Optimal paths for phase boundaries

We introduce a multi-scale model for a two-phase material. The model is on the finest scale a stochastic process. The effective behaviour on larger scales is governed by deterministic nonlinear evolution equations. Due to the stochasticity on the finest scale, deviations from these limit evolution laws can happen with small probability. We describe the most likely among those deviations when we enforce a fast motion on a manifold of stationary solutions. The most likely path is the minimiser of an appropriate action functional.

Joint work with Giovanni Bellettini, Anna DeMasi, Dimitrios Tsagkarogiannis and Errico Presutti.