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An introduction to molecular dynamics

De Gabriel Stoltz

Apparaît dans la collection : MoMaS Conference / Colloque MoMaS

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.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.18631103
  • Citer cette vidéo Stoltz, Gabriel (18/11/2014). An introduction to molecular dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18631103
  • URL https://dx.doi.org/10.24350/CIRM.V.18631103

Bibliographie

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