Hydrodynamic limit for a boundary-driven ...
Type de document :
Pré-publication ou Document de travail
Titre :
Hydrodynamic limit for a boundary-driven facilitated exclusion process
Auteur(s) :
da Cunha, Hugo [Auteur]
Erignoux, Clement [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Modélisation multi-échelle des dynamiques cellulaires : application à l'hématopoïese [DRACULA]
Institut Camille Jordan [ICJ]
Systèmes de particules et systèmes dynamiques [Paradyse]
Simon, Marielle [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Institut Camille Jordan [ICJ]
Erignoux, Clement [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Probabilités, statistique, physique mathématique [PSPM]
Modélisation multi-échelle des dynamiques cellulaires : application à l'hématopoïese [DRACULA]
Institut Camille Jordan [ICJ]
Systèmes de particules et systèmes dynamiques [Paradyse]
Simon, Marielle [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Probabilités, statistique, physique mathématique [PSPM]
Institut Camille Jordan [ICJ]
Date de publication :
2024-01-29
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic ...
Lire la suite >We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in order to enforce ergodicity. We study in details its stationary states in various settings, and use them in order to derive its hydrodynamic limit as $N\to\infty$, in the diffusive space-time scaling, when the initial density profile is supercritical. More precisely, the macroscopic density of particles evolves in the bulk according to a fast diffusion equation as in the periodic case, and besides, we show that the boundary-driven FEP exhibits a very peculiar behaviour: unlike for the classical SSEP, and due to the two-phased nature of the FEP, the reservoirs impose Dirichlet boundary conditions which do not coincide with their equilibrium densities. The proof is based on the classical entropy method, but requires significant adaptations to account for the FEP's non-product stationary states and to deal with the non-equilibrium setting.Lire moins >
Lire la suite >We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in order to enforce ergodicity. We study in details its stationary states in various settings, and use them in order to derive its hydrodynamic limit as $N\to\infty$, in the diffusive space-time scaling, when the initial density profile is supercritical. More precisely, the macroscopic density of particles evolves in the bulk according to a fast diffusion equation as in the periodic case, and besides, we show that the boundary-driven FEP exhibits a very peculiar behaviour: unlike for the classical SSEP, and due to the two-phased nature of the FEP, the reservoirs impose Dirichlet boundary conditions which do not coincide with their equilibrium densities. The proof is based on the classical entropy method, but requires significant adaptations to account for the FEP's non-product stationary states and to deal with the non-equilibrium setting.Lire moins >
Langue :
Anglais
Projet ANR :
Commentaire :
44 pages
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