The string method as a dynamical system
 Maria Cameron (CIMS)


The string method is a numerical scheme for exploring complex potential landscapes. It is typically used to find mountain pass separating local minima, thereby determining (under suitable hypotheses) the pathways and rates of thermally-activated transitions between metastable states. Before discretization, the string method can be viewed as an evolution law for curves. We examine its large-time behavior, asking in particular whether it converges to a steady state (a ``minimum energy path or MEP''). The answer is negative in general; we give a collection of examples accompanied with movies demonstrating different types of complex large-time behavior of the evolving path. The answer is affirmative, however, under suitable hypotheses on the structure of the energy landscape or the choice of the initial curve.

This is a joint work with Bob kohn and Eric Vanden-Eijnden.