Computation of Essential Molecular Dynamics by Subdivision Techniques

Abstract

The paper presents the concept of a new type of algorithm for the numerical computation of what the authors call the essential dynamics of molecular systems. Mathematically speaking, such systems are described by Hamiltonian di#erential equations. In the bulk of applications, individual trajectories are of no specific interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynamical systems, such information is contained in the natural invariant measure (infinite relaxation time) or in almost invariant sets ("large" finite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is di#erent to both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by sh...