1
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Lukyanets SP, Kliushnichenko OV. Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle. Phys Rev E 2024; 109:054103. [PMID: 38907458 DOI: 10.1103/physreve.109.054103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 04/08/2024] [Indexed: 06/24/2024]
Abstract
We consider a nonequilibrium transition that leads to the formation of nonlinear steady-state structures due to the gas flow scattering on a partially penetrable obstacle. The resulting nonequilibrium steady state (NESS) corresponds to a two-domain gas structure attained at certain critical parameters. We use a simple mean-field model of the driven lattice gas with ring topology to demonstrate that this transition is accompanied by the emergence of local invariants related to a complex composed of the obstacle and its nearest gas surrounding, which we refer to as obstacle edges. These invariants are independent of the main system parameters and behave as local first integrals, at least qualitatively. As a result, the complex becomes insensitive to the noise of external driving field within the overcritical domain. The emerged invariants describe the conservation of the number of particles inside the obstacle and strong temporal synchronization or correlation of gas states at obstacle edges. Such synchronization guarantees the equality to zero of the total edge current at any time. The robustness against external drive fluctuations is shown to be accompanied by strong spatial localization of induced gas fluctuations near the domain wall separating the depleted and dense gas phases. Such a behavior can be associated with nonequilibrium protection effect and synchronization of edges. The transition rates between different NESSs are shown to be different. The relaxation rates from one NESS to another take complex and real values in the sub- and overcritical regimes, respectively. The mechanism of these transitions is governed by the generation of shock waves at the back side of the obstacle. In the subcritical regime, these solitary waves are generated sequentially many times, while only a single excitation is sufficient to rearrange the system state in the overcritical regime.
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Affiliation(s)
- S P Lukyanets
- Department of Theoretical Physics, Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kyiv, Ukraine
| | - O V Kliushnichenko
- Department of Theoretical Physics, Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kyiv, Ukraine
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2
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Blom K, Song K, Vouga E, Godec A, Makarov DE. Milestoning estimators of dissipation in systems observed at a coarse resolution. Proc Natl Acad Sci U S A 2024; 121:e2318333121. [PMID: 38625949 PMCID: PMC11047069 DOI: 10.1073/pnas.2318333121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 03/14/2024] [Indexed: 04/18/2024] Open
Abstract
Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.
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Affiliation(s)
- Kristian Blom
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Kevin Song
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Etienne Vouga
- Department of Computer Science, University of Texas at Austin, Austin, TX78712
| | - Aljaž Godec
- Mathematical biophysics Group, Max Planck Institute for Multidisciplinary Sciences, Göttingen37077, Germany
| | - Dmitrii E. Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX78712
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3
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Santra S, Singh P. Exact fluctuation and long-range correlations in a single-file model under resetting. Phys Rev E 2024; 109:034123. [PMID: 38632800 DOI: 10.1103/physreve.109.034123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/24/2024] [Indexed: 04/19/2024]
Abstract
Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behavior of a system as exemplified by the emergence of nonequilibrium properties and expedition of search processes. Herein we explore the ramifications of stochastic resetting in the context of a single-file system called random average process (RAP) in one dimension. In particular, we focus on the dynamics of tracer particles and analytically compute the variance, equal time correlation, autocorrelation, and unequal time correlation between the positions of different tracer particles. Our study unveils that resetting gives rise to rather different behaviors depending on whether the particles move symmetrically or asymmetrically. For the asymmetric case, the system for instance exhibits a long-range correlation which is not seen in absence of the resetting. Similarly, in contrast to the reset-free RAP, the variance shows distinct scalings for symmetric and asymmetric cases. While for the symmetric case, it decays (towards its steady value) as ∼e^{-rt}/sqrt[t], we find ∼te^{-rt} decay for the asymmetric case (r being the resetting rate). Finally, we examine the autocorrelation and unequal time correlation in the steady state and demonstrate that they obey interesting scaling forms at late times. All our analytical results are substantiated by extensive numerical simulations.
