Session
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Invited speaker
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Presentations
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From Langevin dynamics to kinetic Monte Carlo: the quasi-stationary distribution approach Ecole des Ponts ParisTech, France We will present a mathematical framework to draw a rigorous connection between microscopic and mesoscopic models to describe the evolutions of materials at the atomistic scale: molecular dynamics, namely Langevin or overdamped Langevin dynamics, and kinetic Monte Carlo (a.k.a. Markov State Models), namely jump Markov processes with values in a discrete state space. This analysis is useful to analyze and justify numerical methods which use the jump Markov model underlying the molecular dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques à la D. Perez and A.F. Voter). It also provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models. References: - G. Di Gesù, T. Lelièvre, D. Le Peutrec and B. Nectoux, Sharp asymptotics of the first exit point density, Annals of PDE, 5(1), 2019. - T. Lelièvre, Mathematical foundations of Accelerated Molecular Dynamics methods, In: W. Andreoni and S. Yip (Eds), Handbook of Materials Modeling, Springer, 2018. - T. Lelièvre, M. Ramil and J. Reygner, Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence, Stochastic Processes and their Applications, 144, 176-201, (2022). |