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From Langevin dynamics to kinetic Monte Carlo: mathematical foundations of accelerated dynamics algorithms
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**Speaker**:
Tony Lelièvre (Ecole des Ponts ParisTech)
**Occasion**: Mathematical and Computational Materials Science**Date**:
February 17, 2021

**Abstract**:
We will discuss models used in classical molecular dynamics, and some mathematical questions raised by their simulations. In particular, we will present recent results on the connection between a metastable Markov process with values in a continuous state space (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process with values in a discrete state space. This is useful to analyze and justify numerical methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques à la 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, Jump Markov models and transition state theory: the Quasi-Stationary Distribution approach, Faraday Discussion, 195, 2016.

– G. Di Gesù, T. Lelièvre, D. Le Peutrec et 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.