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Affiliation(s)
- Saikat Santra
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Prashant Singh
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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4
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Hartmann AK, Meerson B. First-passage area distribution and optimal fluctuations of fractional Brownian motion. Phys Rev E 2024; 109:014146. [PMID: 38366541 DOI: 10.1103/physreve.109.014146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Accepted: 01/08/2024] [Indexed: 02/18/2024]
Abstract
We study the probability distribution P(A) of the area A=∫_{0}^{T}x(t)dt swept under fractional Brownian motion (fBm) x(t) until its first passage time T to the origin. The process starts at t=0 from a specified point x=L. We show that P(A) obeys exact scaling relation P(A)=D^{1/2H}/L^{1+1/H}Φ_{H}(D^{1/2H}A/L^{1+1/H}), where 0
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Affiliation(s)
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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5
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Rizkallah P, Sarracino A, Bénichou O, Illien P. Absolute Negative Mobility of an Active Tracer in a Crowded Environment. PHYSICAL REVIEW LETTERS 2023; 130:218201. [PMID: 37295085 DOI: 10.1103/physrevlett.130.218201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Revised: 02/17/2023] [Accepted: 04/11/2023] [Indexed: 06/12/2023]
Abstract
Absolute negative mobility (ANM) refers to the situation where the average velocity of a driven tracer is opposite to the direction of the driving force. This effect was evidenced in different models of nonequilibrium transport in complex environments, whose description remains effective. Here, we provide a microscopic theory for this phenomenon. We show that it emerges in the model of an active tracer particle submitted to an external force and which evolves on a discrete lattice populated with mobile passive crowders. Resorting to a decoupling approximation, we compute analytically the velocity of the tracer particle as a function of the different parameters of the system and confront our results to numerical simulations. We determine the range of parameters where ANM can be observed, characterize the response of the environment to the displacement of the tracer, and clarify the mechanism underlying ANM and its relationship with negative differential mobility (another hallmark of driven systems far from the linear response).
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Affiliation(s)
- Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Dipartimento di Ingegneria, Università della Campania Luigi Vanvitelli, 81031 Aversa (CE), Italy
- Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185, Rome, Italy
| | - 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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6
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Grabsch A, Rizkallah P, Illien P, Bénichou O. Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond. PHYSICAL REVIEW LETTERS 2023; 130:020402. [PMID: 36706397 DOI: 10.1103/physrevlett.130.020402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 12/07/2022] [Indexed: 06/18/2023]
Abstract
Tracer dynamics in the symmetric exclusion process (SEP), where hard-core particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by an external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference and higher-order moments but only in the high-density limit. Here, we provide a general hydrodynamic framework that allows us to determine the first cumulants of the bath-tracer correlations and of the tracer's position in function of the driving force, up to quadratic order (beyond linear response). This result constitutes the first determination of the bias dependence of the variance of a driven tracer in the SEP for an arbitrary density. The framework presented here can be applied, beyond the SEP, to more general configurations of a driven tracer in interaction with obstacles in one dimension.
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Affiliation(s)
- Aurélien Grabsch
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Rizkallah
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 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
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7
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Meerson B, Bénichou O, Oshanin G. Path integrals for fractional Brownian motion and fractional Gaussian noise. Phys Rev E 2022; 106:L062102. [PMID: 36671110 DOI: 10.1103/physreve.106.l062102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 11/23/2022] [Indexed: 12/15/2022]
Abstract
Wiener's path integral plays a central role in the study of Brownian motion. Here we derive exact path-integral representations for the more general fractional Brownian motion (FBM) and for its time derivative process, fractional Gaussian noise (FGN). These paradigmatic non-Markovian stochastic processes, introduced by Kolmogorov, Mandelbrot, and van Ness, found numerous applications across the disciplines, ranging from anomalous diffusion in cellular environments to mathematical finance. Their exact path-integral representations were previously unknown. Our formalism exploits the Gaussianity of the FBM and FGN, relies on the theory of singular integral equations, and overcomes some technical difficulties by representing the action functional for the FBM in terms of the FGN for the subdiffusive FBM and in terms of the derivative of the FGN for the super-diffusive FBM. We also extend the formalism to include external forcing. The exact and explicit path-integral representations make inroads in the study of the FBM and FGN.
