Numerical methods in molecular dynamics.
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.
One of the numerical difficulty is 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 propose a mathematical analysis of accelerated dynamics methods which have been introduced by A.F. Voter to generate efficiently metastable dynamics.