Exact domain wall theory for deterministic TASEP with parallel update

Cividini, Julien; Hilhorst, H. J.; Appert-Rolland, Cécile

doi:10.1088/1751-8113/47/22/222001

Cited by 9 publications

(15 citation statements)

References 33 publications

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“…This may allow for finding dualities and non-Abelian symmetries in these processes. Our results also indicate a link between current fluctuations [78,73,3,46,58,40,20] and the dynamics of shocks [69,9,8,10,22] via self-duality since for both problems the same duality functions are used.…”

Section: Setting Of the Problemsupporting

confidence: 53%

Self-duality and shock dynamics in the n-species priority ASEP

Belitsky

Schütz

2018

Stochastic Processes and their Applications

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Section: Setting Of the Problemsupporting

confidence: 53%

Self-duality and shock dynamics in the n-species priority ASEP

Belitsky

Schütz

2018

Stochastic Processes and their Applications

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“…Actually the DW theory postulates that the motion of the wall can be described by the master equation of a biased random walk [103] with the hopping rates (21). While this is relevant for the random sequential update, it can be shown [80] that in the case of a deterministic TASEP with parallel update, a non-Markovian evolution equation has to be used: There is a memory effect over one time-step. Note that in this special case, the domain wall theory is not phenomenological anymore, but can be made exact even at the microscopic scale.…”

Section: Domain Wall Approachmentioning

confidence: 99%

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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“…This flag was introduced in Ref. [42] to track the location of the shock in pure TASEP with parallel update, and obeys the following motion rules:…”

Section: Domain Wall Dynamicsmentioning

confidence: 99%

On-site residence time in a driven diffusive system: Violation and recovery of a mean-field description

et al. 2016

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We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using Domain wall theory (DWT), we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually interactive LK (TASEP + MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.

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Exact domain wall theory for deterministic TASEP with parallel update

Cited by 9 publications

References 33 publications

Self-duality and shock dynamics in the n-species priority ASEP

Self-duality and shock dynamics in the n-species priority ASEP

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

On-site residence time in a driven diffusive system: Violation and recovery of a mean-field description

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