Effective dynamics using conditional expectations

Wednesday, February 25, 2009 - 1:00pm - 2:00pm
Lind 409
Frédéric Legoll (École Nationale des Ponts-et-Chaussées)
We consider a system described by its position Xt, that evolves according to the overdamped Langevin equation. At equilibrium, the statistics of X are given by the Boltzmann-Gibbs measure. Suppose that we are only interested in some given low-dimensional function ξ(X) of the complete variable (the so-called reaction coordinate). The statistics of ξ are completely determined by the free energy associated to this reaction coordinate. In this work, we try and design an effective dynamics on ξ, that is a low-dimensional dynamics which is a good approximation of ξ(Xt). Using conditional expectations, we build an original dynamics, whose accuracy is supported by error estimates obtained following an entropy-based approach. Numerical simulations will illustrate the accuracy of the proposed dynamics according to various criteria.

This is joint work with T. Lelievre (ENPC and INRIA).