Dynamic large deviations: nucleation and growth in phase transitions and avalanches in random hamiltonian systems

动态大偏差：随机哈密顿系统中相变和雪崩的成核和生长

• 批准号: 104322153
• 负责人: Professor Dr. Matthias Röger
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/104322153?language=en
• 关键词: Dynamic; large; deviations; nucleation; growth

Stochastic perturbations allow for large deviations from the deterministic evolutions, as for example the escape from (deterministically) stationary states. We investigate dynamic large deviations in two different contexts: mesoscale models for the evolution of phase boundaries in multi-phase materials, and overdamped Langevin dynamics with a 'wiggly' potential as a possible model for avalanches.The focus of the first problem is on the existence and qualitative properties of good rate functionals and the characterisation of minimisers under constraints on the macroscopic evolution. A particular example is the switching (tunneling) between stationary states of the deterministic evolution.The aim of the second problem is to identify a stochastic dynamic in a suitable large deviations scaling of a simplified random Hamiltonian system with a potential that has a highly oscillating ('wiggly') part. The main question is whether this can serve as a model for avalanches.

随机扰动允许从确定性演化中产生大的偏差，例如从（确定性的）稳定状态中逃脱。我们研究了两种不同背景下的动态大偏差：多相材料中相边界演化的中尺度模型，以及雪崩可能的“摆动”势的过阻尼朗之万动力学模型。第一个问题的重点是好的速率泛函的存在性和定性性质，以及在宏观演化约束下的最小值的特征。一个特殊的例子是确定性进化的固定状态之间的切换（隧穿）。第二个问题的目的是在一个具有高度振荡（“摆动”）部分的简化随机哈密顿系统的合适的大偏差标度中识别随机动力学。主要的问题是，这是否可以作为雪崩的模型。