Shocks in the asymmetric simple exclusion process in a discrete-time update

Pigorsch, C.; Schütz, Gunter M.

doi:10.1088/0305-4470/33/44/306

Cited by 35 publications

(50 citation statements)

References 19 publications

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“…Some other updates that we will not discuss further here have been proposed, such as sequential update ordered backward or forward in space [45,55,54,291,116] or sublattice update [158,121,287,290]. They can be seen as particular realisations of the frozen shuffle update.…”

Section: Update Schemementioning

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: Update Schemementioning

confidence: 99%

“…This observation can be used to provide a coarse grained description of the system dynamics (valid in the aforementionned part of the phase diagram): the so-called domain wall approach [205,287].…”

Section: Domain Wall Approachmentioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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“…The time evolution is encoded in the transfer matrix of the 2-d model, e.g., the discrete-time ASEP with a sublattice parallel update corresponds to the six-vertex model [34,142,36,37]. For three-states models the construction is entirely analogous and leads to higher vertex models.…”

Section: Closely Related Models Not Covered In This Reviewmentioning

confidence: 99%

“…This is the result of a q-deformed SU(2)-symmetry of the Heisenberg quantum Hamiltonian that generates the time evolution of the process. For this value of the asymmetry (or, equivalently, arbitrary asymmetry, but special density ρ 2 ) the time evolution of the shock measure has been calculated exactly both for the continuous-time ASEP [87] and for a discrete-time variant [37]. The shock position performs a lattice random walk with rates given by the currents and densities in the two branches of the shock.…”

Section: Steady States With One B-particlementioning

confidence: 99%

Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles

Schütz

2003

J. Phys. A: Math. Gen.

137

136

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Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence in nonequilibrium steady states, even if translational invariance is not broken by defects or open boundaries. If both particle species are conserved, the temporal behaviour is largely unexplored, but first results of current work on the transition from the microscopic to the macroscopic scale yield exact coupled nonlinear hydrodynamic equations and indicate the emergence of novel types of shock waves which are collective excitations stabilized by the flow of microscopic fluctuations. We review the basic stationary and dynamic properties of these systems, highlighting the role of conservation laws and kinetic constraints for the hydrodynamic behaviour, the microscopic origin of domain wall (shock) stability and the coarsening dynamics of domains during phase separation.

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“…When a boundary is open, the particles are allowed to enter or leave the lattice from there. The shocks in the PASEP, which are defined as the sharp discontinuities in the density profile of the particles, might appear in both the continuous-and discrete-time updating schemes [1,2,3]. The steady-state of the PASEP can be easily calculated when a product shock measure in the system has a simple random walk dynamics.…”

mentioning

confidence: 99%

Discrete-time analysis of traveling wave solutions and steady state of a PASEP with open boundaries

Masharian

Zamani

2010

J. Phys. A: Math. Theor.

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Abstract. We consider the dynamics of a single shock in a Partially Asymmetric Simple Exclusion Process (PASEP) on a finite lattice with open boundaries in sublattice-parallel updating scheme. We then construct the steady-state of the system by considering a linear superposition of these shocks. It is shown that this steadystate can be also written in terms of a product of four non-commuting matrices. One of the main results obtained here is that these matrices have exactly the same generic structure of the matrices first introduced in [7] indicating that the steady-state of a onedimensional driven-diffusive system can be written as a linear superposition of product shock measures. It is easy now to explain the two-dimensional matrix representation of the PASEP with parallel dynamics introduced in [8,9].

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Shocks in the asymmetric simple exclusion process in a discrete-time update

Cited by 35 publications

References 19 publications

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles

Discrete-time analysis of traveling wave solutions and steady state of a PASEP with open boundaries

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