English
An introduction to molecular dynamics
Post-edited
Auteurs : Stoltz, Gabriel (Auteur de la conférence)
CIRM (Editeur )
60H10 - Stochastic ordinary differential equations
65C30 - Stochastic differential and integral equations
82B31 - Stochastic methods
82B80 - Numerical methods in equilibrium statistical mechanics
82C31 - Stochastic methods in time-dependent statistical mechanics (Fokker-Planck, Langevin, etc.)
82C70 - Transport processes
CIRM (Editeur )
Résumé :
The aim of this two-hour lecture is to present the mathematical underpinnings of some common numerical approaches to compute average properties as predicted by statistical physics. The first part provides an overview of the most important concepts of statistical physics (in particular thermodynamic ensembles). The aim of the second part is to provide an introduction to the practical computation of averages with respect to the Boltzmann-Gibbs measure using appropriate stochastic dynamics of Langevin type. Rigorous ergodicity results as well as elements on the estimation of numerical errors are provided. The last part is devoted to the computation of transport coefficients such as the mobility or autodiffusion in fluids, relying either on integrated equilibrium correlations à la Green-Kubo, or on the linear response of nonequilibrium dynamics in their steady-states.
Codes MSC : 60H10 - Stochastic ordinary differential equations
65C30 - Stochastic differential and integral equations
82B31 - Stochastic methods
82B80 - Numerical methods in equilibrium statistical mechanics
82C31 - Stochastic methods in time-dependent statistical mechanics (Fokker-Planck, Langevin, etc.)
82C70 - Transport processes
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 27/11/14 Date de Captation : 18/11/14 Sous Collection : Research talks Catégorie arXiv : Numerical Analysis ; Analysis of PDEs ; Probability Domaine(s) : Analyse Numérique & Calcul Formel ; EDP ; Probabilités & Statistiques Format : QuickTime (.mov) Durée : 01:57:50 Audience : Chercheurs Download : https://videos.cirm-math.fr/2014-11-18_Stoltz.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : MoMaS Conference / Colloque MoMaSOrganisateurs de la Rencontre : Allaire, Grégoire ; Cances, Clément ; Ern, Alexandre ; Herbin, Raphaèle ; Lelièvre, Tony Dates : 17/11/14 - 20/11/14 Année de la rencontre : 2014 URL de la Rencontre : https://www.cirm-math.fr/Archives/?EX=in...
Données de citation
DOI : 10.24350/CIRM.V.18631103Citer cette vidéo: Stoltz, Gabriel (2014). An introduction to molecular dynamics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18631103 URI : http://dx.doi.org/10.24350/CIRM.V.18631103 |
Bibliographie
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