Tonelli Principle: finite reduction and fixed energy Molecular Dynamics trajectories

摘要

We propose a novel theoretical and practical alternative to the Maupeituis functional in the field of molecular dynamics: Tonelli functional [1], Our aim is to adapt this technique to the study of rare events where the initial and the final state of a system are known and we look for transition paths. We reached it with a rigorous mathematical development of the functional and an efficient numerical algorithm, We couple the Tonelli functional with an exact finite dimensional reduction: this is not far from a multiscale approach Indeed, the reduction will help the study of the high frequencies of the systems. It can be seen as a magnifying glass for atomic trajectories. A test on a 38-atom Lennaid-.Iones cluster shows the main features of our work.