Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji

doi:10.1088/0305-4470/39/29/004

Cited by 28 publications

(34 citation statements)

References 21 publications

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“…In this paper, we focus on probabilistic extension of BCA (PBCA). It is partially equivalent to the 'totally' ASEP (TASEP) obtained by restricting the motion of particles of ASEP to the only one direction [8,9,10]. However, there is a difference between PBCA and TASEP about the updating way of particle positions.…”

Section: Introductionmentioning

confidence: 99%

New approach to evaluate the asymptotic distribution of particle systems expressed by probabilistic cellular automata

Endo

2020

Japan J. Indust. Appl. Math.

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We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.

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Section: Introductionmentioning

confidence: 99%

New approach to evaluate the asymptotic distribution of particle systems expressed by probabilistic cellular automata

Endo

2020

Japan J. Indust. Appl. Math.

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“…It is rather difficult, however, to define parallel update dynamics for a system with an infinite number of particles, since the number of updated sites can be infinity, i.e., | A t | = ∞ using the notation in Sec.I. Kanai et al [10] overcame this difficulty and determined the thermodynamic limit of average velocity (13). They obtained the differential equation which governs the average velocity and took the thermodynamic limit in the equation.…”

Section: Discussionmentioning

confidence: 99%

“…are assumed to be functions of p and ρ. Putting (33) and (34) into (30) and its modification obtained by setting L → L − 1, and taking the thermodynamic limit K → ∞ with ρ = L/K = const., the first terms in (33) and (34) are determined as [10] v…”

Section: A Riccati Equationsmentioning

confidence: 99%

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Velocity correlations of a discrete-time totally asymmetric simple-exclusion process in stationary state on a circle

Yamada

Katori

2011

Phys. Rev. E

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The discrete-time version of totally asymmetric simple-exclusion process (TASEP) on a finite one-dimensional lattice is studied with the periodic boundary condition. Each particle at a site hops to the next site with probability 0≤p≤1 if the next site is empty. This condition can be rephrased by the condition that the number n of vacant sites between the particle and the next particle is positive. Then the average velocity is given by a product of the hopping probability p and the probability that n≥1. By mapping the TASEP to another driven diffusive system called the zero-range process, it is proved that the distribution function of vacant sites in the stationary state is exactly given by a factorized form. We define k-particle velocity correlation function as the expectation value of a product of velocities of k particles in the stationary distribution. It is shown that it does not depend on positions of k particles on a circle but depends only on the number k. We give explicit expressions for all velocity correlation functions using the Gauss hypergeometric functions. Covariance of velocities of two particles is studied in detail, and we show that velocities become independent asymptotically in the thermodynamic limit.

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“…The average velocity is then given using random sequential update rule as ω avg = ω 2 . J ρ N = ω 2 .p(1 − ρ N ) [13][14][15], where J is the average current in the system, p = f sb and ω 2 is the normalization constant. Inset of Fig.…”

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confidence: 99%

Tuning of friction noise by accessing the rolling-sliding option

Das

Ghosh

2020

Phys. Rev. Research

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Variable power transmission in mechanical systems is often achieved by devices, e.g., clutches and brakes, that use dry friction. In these systems, the variability in power transmission is brought about by engaging and disengaging the friction plates. Though commonly used, this method of making the coupling noisy is not as versatile as their electrical analog. An alternative method would be to intermittently vary the frictional force. In this paper, we demonstrate a self-organized way to tune the noise in the frictional coupling between two surfaces which are in relative motion with each other. This is achieved by exploiting the complexity that arises from the frictional interaction of the balls which are placed in a circular groove between the surfaces. The extent of floppiness in the coupling is related to the rate at which the balls make transitions between their rolling and sliding states. If the moving surface is soft and the static surface is hard we show that with increasing filling fraction of the balls the transitions between rolling and sliding against the static surface give way to the transitions between rolling and sliding against the moving surface. As a consequence, the noise in the coupling is large for both small and large filling fraction with a dip in the middle. In contrast, the sliding with the static surface is suppressed if the moving pate is hard and the noise in the coupling decreases monotonically with the filling fraction of the balls. arXiv:2002.04231v1 [cond-mat.soft]

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Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

Cited by 28 publications

References 21 publications

New approach to evaluate the asymptotic distribution of particle systems expressed by probabilistic cellular automata

New approach to evaluate the asymptotic distribution of particle systems expressed by probabilistic cellular automata

Velocity correlations of a discrete-time totally asymmetric simple-exclusion process in stationary state on a circle

Tuning of friction noise by accessing the rolling-sliding option

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