Moderate deviations from the hydrodynamic limit of the symmetric exclusion process

2003 ◽  
Vol 46 (5) ◽  
pp. 577 ◽  
Author(s):  
Fuqing GAO
Keyword(s):  
Hydrodynamic Limit ◽  
Exclusion Process ◽  
Moderate Deviations

scholarly journals Hydrodynamic limit for a facilitated exclusion process

2020 ◽  
Vol 56 (1) ◽  
pp. 667-714
Author(s):  
Oriane Blondel ◽  
Clément Erignoux ◽  
Makiko Sasada ◽  
Marielle Simon
Keyword(s):  
Hydrodynamic Limit ◽  
Exclusion Process

scholarly journals Dynamics of interacting particle systems

2020 ◽  
Vol 68 ◽  
pp. 52-72
Author(s):  
Oriane Blondel ◽  
Aurelia Deshayes ◽  
Cyril Labbé ◽  
Laure Marêché ◽  
Marielle Simon
Keyword(s):  
Hydrodynamic Limit ◽  
Interacting Particle Systems ◽  
Mixing Time ◽  
Exclusion Process ◽  
Front Propagation ◽  
Particle Systems ◽  
Asymmetric Exclusion Process ◽  
Cutoff Phenomenon ◽  
Interacting Particle ◽  
Dynamical Properties

We collect here recent results covering various aspects of the dynamical properties of interacting particle systems. In Section 1 we study the hydrodynamic limit of a facilitated exclusion process. Section 2 evidences a cutoff phenomenon for the mixing time of the weakly asymmetric exclusion process. Section 3 presents a study of the infection time in the Duarte model. Finally, Section 4 presents the study of a front propagation in the FA-If model.

scholarly journals Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

2019 ◽  
Vol 178 (1) ◽  
pp. 75-116
Author(s):  
Bart van Ginkel ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Riemannian Manifold ◽  
Heat Equation ◽  
Random Walks ◽  
Hydrodynamic Limit ◽  
Compact Riemannian Manifold ◽  
Exclusion Process ◽  
Density Field ◽  
Random Grids ◽  
Empirical Density

Abstract We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.

scholarly journals Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

2020 ◽  
Vol 75 (5) ◽  
pp. 449-463
Author(s):  
Dominik Lips ◽  
Artem Ryabov ◽  
Philipp Maass
Keyword(s):  
Current Density ◽  
Lattice Gas ◽  
Yukawa Potential ◽  
Exclusion Process ◽  
Quantum Spin ◽  
Nonequilibrium Steady States ◽  
Interacting Particles ◽  
Driven Diffusive Systems ◽  
Periodic Potentials ◽  
Symmetry Effect

AbstractDriven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

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