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An introduction to molecular dynamics

By Gabriel Stoltz

Appears in 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.

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Citation data

  • DOI 10.24350/CIRM.V.18631103
  • Cite this video 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

Bibliography

  • Allen, M.P. and Tildesley, D.J. Computer simulation of liquids. Oxford: Oxford University Press, 1987 - https://www.zbmath.org/?q=an:0703.68099
  • 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
  • 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
  • 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
  • Frenkel, D. and Smit, B. Understanding Molecular Simulation: from Algorithms to Applications. San Diego : Academic Press, 2002
  • 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
  • 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
  • Rapaport, D.C. The Art of Molecular Dynamics Simulations. 2nd ed. Cambridge: Cambridge University Press, 2004 - http://dx.doi.org/10.1017/CBO9780511816581
  • 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
  • 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
  • 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
  • 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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