Phase diagrams of two-lane driven diffusive systems

Evans, Martin R.; Kafri, Yariv; Sugden, Kate; Tailleur, Julien

doi:10.1088/1742-5468/2011/06/p06009

Cited by 44 publications

(69 citation statements)

References 45 publications

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“…Here however, the inner structure of the shock pair interfere with the adaptation layer so that the stationary state is more difficult to predict. The characteristics of the stationary state, and in particular the phase diagram, were studied first in [155] in the case of very asymetric lane changes, and more recently obtained for more general rules from a stability analysis of the mean-field profiles [119]. The case of back-stepping was also considered [119,367].…”

Section: Multi-lane Uni-directional Transport With Bulk Lane Changesmentioning

confidence: 99%

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Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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Cells are the elementary units of living organisms, which are able to carry out many vital functions. These functions rely on active processes on a microscopic scale. Therefore, they are strongly out-of-equilibrium systems, which are driven by continuous energy supply. The tasks that have to be performed in order to maintain the cell alive require transportation of various ingredients, some being small, others being large. Intracellular transport processes are able to induce concentration gradients and to carry objects to specific targets. These processes cannot be carried out only by diffusion, as cells may be crowded, and quite elongated on molecular scales. Therefore active transport has to be organized.The cytoskeleton, which is composed of three types of filaments (microtubules, actin and intermediate filaments), determines the shape of the cell, and plays a role in cell motion. It also serves as a road network for a special kind of vehicles, namely the cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach.It is a central issue to understand how intracellular transport driven by molecular motors is regulated. The interest for this type of question was enhanced when it was discovered that intracellular transport breakdown is one of the signatures of some neuronal diseases like the Alzheimer.We give a survey of the current knowledge on microtubule based intracellular transport. Our review includes on the one hand an overview of biological facts, obtained from experiments, and on the other hand a presentation of some modeling attempts based on cellular automata. We present some background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. Some important characteristics of axonal transport is that it takes place in a confined environment; Besides several types of motors are involved, that move in opposite directions. It is a challenge to understand how this bidirectional transport is organized. We review several features that could contribute to the efficiency of bidirectional transport in the axon, including in particular the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we also discuss some open questions that may be relevant for future research in this field.

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Section: Multi-lane Uni-directional Transport With Bulk Lane Changesmentioning

confidence: 99%

“…The properties of the stationary state for such a two-lane model, and in particular the density profile, have been calculated by M.R. Evans et al in [119].…”

Section: Nd Lipowskymentioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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“…The length scale associated with the exponential approach to the bulk diverges at these special values [13,15].…”

Section: A Constant Bulk Profilementioning

confidence: 95%

“…A steady particle current is sustained through withdrawal of particles from the other boundary at a given rate. This simple model was later followed by more general systems involving more than one species of particles [2,6,7], more complicated lattice [8][9][10][11][12][13][14] or dynamics of particles [15] etc. All these models have a few common, basic features such as hopping of particles with bias in one direction and hence a nonzero particle flux, mutual exclusion between the particles and open boundaries with particle injection and withdrawal at given rates.…”

Section: Introductionmentioning

confidence: 99%

“…Although this is a much bigger issue concerning the entire subject of non-equilibrium statistical mechanics, lack of a general framework even for these driven systems is surprising. Due to the presence of more than one density variable, driven multi-lane systems [8][9][10][11][12][13][14], in general, are technically challenging. Previous studies on two lane systems, with particle occupancy on one lane affecting the hopping on the other, show that this issue requires a generalization of the extremal current principle [14] which has been used earlier to predict the phase diagram of a single lane ASEP involving a single density variable [15,21].…”

Section: Introductionmentioning

confidence: 99%

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Phase-plane analysis of driven multi-lane exclusion models

Yadav¹,

Singh²,

Mukherji³

2012

J. Stat. Mech.

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We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed point based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.

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One-Dimensional Particle Processes with Acceleration/Braking Asymmetry

2012

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The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental Diagram of traffic and to be associated to hysteresis effects of traffic flow. We study this question in the context of exclusion and queueing processes, by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t. the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability are observed, depending on the level of the aforementioned asymmetry. In addition, we provide a large deviation formulation of the fundamental diagram which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.

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Phase diagrams of two-lane driven diffusive systems

Cited by 44 publications

References 45 publications

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Phase-plane analysis of driven multi-lane exclusion models

One-Dimensional Particle Processes with Acceleration/Braking Asymmetry

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