The Mirrors Model : Macroscopic Diffusion Without Noise or Chaos

Abstract : We consider a discrete version of the mirrors model in a finite d-dimensional domain and connected to particles reservoirs at fixed chemical potentials. The dynamics is purely deterministic and non-ergodic. We study the macroscopic current of particles in the stationary regime. We show first that when the size of the system goes to infinity, the behaviour of the stationary current of particles is governed by the proportion of orbits crossing the system. Using this approach, we show that Fick's law relating the stationary macroscopic current of particles to the concentration difference holds in three dimensions and above. The negative correlations between crossing orbits play a key role in the argument.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01166482
Contributeur : Raphael Lefevere <>
Soumis le : lundi 22 juin 2015 - 19:18:14
Dernière modification le : lundi 29 mai 2017 - 14:25:44
Document(s) archivé(s) le : mardi 15 septembre 2015 - 20:52:32

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1506.04727v3.pdf
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  • HAL Id : hal-01166482, version 1
  • ARXIV : 1506.04727

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UPMC | PMA | USPC

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Yann Chiffaudel, Raphaël Lefevere. The Mirrors Model : Macroscopic Diffusion Without Noise or Chaos. 2015. <hal-01166482>

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