Optimal Paths for Spatially Extended Metastable Systems Driven by Noise
  The least action principle is exploited as a simulation tool to find the optimal dynamic path for spatially extended systems driven by a small noise. Applications are presented for thermally activated switching of a spatially-extended bistable system as well as the switching dynamics of magnetic thin films. The issue of nucleation versus propagation is discussed and the scaling for the number of nucleation events as a function of the terminal time and other material parameters is computed. 
E. Weinan, Weiqing Ren, Eric Vanden-Eijnden