Theoretical Studies of Noise-Induced Escape in the Absence of Detailed Balance

缺乏详细平衡时噪声引起的逃逸的理论研究

• 批准号: 9800979
• 负责人: Robert Maier
• 金额: $ 18.15万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-15 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9800979&HistoricalAwards=false
• 关键词: Theoretical; Studies; Noise; Induced; Escape

This project will study stochastically modelled physical systems in which escape from a metastable state is induced by weak random perturbations, or noise. The stochastic models will, in general, lack the property of detailed balance. Such models arise naturally in many physical contexts, including the study of glasses and the study of rate processes in chemical physics, where the random perturbations are due to thermal fluctuations. Problems to be investigated include widespread but little- analysed phenomena such as escape from a stable or over an unstable limit cycle, escape over an unstable fixed point, and critical behavior due to an incipient bifurcation of the most probable noise-induced escape path. The mathematical challenges presented by these sorts of problem have impeded progress, so that understanding trails far behind the systematic understanding of the older (Kramers) problem of stochastic escape, in stochastic models exhibiting detailed balance. To study models without detailed balance, both numerical and analytical techniques will be applied. The latter include matched asymptotic expansions and Hamilton- Jacobi theory.

本计画将研究随机模拟的物理系统，其中由弱随机扰动或噪音引起的亚稳态逃逸。 一般来说，随机模型缺乏细节平衡的性质。 这种模型在许多物理背景下自然出现，包括玻璃的研究和化学物理中的速率过程的研究，其中随机扰动是由于热波动。 要研究的问题包括广泛但很少分析的现象，如从稳定或不稳定极限环逃逸，逃逸超过不稳定的固定点，以及由于最可能的噪声诱导逃逸路径的初始分叉引起的临界行为。因此，理解远远落后于系统的理解旧（克莱默斯）问题的随机逃逸，在随机模型表现出详细的平衡。 为了研究没有详细平衡的模型，将应用数值和分析技术。 后者包括匹配渐近展开和汉密尔顿-雅可比理论。