Diffusive Limit of the Asymmetric Simple Exclusion: The Navier-Stokes Correction

1994 ◽  
pp. 43-51
Author(s):  
R. Esposito ◽  
R. Marra ◽  
H. T. Yau
Keyword(s):  
Navier Stokes ◽  
Diffusive Limit ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

ERRATUM: "DIFFUSIVE LIMIT OF ASYMMETRIC SIMPLE EXCLUSION"

1996 ◽  
Vol 08 (06) ◽  
pp. 905-905
Author(s):  
R. ESPOSITO ◽  
R. MARRA ◽  
H. T. YAU
Keyword(s):  
Diffusive Limit ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

scholarly journals DIFFUSIVE LIMIT OF ASYMMETRIC SIMPLE EXCLUSION

1994 ◽  
Vol 06 (05a) ◽  
pp. 1233-1267 ◽  
Author(s):  
R. ESPOSITO ◽  
R. MARRA ◽  
H. T. YAU
Keyword(s):  
Exclusion Process ◽  
Variational Formula ◽  
Constant Density ◽  
Diffusion Matrix ◽  
Initial State ◽  
Time Scaling ◽  
Diffusive Limit ◽  
Asymmetric Simple Exclusion ◽  
Fixed Reference ◽  
Simple Exclusion

We consider the asymmetric simple exclusion process on the lattice [Formula: see text] with periodic b.c. for d ≥ 3, in the diffusive space-time scaling with parameter ε. Assume the initial state is a product of Bernoulli measures with density of order ε, up to a fixed reference constant density θ. We prove that the density at time t is given to first order by θ − εm(x − ε−1vt, t) with v a uniform velocity depending on θ and the dynamics and m(z, t) satisfies the d-dimensional viscous Burgers equation. The diffusion matrix is given by a variational formula related to the Green-Kubo formula and it is strictly bigger than the diffusion matrix for the corresponding symmetric exclusion process.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

A stochastic airplane boarding model in a framework of ASEP with distinguishable particles

2018 ◽  
Vol 29 (10) ◽  
pp. 1850093
Author(s):  
ShengJie Qiang ◽  
Bin Jia ◽  
QingXia Huang
Keyword(s):  
Removal Rate ◽  
Exclusion Process ◽  
System Size ◽  
Nonequilibrium Systems ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Maximum Current ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The Difference

The asymmetric simple exclusion process (ASEP) is a paradigmatic model for nonequilibrium systems and has been used in many applications. Airplane boarding provides another interesting example where this framework can be applied. We propose a simple model for boarding process, in which a particle moves along a one-dimensional aisle after being injected, and finally is removed at a reserved site. Different from the typical ASEP model, particles are removed in a disorderly or a parallel way. Detailed calculations and discussions of some related characteristics, such as mean boarding time and parallelism indicator, are provided based on Monte-Carlo simulations. Results show that three phases exist in the boarding process: free-flow, jamming and maximum current. Transitions between these phases are governed by the difference between the injection and removal rate. Further analysis shows how the scaling behavior depends on the system size and the boarding conditions. Those results emphasize the importance of utilizing the whole length of the aisle to reduce the boarding time when designing an efficient boarding strategy.

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