Search results for "Exclusion process"

showing 3 items of 3 documents

Queuing transitions in the asymmetric simple exclusion process

2003

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as $\delta \rho\sim x^{-\nu}$ with $\nu={1/3}$, and $x$ is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent $\nu={1/3}$ is universal and independent of the dynamic exponent of the underlying…

Queueing theoryPhase transitionStatistical Mechanics (cond-mat.stat-mech)FOS: Physical sciencesAsymmetric simple exclusion process01 natural sciences010305 fluids & plasmasFlow (mathematics)Quantum mechanics0103 physical sciencesExponentStatistical physics010306 general physicsHeuristic argumentQueueScalingCondensed Matter - Statistical MechanicsMathematicsPhysical Review E
researchProduct

Juggler's exclusion process

2012

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.

Statistics and Probabilityset-valued Markov processmaximum entropy60K35 82C41General Mathematics82C41FOS: Physical sciencesMarkov process01 natural sciencespositive recurrencesymbols.namesakeGravitational potentialMarkov renewal process0103 physical sciencesjuggling patternFOS: MathematicsErgodic theory0101 mathematicsGibbs measureMathematical PhysicsMathematicsDiscrete mathematicsnoncolliding random walkProbability (math.PR)ta111010102 general mathematicsErgodicityMathematical analysisExclusion processMathematical Physics (math-ph)Gibbs measureDistribution (mathematics)set-avoiding memoryless distribution60K35Jumpsymbolsergodicity010307 mathematical physicsStatistics Probability and UncertaintyMathematics - Probability
researchProduct

Totally asymmetric exclusion process fed by using a non-Poissonian clock

2015

In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function. peerReviewed

Waiting timePartition function (quantum field theory)ta114Stochastic processProcess (computing)non-Poissonian clockJump ratesymbols.namesakesymbolsasymmetric exclusion processStatistical physicsKinetic Monte CarloPareto distributionfysiikkaphysicsMathematicsPhysical Review E
researchProduct