Title :

Towards an $H$-theorem for granular gases

Author(s) :

Garcia de Soria, Maria Isabel [Auteur]
Universidad de Sevilla = University of Seville
Maynar, Pablo [Auteur]
Universidad de Sevilla = University of Seville
Mischler, Stéphane [Auteur]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mouhot, Clément [Auteur]
Department of Pure Mathematics and Mathematical Statistics [DPMMS]
Rey, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Trizac, Emmanuel [Auteur]
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]

Journal title :

Journal of Statistical Mechanics: Theory and Experiment

Pages :

P11009

Publisher :

IOP Publishing

Publication date :

2015-12-13

ISSN :

1742-5468

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]

English abstract : [en]

The H-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards ...
Show more >The H-theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribution of the gas to evolve irreversibly towards equilibrium. As such, the theorem could not be generalized to account for dissipative systems: the conservative nature of collisions is an essential ingredient in the standard derivation. For a dissipative gas of grains, we construct here a simple functional H related to the original H, that can be qualified as a Lyapunov functional. It is positive, and results backed by three independent simulation approaches (a deterministic spectral method, the stochastic Direct Simulation Monte Carlo technique, and Molecular Dynamics) indicate that it is also non-increasing. Both driven and unforced cases are investigated.Show less >

Language :

Anglais

Popular science :

Non

Comment :

14 pages, 5 figures

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL