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An introduction to molecular dynamics
Post-edited
Authors : Stoltz, Gabriel (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 27/11/14 Conference Date : 18/11/14 Subseries : Research talks arXiv category : Numerical Analysis ; Analysis of PDEs ; Probability Mathematical Area(s) : Numerical Analysis & Scientific Computing ; PDE ; Probability & Statistics Format : QuickTime (.mov) Video Time : 01:57:50 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-11-18_Stoltz.mp4 
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Information on the Event
Event Title : MoMaS Conference / Colloque MoMaSEvent Organizers : Allaire, Grégoire ; Cances, Clément ; Ern, Alexandre ; Herbin, Raphaèle ; Lelièvre, Tony Dates : 17/11/14 - 20/11/14 Event Year : 2014 Event URL : https://www.cirm-math.fr/Archives/?EX=in...
Citation Data
DOI : 10.24350/CIRM.V.18631103Cite 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 |
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
