Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools

Understand

Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects.

• At the core of the theory lies the minimization of an action functional, which in many cases of interest has to be computed by numerical means.
• Here we review the theoretical and computational aspects behind these calculations, and propose an algorithm that simplifies the geometric minimum action method to minimize the action in the space of arc-length parametrized curves.
• We then illustrate this algorithm's capabilities by applying it to various examples from material sciences, fluid dynamics, atmosphere/ocean sciences, and reaction kinetics.