EVENT DETAILS AND ABSTRACT

Title: Hyperbolic periodic orbits, heteroclinic connections, and semi-analytical characterization of rare events in some nongradient systems
Speaker: Professor Molei Tao
Speaker Info: Georgia Tech
Brief Description:
Special Note:
Abstract:

We consider dynamical system perturbed by small Gaussian noises, with a goal of quantifying how noises can affect the dynamics. More precisely, most likely noise-induced dynamics are understood by maximizing transition rate provided by Freidlin-Wentzell large deviation theory. In gradient systems (i.e., non-equilibrium statistical mechanics modeled by reversible diffusion processes), metastable transitions were well understood and known to cross separatrices at saddle points. We instead investigate nongradient systems (possibly irreversible) using a developed tool of (generalized) orthogonal decomposition. A different type of transitions, which cross hyperbolic periodic orbits, will be demonstrated. Corresponding numerical tools for both identifying such periodic orbits and computing transition paths will be described. The Langevin model of stochastic mechanical systems will also be investigated and extended, with emphasis on how its metastable transition can differ from the overdamped (reversible) case. Finally, numerical approaches for general nongradient systems will be discussed. If time permits, I will also mention how these results can help design control strategies and utilize the effects of noise.