Finding Transition Pathways on Manifolds

TL;DR

This paper extends large deviation theory to analyze noise-induced transition paths on manifolds, proposing new action functionals and numerical methods, with applications to molecular conformational transitions.

Contribution

It generalizes Freidlin-Wentzell theory to manifolds and develops numerical algorithms for constrained transition path computation.

Findings

Derived new action functionals for manifold-constrained systems.

Numerically computed transition paths for molecular conformations.

Validated methods with examples in polymer science.

Abstract

We consider noise-induced transition paths in randomly perturbed dynami- cal systems on a smooth manifold. The classical Freidlin-Wentzell large devia- tion theory in Euclidean spaces is generalized and new forms of action functionals are derived in the spaces of functions and the space of curves to accommodate the intrinsic constraints associated with the manifold. Numerical meth- ods are proposed to compute the minimum action paths for the systems with constraints. The examples of conformational transition paths for a single and double rod molecules arising in polymer science are numerically investigated.