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Affiliation(s)
- Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, CNRS, Sorbonne Université, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Gleb Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, UMR CNRS 7600, CNRS, Sorbonne Université, 4 Place Jussieu, 75252 Paris Cedex 05, France.,Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
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8
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Cerasoli S, Ciliberto S, Marinari E, Oshanin G, Peliti L, Rondoni L. Spectral fingerprints of nonequilibrium dynamics: The case of a Brownian gyrator. Phys Rev E 2022; 106:014137. [PMID: 35974646 DOI: 10.1103/physreve.106.014137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally relevant model of such a system-the so-called Brownian gyrator-a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under nonequilibrium conditions, while no net rotation takes place under equilibrium ones. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in nonequilibrium. We show that indeed one can conclusively distinguish between equilibrium and nonequilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a nonequilibrium dynamics.
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Affiliation(s)
- Sara Cerasoli
- Department of Civil and Environmental Engineering, Princeton University, Princeton New Jersey 08544, USA
| | - Sergio Ciliberto
- Laboratoire de Physique (UMR CNRS 567246), Ecole Normale Supérieure, Allée d'Italie, 69364 Lyon, France
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Luca Peliti
- Santa Marinella Research Institute, Santa Marinella, Italy
| | - Lamberto Rondoni
- Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
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9
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Rizkallah P, Sarracino A, Bénichou O, Illien P. Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment. PHYSICAL REVIEW LETTERS 2022; 128:038001. [PMID: 35119883 DOI: 10.1103/physrevlett.128.038001] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.
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Affiliation(s)
- Pierre Rizkallah
- Sorbonne Université, CNRS, Laboratoire de Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Alessandro Sarracino
- Dipartimento di Ingegneria, Università della Campania "Luigi Vanvitelli", 81031 Aversa (CE), Italy
| | - 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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10
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Hartich D, Godec A. Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion. PHYSICAL REVIEW LETTERS 2021; 127:080601. [PMID: 34477441 DOI: 10.1103/physrevlett.127.080601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.
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Affiliation(s)
- David Hartich
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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11
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Abbaspour L, Klumpp S. Enhanced diffusion of a tracer particle in a lattice model of a crowded active system. Phys Rev E 2021; 103:052601. [PMID: 34134202 DOI: 10.1103/physreve.103.052601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 03/15/2021] [Indexed: 11/07/2022]
Abstract
Living systems at the subcellular, cellular, and multicellular levels are often crowded systems that contain active particles. The active motion of these particles can also propel passive particles, which typically results in enhanced effective diffusion of the passive particles. Here we study the diffusion of a passive tracer particle in such a dense system of active crowders using a minimal lattice model incorporating particles pushing each other. We show that the model exhibits several regimes of motility and quantify the enhanced diffusion as a function of density and activity of the active crowders. Moreover, we demonstrate an interplay of tracer diffusion and clustering of active particles, which suppresses the enhanced diffusion. Simulations of mixtures of passive and active crowders show that a rather small fraction of active particles is sufficient for the observation of enhanced diffusion.
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Affiliation(s)
- Leila Abbaspour
- Institute for the Dynamics of Complex Systems and Max Planck School Matter to Life, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Stefan Klumpp
- Institute for the Dynamics of Complex Systems and Max Planck School Matter to Life, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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12
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Khatri N, Burada PS. Confined diffusion in a random Lorentz gas environment. Phys Rev E 2020; 102:012137. [PMID: 32794985 DOI: 10.1103/physreve.102.012137] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 06/30/2020] [Indexed: 11/07/2022]
Abstract
We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacle density η and the scaling parameter f, which is the ratio of work done to the particles to available thermal energy. We show that, when the thermal fluctuations dominate over the external force, i.e., small f regime, particles get trapped in the given environment when the system percolates at the critical obstacle density η_{c}≈1.2. However, as f increases, we observe that particle trapping occurs prior to η_{c}. In particular, we find a relation between η and f which provides an estimate of the minimum η up to a critical scaling parameter f_{c} beyond which the Fick-Jacobs description is invalid. Prominent transport features like nonmonotonic behavior of the nonlinear mobility, anomalous diffusion, and greatly enhanced effective diffusion coefficient are explained for various strengths of f and η. Also, it is interesting to observe that particles exhibit different kinds of diffusive behaviors, i.e., subdiffusion, normal diffusion, and superdiffusion. These findings, which are genuine to the confined and random Lorentz gas environment, can be useful to understand the transport of small particles or molecules in systems such as molecular sieves and porous media, which have a complex heterogeneous environment of the freezing obstacles.
