1
|
Slanina F, Kotrla M. Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores. Phys Rev E 2023; 107:064606. [PMID: 37464715 DOI: 10.1103/physreve.107.064606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 06/09/2023] [Indexed: 07/20/2023]
Abstract
The system of driven dense colloid mixtures is studied in one-, two-, and three-dimensional geometries. We calculate the diffusion coefficients and mobilities for each particle type, including cross-terms, in a hydrodynamic limit, using a mean-field-type approximation. The set of nonlinear diffusion equations are then solved. In one dimension, analytical results are possible. We show that in mixtures, the "Brazil nut" phenomenon, or depletion of larger particles by force of smaller ones, appears quite generically. We calculate the ratchet current and quantify the capability of sorting particles according to their size. We also indicate that the "Brazil nut" effect lies behind the possibility of perfect separation, where large and big particles travel in strictly opposite direction.
Collapse
Affiliation(s)
- František Slanina
- Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic
| | - Miroslav Kotrla
- Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic
| |
Collapse
|
2
|
Slanina F, Kotrla M, Netočný K. Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores. Phys Rev E 2022; 106:014610. [PMID: 35974637 DOI: 10.1103/physreve.106.014610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 07/05/2022] [Indexed: 06/15/2023]
Abstract
The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For the one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In the two-component system, the correlation function behaves in a more complicated manner: Its sign oscillates but the envelope decays again very slowly and the decay is compatible with a power law with an exponent somewhat lower than 2. Therefore, our generalization of the ASEP belongs to a different universality class from the ensemble of generalized ASEP models which are mappable to zero-range processes.
Collapse
Affiliation(s)
- František Slanina
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 18221 Praha, Czech Republic
| | - Miroslav Kotrla
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 18221 Praha, Czech Republic
| | - Karel Netočný
- Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 18221 Praha, Czech Republic
| |
Collapse
|
3
|
Lei Y, Su Z. Hydrodynamic Limit for the d-Facilitated Exclusion Process. J THEOR PROBAB 2022. [DOI: 10.1007/s10959-022-01172-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
4
|
Blondel O, Erignoux C, Sasada M, Simon M. Hydrodynamic limit for a facilitated exclusion process. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2020. [DOI: 10.1214/19-aihp977] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
The invariant measures and the limiting behaviors of the facilitated TASEP. Stat Probab Lett 2019. [DOI: 10.1016/j.spl.2019.108557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
6
|
Chatterjee A, Mohanty PK. Multichain models of conserved lattice gas. Phys Rev E 2017; 96:042120. [PMID: 29347572 DOI: 10.1103/physreve.96.042120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2017] [Indexed: 06/07/2023]
Abstract
Conserved lattice-gas models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents β=1=ν=η, whereas the same on a ladder belong to directed percolation (DP) universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder forces the APT to be in the DP class. To substantiate this we introduce a class of restricted conserved lattice-gas models on a multichain system (M×L square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains, in the thermodynamic limit L→∞, these models exhibit APT at ρ_{c}=1/2(1+1/M) with β=1. On the other hand, for even-chain systems transition occurs at ρ_{c}=1/2 with β=1,2 for M=2,4, respectively, and β=3 for M≥6. We illustrate this unusual critical behavior analytically using a transfer-matrix method.
Collapse
Affiliation(s)
- Arijit Chatterjee
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - P K Mohanty
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| |
Collapse
|
7
|
Chatterjee A, Mohanty PK. Multicritical absorbing phase transition in a class of exactly solvable models. Phys Rev E 2017; 94:062141. [PMID: 28085348 DOI: 10.1103/physreve.94.062141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Indexed: 11/06/2022]
Abstract
We study diffusion of hard-core particles on a one-dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value n+1; an initial separation larger than n+1 can however decrease. These models undergo an absorbing state phase transition when the conserved particle density of the system falls below a critical threshold ρ_{c}=1/(n+1). We find that the ϕ_{k}, the density of 0-clusters (0 representing vacancies) of size 0≤k<n, vanish at the transition point along with activity density ρ_{a}. The steady state of these models can be written in matrix product form to obtain analytically the static exponents β_{k}=n-k and ν=1=η corresponding to each ϕ_{k}. We also show from numerical simulations that, starting from a natural condition, ϕ_{k}(t)s decay as t^{-α_{k}} with α_{k}=(n-k)/2 even though other dynamic exponents ν_{t}=2=z are independent of k; this ensures the validity of scaling laws β=αν_{t} and ν_{t}=zν.
Collapse
Affiliation(s)
- Arijit Chatterjee
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - P K Mohanty
- CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India
| |
Collapse
|
8
|
Basu U. Phase separation transition in a nonconserved two-species model. Phys Rev E 2017; 94:062137. [PMID: 28085388 DOI: 10.1103/physreve.94.062137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2016] [Indexed: 11/07/2022]
Abstract
A one-dimensional stochastic exclusion process with two species of particles, + and -, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show that, in the limiting case where density of negative particles vanishes, the system undergoes a phase separation transition where a macroscopic domain of vacancies form in front of a single surviving negative particle. We also show that the phase-separated state is associated with a diverging correlation length for any density and that the critical exponents characterizing the behavior in this region are different from those at the transition line. The static and the dynamical critical exponents are obtained from the exact solution and numerical simulations, respectively.
