Phase-plane analysis of driven multi-lane exclusion models

Yadav, Vandana; Singh, Rajesh Kumar; Mukherji, Sutapa

doi:10.1088/1742-5468/2012/04/p04004

Cited by 13 publications

(16 citation statements)

References 28 publications

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“…Notice that for ρ = 0 the γ ρ (ω) is same as γ(ω) defined in (17) for the independent particles case. Then, using (46), yields the expression for the density profile, This is the complete solution of profile, with the f p (ω n ) defined in (D.7). Note, the density difference vanishes as → 0, as expected.…”

Section: Discussionmentioning

confidence: 99%

Non-local response in a lattice gas under a shear drive

Sadhu¹,

Majumdar²,

Mukamel³

2014

J. Phys. A: Math. Theor.

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Abstract. In equilibrium, the effect of a spatially localized perturbation is typically confined around the perturbed region. Quite contrary to this, in a non-equilibrium stationary state often the entire system is affected. This appears to be a generic feature of non-equilibrium. We study such non-local response in the stationary state of a lattice gas with a shear drive at the boundary which keeps the system out of equilibrium. We show that a perturbation in the form of a localized blockage at the boundary, induces algebraically decaying density and current profile. In two examples, non-interacting particles and particles with simple exclusion, we analytically derive the power-law tail of the profiles.

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Section: Discussionmentioning

confidence: 99%

Non-local response in a lattice gas under a shear drive

Sadhu¹,

Majumdar²,

Mukamel³

2014

J. Phys. A: Math. Theor.

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“…The stability analysis shows that the lower branch (ab) is unstable while upper branch (bc) is stable. Geometrically, a downward shock is possible if a point on the curve in upper branch can be connected to a point in the lower branch by a vertical line [32]. One can easily see from the direction of vertical arrows that it is not possible to get a downward shock in lane-B.…”

Section: Shock Dynamicsmentioning

confidence: 99%

Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: Phase diagrams and boundary layers

Gupta

Dhiman

2014

Phys. Rev. E

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We study an open system composed of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk. The particles are allowed to change their lane from lane-A to lane-B, but not conversely. We investigate the steady-state behavior of the system using boundary layer analysis on continuum mean-field equations to provide the phase diagram. The structure of the phase diagram is quite complex and provides a complete insight about the steady-state dynamics. We examine two kinds of transitions in the phase plane: bulk transitions and surface transitions, qualitatively as well as quantitatively. The dynamics of shock formation, localization and their dependence on the system parameters and boundary rates have been investigated. We also justify the non-existence of downward shock in both the lanes using fixed point theory. Further, we examine the effect of increasing lane-changing rate on the steady-state dynamics and observe that the number of steady-state phases reduces with increase in lane-changing rate. Our theoretical results are supported with extensive Monte-Carlo simulation results.

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“…Some previous work has discussed fixedpoints of TASEP models [13,41]. Yadav et al used phase-plane analysis of a fixed-point-based boundary layer method to study multi-lane TASEP models [48]. Here we undertake a detailed study of the model's phase-space flows and fixed points and along with an analytic phase-plane solution.…”

Section: Introductionmentioning

confidence: 97%

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

Kuan

Betterton

2016

Phys. Rev. E

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Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase-plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the density-density phase plane, where we find an analytic solution to the mean field model. By studying the phase-space flows, we determine the model’s fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions.

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Phase-plane analysis of driven multi-lane exclusion models

Cited by 13 publications

References 28 publications

Non-local response in a lattice gas under a shear drive

Non-local response in a lattice gas under a shear drive

Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: Phase diagrams and boundary layers

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

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