analyzed using the concept of random walks. For a single random walker, the mean waiting times for uphill and downhill transitions between neighboring sites are equal. Here we investigate the uphill/downhill symmetry of waiting times for transitions of a tracer in crowded environment using exactly solvable one-dimensional stochastic models. It is found that, unexpectedly, the time to move in the direction of the bias (downhill) is always longer than the time to move against the bias (uphill). The degree of asymmetry depends on the particle density, the strength of the bias, and the size of the system. The microscopic origin of the symmetry breaking is discussed.
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Affiliation(s)
- Jaeoh Shin
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Anatoly B Kolomeisky
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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14
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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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15
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Zhang L, Xiao Z, Chen X, Chen J, Wang W. Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields. ACS NANO 2019; 13:8842-8853. [PMID: 31265246 DOI: 10.1021/acsnano.9b02100] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO2-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.
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Affiliation(s)
- Liangliang Zhang
- School of Materials Science and Engineering , Harbin Institute of Technology (Shenzhen) , Shenzhen , Guangdong 518055 , China
| | - Zuyao Xiao
- School of Materials Science and Engineering , Harbin Institute of Technology (Shenzhen) , Shenzhen , Guangdong 518055 , China
| | - Xi Chen
- School of Materials Science and Engineering , Harbin Institute of Technology (Shenzhen) , Shenzhen , Guangdong 518055 , China
| | - Jingyuan Chen
- School of Materials Science and Engineering , Harbin Institute of Technology (Shenzhen) , Shenzhen , Guangdong 518055 , China
| | - Wei Wang
- School of Materials Science and Engineering , Harbin Institute of Technology (Shenzhen) , Shenzhen , Guangdong 518055 , China
- IBS Center for Soft and Living Matter , Institute of Basic Science , Ulsan 44919 , Republic of Korea
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16
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Debnath T, Ghosh PK, Li Y, Marchesoni F, Nori F. Active diffusion limited reactions. J Chem Phys 2019; 150:154902. [DOI: 10.1063/1.5081125] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Affiliation(s)
- Tanwi Debnath
- Department of Chemistry, University of Calcutta, Kolkata 700009, India
| | - Pulak K. Ghosh
- Department of Chemistry, Presidency University, Kolkata 700073, India
| | - Yunyun Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China
| | - Fabio Marchesoni
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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17
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Tracer diffusion in crowded narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:443001. [PMID: 30211693 DOI: 10.1088/1361-648x/aae13a] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.
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Affiliation(s)
- O Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 4 Place Jussieu, 75252 Paris Cedex 05, France
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18
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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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19
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Farrell SG, Rutenberg AD. Anomalously slow transport in single-file diffusion with slow binding kinetics. Phys Rev E 2018; 98:022114. [PMID: 30253590 DOI: 10.1103/physreve.98.022114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2017] [Indexed: 01/28/2023]
Abstract
We computationally study the effects of binding kinetics to the channel wall, leading to transient immobility, on the diffusive transport of particles within narrow channels, that exhibit single-file diffusion (SFD). We find that slow binding kinetics leads to an anomalously slow diffusive transport. Remarkably, the scaled diffusivity D[over ̂] characterizing transport exhibits scaling collapse with respect to the occupation fraction p of sites along the channel. We present a simple "cage-physics" picture that captures the characteristic occupation fraction p_{scale} and the asymptotic 1/p^{2} behavior for p/p_{scale}≳1. We confirm that subdiffusive behavior of tracer particles is controlled by the same D[over ̂] as particle transport.
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Affiliation(s)
- Spencer G Farrell
- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2
| | - Andrew D Rutenberg
- Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2
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20
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Ramírez-Garza OA, Méndez-Alcaraz JM, González-Mozuelos P. Structural and dynamic inhomogeneities induced by curvature gradients in elliptic colloidal halos of paramagnetic particles. J Chem Phys 2017; 146:194903. [PMID: 28527452 DOI: 10.1063/1.4983496] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Paramagnetic colloidal particles distributed along an ellipse are used as a model system to study the effects of curvature gradients on the structure and dynamics of colloids in curved manifolds. Unlike what happens for circular and spherical systems, in the present case, the equilibrium one-particle distribution function displays inhomogeneities due to the changing curvature along the ellipse. The ensuing effects on the two-body correlations are also analyzed, leading to the observation of anisotropic and long-ranged effects. Another noticeable consequence is the slowing down of the self-diffusion of these particles, which for large eccentricities may induce metastable states; this is evaluated by means of the time-dependent self-distribution.
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Affiliation(s)
- O A Ramírez-Garza
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
| | - J M Méndez-Alcaraz
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
| | - P González-Mozuelos
- Departamento de Física, Cinvestav del I. P. N., Ave. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, C.P. 07360, Mexico
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