Mathematical Colloquium

Friday, December 08 2017, 2:15pm

Molecular dynamics and mathematics

Tony Lelievre (Ecole des Ponts ParisTech)

Abstract: Molecular dynamics is now a very widely used tool to study by numerical simulations the matter at the molecular level. It is used in various fields, such as biology, chemistry or materials science in order to relate the macroscopic properties of matter to its atomistic features for various applications: protein structure prediction, drug design, dynamics of defects in crystals, exploration of the properties of new materials, etc...

Despite the increasing computational power, it remains in some practical cases difficult to simulate a sufficently large number of atoms over sufficiently long timescales to obtain predicitive and precise results. Mathematics play a fundamental role to derive coarse-grained models and to analyze and improve algorithms which are used to bridge space and time scales. One of the numerical difficulty is indeed related to timescales: the typical timescale of a molecular dynamics simulation is much smaller than the typical timescale at which the crucial events, from a macroscopic viewpoint, occur. This is related to the metastability of a molecular dynamics trajectory.

Many methods have been proposed in the molecular dynamics community to deal with these difficulties, and we will focus on two prototypical ones for which a mathematical analysis gives useful insights. We will first present adaptive importance sampling techniques, which have been proposed to sample efficiently statistical ensembles. Then, we will describe a mathematical analysis of accelerated dynamics methods which have been introduced by A.F. Voter to generate efficiently metastable dynamics.

Location:  Raum 115 im Rogowski Gebäude, Schinkelstr 2, 52062 Aachen (Seminarraum von AICES)