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Affiliation(s)
- Narender Khatri
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - P S Burada
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.,Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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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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Malgaretti P, Oshanin G, Talbot J. Special issue on transport in narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:270201. [PMID: 31025626 DOI: 10.1088/1361-648x/ab1548] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Affiliation(s)
- Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany. Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC (UMR CNRS 7600), 4 Place Jussieu, CEDEX 05, 75252 Paris, France
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15
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Agranov T, Krapivsky PL, Meerson B. Occupation-time statistics of a gas of interacting diffusing particles. Phys Rev E 2019; 99:052102. [PMID: 31212513 DOI: 10.1103/physreve.99.052102] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2019] [Indexed: 11/07/2022]
Abstract
The time that a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently, the joint occupation-time statistics of an ensemble of noninteracting particles was addressed using the single-particle statistics. Here we employ the macroscopic fluctuation theory (MFT) to study the occupation-time statistics of many interacting particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of noninteracting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.
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Affiliation(s)
- Tal Agranov
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - Baruch Meerson
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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16
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Barré C, Page G, Talbot J, Viot P. Recurrence dynamics of particulate transport with reversible blockage: From a single channel to a bundle of coupled channels. Phys Rev E 2019; 99:042119. [PMID: 31108653 DOI: 10.1103/physreve.99.042119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Indexed: 11/07/2022]
Abstract
We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of N_{c} identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting particle flux (or throughput) and the probability that the bundle is open. For a constant entering flux, the bundle evolves through a transient regime to a steady state. We present analytic solutions for the stationary properties of a single channel with capacity N≤3 and for a bundle of channels each of capacity N=1. For larger values of N and N_{c}, the system's steady state behavior is explored by numerical simulation. Depending on the deblocking time, the exiting flux either increases monotonically with intensity or displays a maximum at a finite intensity. For large N we observe an abrupt change from a state with few blockages to one in which the bundle is permanently blocked and the exiting flux is due entirely to the release of blocked particles. We also compare the relative efficiency of coupled and uncoupled bundles. For N=1 the coupled system is always more efficient, but for N>1 the behavior is more complex.
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Affiliation(s)
- Chloé Barré
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75005 Paris Cedex 05, France
| | - Gregory Page
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75005 Paris Cedex 05, France
| | - Julian Talbot
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75005 Paris Cedex 05, France
| | - Pascal Viot
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, 75005 Paris Cedex 05, France
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Chatterjee R, Segall N, Merrigan C, Ramola K, Chakraborty B, Shokef Y. Motion of active tracer in a lattice gas with cross-shaped particles. J Chem Phys 2019; 150:144508. [DOI: 10.1063/1.5085769] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Rakesh Chatterjee
- School of Mechanical Engineering and Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Nimrod Segall
- School of Mechanical Engineering and Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Carl Merrigan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - Kabir Ramola
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500107, India
| | - Bulbul Chakraborty
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - Yair Shokef
- School of Mechanical Engineering and Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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18
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Puertas AM, Malgaretti P, Pagonabarraga I. Active microrheology in corrugated channels. J Chem Phys 2018; 149:174908. [DOI: 10.1063/1.5048343] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Antonio M. Puertas
- Department of Applied Physics, Universidad de Almería, 04120 Almería, Spain
| | - Paolo Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
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