Collapse
Affiliation(s)
- Urna Basu
- SISSA-International School for Advanced Studies, and INFN, via Bonomea 265, I-34136 Trieste, Italy
| |
Collapse
|
9
|
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.
Collapse
|
10
|
Bhat U, Krapivsky PL. Exclusion processes with avalanches. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012133. [PMID: 25122277 DOI: 10.1103/physreve.90.012133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2014] [Indexed: 06/03/2023]
Abstract
In an exclusion process with avalanches, when a particle hops to a neighboring empty site which is adjacent to an island the particle on the other end of the island immediately hops, and if it joins another island this triggers another hop. There are no restrictions on the length of the islands and the duration of the avalanche. This process is well defined in the low-density region ρ < 1/2. We describe the nature of steady states (on a ring) and determine all correlation functions. For the asymmetric version of the process, we compute the steady state current, and we describe shock and rarefaction waves which arise in the evolution of the step-function initial profile. For the symmetric version, we determine the diffusion coefficient and examine the evolution of a tagged particle.
Collapse
Affiliation(s)
- Uttam Bhat
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| |
Collapse
|
11
|
Bondyopadhyay S. Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062125. [PMID: 24483404 DOI: 10.1103/physreve.88.062125] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2013] [Indexed: 06/03/2023]
Abstract
There are several examples which show that the critical exponents can be dependent on the initial condition of the system. In such situations, there are many systems where various issues related to the universal behavior, e.g., the existence of universality, the splitting of the universality class, scaling violations, whether the initial dependence should persist even after a sufficiently long time or is a transient effect, the reasons for such features, etc. are not yet quite clear. In this article, with the simple example of the conserved lattice gas model (CLG), we investigate such issues and clearly show that under certain situations the asymptotic decay exponents are, in fact, dependent on the initial condition of the system. We show that such an effect arises because of the existence of two competing time scales and identify the initial conditions which capture the universal features of the system.
Collapse
Affiliation(s)
- Sourish Bondyopadhyay
- CMP Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India
| |
Collapse
|
12
|
Krapivsky PL, Olejarz J. Limiting shapes in two-dimensional Ising ferromagnets. Phys Rev E 2013; 87:062111. [PMID: 23848631 DOI: 10.1103/physreve.87.062111] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2013] [Indexed: 11/07/2022]
Abstract
We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.
Collapse
Affiliation(s)
- P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | | |
Collapse
|
13
|
Dong J, Klumpp S, Zia RKP. Entrainment and unit velocity: surprises in an accelerated exclusion process. PHYSICAL REVIEW LETTERS 2012; 109:130602. [PMID: 23030077 DOI: 10.1103/physrevlett.109.130602] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2012] [Indexed: 06/01/2023]
Abstract
We introduce a class of distance-dependent interactions in an accelerated exclusion process inspired by the observation of transcribing RNA polymerase speeding up when "pushed" by a trailing one. On a ring, the accelerated exclusion process steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply J=1-ρ, signifying that the "hole train" travels with unit velocity.
Collapse
Affiliation(s)
- Jiajia Dong
- Department of Physics and Astronomy, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | | | | |
Collapse
|
14
|
Kwon S, Kim Y. Effects of excluded volume interaction on diffusion-reaction processes in crowded environments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041103. [PMID: 22181083 DOI: 10.1103/physreve.84.041103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2011] [Indexed: 05/31/2023]
Abstract
In nonequilibrium phase transitions of reaction-diffusion processes, the irrelevance of excluded volume interaction for the critical properties generally has been accepted due to the rare probability of multiple occupancy at criticality. Moreover, this belief is common sense in scale-free (SF) networks, which correspond to infinite dimensional irregular structures. However, the conventional belief is not satisfied in crowded environments in which the total number of particles is preserved in time. In this paper, we show, by investigating a typical process for epidemic spreading in crowded environments, that excluded volume interaction indeed changes critical behaviors in one dimension and surprisingly even mean-field behaviors in SF networks.
Collapse
Affiliation(s)
- Sungchul Kwon
- Department of Physics, Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea
| | | |
Collapse
|
15
|
Gabel A, Krapivsky PL, Redner S. Facilitated asymmetric exclusion. PHYSICAL REVIEW LETTERS 2010; 105:210603. [PMID: 21231281 DOI: 10.1103/physrevlett.105.210603] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2010] [Indexed: 05/30/2023]
Abstract
We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is occupied, we determine the steady-state current and the distribution of cluster sizes on a ring. We show that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave. This unexpected rarefaction wave discontinuity occurs generally for facilitated exclusion processes.
Collapse
Affiliation(s)
- Alan Gabel
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | | | | |
Collapse
|