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H 2 An introduction to molecular dynamics

Auteurs : Stoltz, Gabriel (Auteur de la Conférence)
CIRM (Editeur )

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computational statistical physics thermodynamic ensemble sampling probability measures Fokker-Planck equation ergodicity of stochastic differential equations discretization of stochastic differential equations metastability overdamped Langevin dynamics Langevin dynamics discretization of the Langevin dynamics computation of transport coefficients linear response autodiffusion and mobility error estimates on transport coefficients

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 (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
82C31 - Stochastic methods (Fokker-Planck, Langevin, etc.)
82C70 - Transport processes

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 27/11/14
    Date de captation : 18/11/14
    Collection : Research talks
    Format : QuickTime (.mov) Durée : 01:57:50
    Domaine : Numerical Analysis & Scientific Computing ; PDE ; Probability & Statistics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-11-18_Stoltz.mp4

Informations sur la rencontre

Nom du congrès : MoMaS Conference / Colloque MoMaS
Organisteurs Congrès : Allaire, Grégoire ; Cances, Clément ; Ern, Alexandre ; Herbin, Raphaèle ; Lelièvre, Tony
Dates : 17/11/14 - 20/11/14
Année de la rencontre : 2014
URL Congrès : https://www.ljll.math.upmc.fr/cances/gdr...

Citation Data

DOI : 10.24350/CIRM.V.18631103
Cite this video as: 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

  1. Allen, M.P. and Tildesley, D.J. Computer simulation of liquids. Oxford: Oxford University Press, 1987 - https://www.zbmath.org/?q=an:0703.68099

  2. Balian, R. From Microphysics to Macrophysics: methods and Applications of Statistical Physics. I. Berlin : Springer, 2007. (Theoretical and Mathematical Physics) - http://dx.doi.org/10.1007/978-3-540-45475-5

  3. Balian, R. From Microphysics to Macrophysics: methods and Applications of Statistical Physics. II. Berlin : Springer, 2007. (Theoretical and Mathematical Physics) - http://dx.doi.org/10.1007/978-3-540-45480-9

  4. Cances, E., Legoll, F. and Stoltz, G. Theoretical and numerical comparison of some sampling methods. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 41 (2007), no. 2, p. 351-389 - http://dx.doi.org/10.1051/m2an:2007014

  5. Frenkel, D. and Smit, B. Understanding Molecular Simulation: from Algorithms to Applications. San Diego : Academic Press, 2002 -

  6. Hairer, E., Lubich, C. and Wanner, G. Geometric numerical integration: structure-preserving algorithms for ordinary differential equations. 2nd ed. Berlin : Springer, 2009. (Springer series in computational mathematics, 31) - http://dx.doi.org/10.1007/3-540-30666-8

  7. Hairer, E., Lubich, C. and Wanner, G. Geometric numerical integration illustrated by the Stormer-Verlet method. Acta Numerica, vol. 12 (2003), p.399-450 - http://dx.doi.org/10.1017/s0962492902000144

  8. Leimkuhler, B.J. and Reich, S. Simulating Hamiltonian dynamics. Cambridge: Cambridge University Press, 2005. (Cambridge monographs on applied and computational mathematics, 14) - http://dx.doi.org/10.1017/cbo9780511614118

  9. Leimkuhler,B. and Matthews, C. Molecular dynamics: with deterministic and stochastic numerical methods. Springer, in press -

  10. Lelievre, T., Rousset, M. and Stoltz, G. Free energy computations: a mathematical perspective. London : Imperial College Press, 2010 - http://ebooks.worldscinet.com/ISBN/9781848162488/toc.shtml

  11. Rapaport, D.C. The Art of Molecular Dynamics Simulations. 2nd ed. Cambridge: Cambridge University Press, 2004 - http://dx.doi.org/10.1017/CBO9780511816581

  12. Rey Bellet, L. Ergodic properties of Markov processes. In S. Attal, A. Joye and C.A. Pillet (Eds.), Open quantum systems II: the Markovian approach (p. 1-39). Berlin : Springer, 2006. (Lecture Notes in Mathematics, 1881) - http://dx.doi.org/10.1007/3-540-33966-3_1

  13. Roux, J.N., Rodts, S. and Stoltz, G. Introduction a la physique statistique et a la physique quantique. Cours ENPC - Département Ingénierie Mathématique et Informatique, 2009 - http://cermics.enpc.fr/~stoltz/poly_phys_stat_quantique.pdf

  14. Schlick, T. Molecular Modeling and Simulation: an interdisciplinary guide. 2nd ed. New York: Springer, 2010 - http://dx.doi.org/10.1007/978-1-4419-6351-2

  15. Tuckerman, M. Statistical Mechanics: theory and Molecular Simulation. Oxford: Oxford University Press, 2010 - https://www.zbmath.org/?q=an:1232.82002



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