Effect of interactions for one-dimensional asymmetric exclusion processes under periodic and bath-adapted coupling environment

Midha, Tripti; Kolomeisky, Anatoly B.; Gupta, Arvind

doi:10.1088/1742-5468/aab022

Cited by 28 publications

(62 citation statements)

References 40 publications

(134 reference statements)

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“…and E is expressed in units of k B T . The above relation follows from the visualization of the process of bond making and bond breaking as opposite reversible chemical reactions [27][28][29]. We also introduce a splitting parameter θ (0 θ 1) that quantifies how the energy E affects the hopping rates q and r.…”

Section: Model Description and Master Equationsmentioning

confidence: 99%

“…The theoretical examination of the TASEP-LK system in the presence of mutual interactions requires an efficient analytical approach that takes into account the correlations to some extent and works well for nonconserving systems. The existing theoretical studies such as cluster mean-field theory [27,29], modified cluster mean-field theory [28], timedensity functional approach [23], etc., are efficient only for the conserved systems. These theories assume that any observable is uniform and independent of the position on the lattice.…”

Section: Correlated Cluster Mean-field Theorymentioning

confidence: 99%

“…Besides LK, the presence of mutual interactions among particles also has a major impact on the steady-state properties of DDS. The driven exclusion processes with nearestneighbor interactions and without LK have been extensively studied for a single [1,16,[19][20][21][22][23][24][25][26][27][28][29] as well as multilane TASEP systems [30,31], using the thermodynamically consistent [27][28][29][30][31] and phenomenological approaches [1,16,[19][20][21][22][23][24][25]. The interactions in these systems are theoretically handled using the cluster mean-field and the modified cluster mean-field approaches.…”

Section: Introductionmentioning

confidence: 99%

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Interactions in nonconserving driven diffusive systems

2018

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Motivated by biological transport phenomena and vehicular traffic flow we investigate the dynamics of interacting molecular motors or interacting vehicles that move along linear filaments (tracks) and can reversibly associate or dissociate from them. To analyze these processes, we introduced a model assimilating the interactions in a totally asymmetric simple exclusion process coupled with nonconserving Langmuir kinetics. The model is analyzed first using the continuum version of the simple mean-field approach that neglects the correlations between the particles. It is shown that even for weak interactions theoretical predictions deviate significantly from computer simulation results. To alleviate the problems, we developed a theoretical method that takes into account some correlations in the system. The effect of interactions on stationary phase diagrams, particle currents, and densities are explicitly evaluated. The analysis of two-point correlation function on the lattice indicates that the correlations are stronger at the locations of localized shocks. Our theoretical calculations are in excellent agreement with Monte Carlo computer simulations.

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Section: Model Description and Master Equationsmentioning

confidence: 99%

Section: Correlated Cluster Mean-field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interactions in nonconserving driven diffusive systems

2018

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“…that is into a product of 2-node and 1-node marginals (see e.g., Reference [25] for a derivation of this property for an equilibrium 1D model with nearest-neighbour interactions, which includes the Hamiltonian Equation (2)). The PA [18,19], as well as the MCAK [12,13] and related techniques [26][27][28][29][30], is based on the assumption that the factorization Equation (14) holds at any time, and this explains why these techniques can give exact results for a bulk NESS. In terms of entropy, we can introduce 1-node and 2-node cluster entropies (in units such that k B = 1)…”

Section: Model and Methodsmentioning

confidence: 99%

“…Specifying the coupling between the system and the reservoirs, that is the rates of particle injection from the left reservoir and extraction to the right reservoir, is a delicate issue, and several choices are possible. We will use the so-called bulk-adapted boundary conditions [11][12][13]26], which make the theory of boundary-induced phase transitions applicable. These conditions can be defined in such a way that they would yield bulk NESS solutions in semi-infinite systems.…”

Section: Model and Methodsmentioning

confidence: 99%

Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

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2019

Entropy

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Dynamical transitions, already found in the high-and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz-Lebowitz-Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz-Lebowitz-Spohn model, and discuss 2 new phenomena which are peculiar to this model. Entropy 2019, 21, 1028 2 of 18 current principles. It was observed [11][12][13] that, in order for this theory to be applicable to models with certain additional interactions, a specific choice of the coupling between the system and the boundary reservoirs must be made.More recently, on the basis of exact results [14-16] on relaxation towards the NESS, a dynamical transition has been identified in the TASEP, that is a singularity in the relaxation rate which does not correspond to any NESS phase transition. The existence of this dynamical transition has also been observed in numerical investigations based on the density matrix renormalization group [17], although a physical interpretation has long been lacking. In the last few years, two of us contributed to showing [18][19][20] that this dynamical transition can be at least qualitatively predicted by suitable mean-field-like approaches and is also exhibited by certain models (for which exact results are not available) which generalize the TASEP by including additional processes or interactions, namely the TASEP with Langmuir kinetics [21,22] and the Antal-Schütz (AS) model [11].The picture which seems to emerge is that, in those NESS phases where the bulk density is determined by one of the boundary reservoirs-that is, the so-called low-density (LD) and high-density (HD) phases-two phases can be identified on the basis of the behaviour of the relaxation rate. In one phase, dubbed slow in Reference [19] and typically located near a coexistence line (where the rate vanishes) in the NESS phase diagram, the relaxation rate depends on both reservoir densities. In the other phase, dubbed fast in Reference [19] and located away from coexistence lines, the relaxation rate depends only on the bulk density, that is, on just one reservoir density. A natural interpretation is that in the fast phase the slowest relaxation mode is a bulk one, while ...

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