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

我们考虑材料中界面的形成和演化模型，其特征在于<$界面能<$时间无关的随机和/或确定性不均匀性在非常小的尺度上的相互作用<$时空相关的噪声建模热波动。目前的项目集中在这样的系统的动力学的两个方面：第一个方面是大时间尺度上的动态大偏差，特别是成核现象;第二个方面涉及（已经开发的）界面的有效演化。我们感兴趣的不均匀性和噪声的影响-这起源于一个较小的规模-这些有效的演变规律在一个大的时空尺度。对于这两个方面，我们的目标是严格的数学结果。我们考虑的模型是平均曲率流（MCF）的随机扰动和几个简化的连续模型的反应扩散型梯度流结构的时空噪声和/或随机或周期性的系数。

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.