NUMERICAL STUDY OF THE TRANSITION OF RARE EVENTS

Abstract

The behavior of stochastic gradient systems is dominated by rare but important transition events between equilibrium states. The system waits at metastable states for most of the time. Once the external activation is large enough to conquer the energy barrier, the transition between metastable states happens rapidly. This time separation is the main difficulty in the computation. We are interested in the optimal transition path between equilibrium states. The Wentzell-Friedlin theory of large deviation reveals that the optimal transition path is the minimum action path. For gradient systems, the minimum action path is simply the minimum energy path (MEP) in the high friction limit. In this thesis we compute the transition paths between equilibrium states of two kinds of gradient systems using the string method.