Noise-Induced Escape in Multistable Systems

本提案旨在支持研究一类广泛的随机过程的工作，这些随机过程涉及从局部稳定状态的吸引力盆地中由噪声引起的逃逸。建议的研究包括分析、数值和实验工作。它特别致力于发展新的概率和渐近技术，测试使用这些技术发现的新理论思想，并随后将其应用于与处于和远离平衡状态的系统中的过渡和松弛过程相关的一系列选定的开放问题。所提议活动的智力价值。本文所述的研究项目的选择是由三个目标指导的。它们是：发展新的数学技术，大大拓宽了可供分析的系统和情况的种类；应用这些技术来解决物理、化学和工程系统中的突出问题；并通过实验和数值两种方式验证由此得出的理论预测。因此，整个研究计划的目标是在我们对受弱噪声干扰的非线性动力系统的理解方面取得重大进展，这是一类跨越许多科学学科的系统。拟议活动的更广泛影响。PI和合作者开发的数学方法将应用于广泛的系统，这些系统放在一起，在各种科学领域都具有根本性的重要性，同时在未来具有很好的技术应用前景。这些包括液晶中的电对流模式形成，小体积中的振荡化学反应，周期性驱动成核，纳米磁体中的磁化反转，以及单价金属纳米线的稳定性。培训将提供给研究生，如果可能的话，来自不同背景的本科生。例如，该提案包括利用光学陷阱在周期性调制电位中研究井间输运的实验/理论合作。这个实验已经处于初始阶段，旨在测试PI和其他人的理论预测，主要由一名研究生进行，他的博士论文将包括这些研究。还应该有一些推广活动，从在当地K-12学校的课堂上演讲到在多学科暑期学校为其他领域的研究生讲课。PI多年来一直定期从事这些活动。PI长期以来一直是大波动和噪声诱发的局部稳定状态逃逸领域的积极贡献者。他和合作者发现了大量以前未被怀疑的现象，并为进一步的探索奠定了基础。本研究将研究弱噪声诱导逃逸问题中一些令人兴奋的基本问题，对速率过程理论和非平衡系统动力学具有广泛的适用性。

Project Summary This proposal is for the support of work to study a broad class of stochastic processes involving noise-induced escape from the basin of attraction of a locally stable state. The proposed research includes analytical, numerical, and experimental work. It particularly aims towards the development of new probabilistic and asymptotic techniques, tests of new theoretical ideas uncovered using these techniques, and their subsequent application to an array of selected open problems associated with transitional and relaxational processes in systems both at and away from equilibrium. Intellectual merit of proposed activity. The choice of research projects described herein is guided by three objectives. They are: development of new mathematical techniques that significantly broaden the variety of systems and situations accessible to analysis; application of these techniques to the solution of outstanding problems in physical, chemical, and engineering systems; and testing, both experimentally and numerically, of the resulting theoretical predictions. The overall research program thereby aims towards a significant advance in our understanding of nonlinear dynamical systems perturbed by weak noise, a class of systems that cuts across many scientific disciplines. Broader impact of proposed activity. Mathematical methods developed by the PI and collaborators will be applied to a broad range of systems that, put together, are of fundamental importance in a variety of scientific fields, and at the same time have promising future technological applications. These include electroconvective pattern formation in liquid crystals, oscillating chemical reactions in small volumes, periodically driven nucleation, magnetization reversal in nanomagnets, and stability of monovalent metallic nanowires. Training will be provided to graduate and, if possible, undergraduate students from diverse backgrounds. For example, the proposal includes an experimental/theoretical collaboration in the study of transport between wells in periodically modulated potentials, employing optical traps. The experiment, which is already in the initial stages, is designed to test theoretical predictions of the PI and others, and is largely being carried out by a graduate student whose Ph.D. thesis will include these studies. There should also be a number of resulting outreach activities, ranging from presentations to classes at local K-12 schools to lectures to graduate students in other fields at multidisciplinary summer schools. The PI has regularly engaged in these activities for many years. The PI has been a long-time active contributor to the field of large fluctuations and noise induced escape from a locally stable state. He and collaborators have uncovered a large number of previously unsuspected phenomena, and have laid the groundwork for further explorations. The research described in this proposal will study some exciting and fundamental questions in the problem of escape induced by weak noise, with wide applicability to the theory of rate processes and the dynamics of nonequilibrium systems.