Multi-scale analysis of phase boundaries under the influence of fluctuations and random fields

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We consider models for the formation and evolution of interfaces in materials which are characterised by the interplay of¿ the interfacial energy¿ time-independent random and/or deterministic inhomogeneities on a very small scale¿ space-time dependent noise modelling thermal fluctuations.The current project is focused on two aspects of the dynamics of such systems: The first aspect are dynamic large deviations on large time scales and, in particular, the phenomenon of nucleation.The second aspect concerns the effective evolution of an (already developed) interface. We are interested in the influence of the inhomogeneities and the noise - which originate on a smaller scale - on these effective evolution laws on a large time-space scale. For both aspects we aim at rigorous mathematical results. The models we consider are Mean Curvature Flow (MCF) with random perturbations and several simplified continuum models of reaction-diffusion type of gradient-flow structure with space-time noise and/or with random or periodic coefficients.