Noise-Induced Escape in Multistable Systems

项目摘要本提案旨在支持研究一大类随机过程的工作，这些过程涉及噪声诱导的从局部稳定状态的吸引盆逃逸。拟议的研究包括分析，数值和实验工作。它特别旨在发展新的概率和渐近技术，测试新的理论思想，发现使用这些技术，及其随后的应用程序的一系列选定的开放的问题与过渡和松弛过程中的系统都在和远离平衡。拟议活动的知识价值。本文所述的研究项目的选择是由三个目标指导。它们是：发展新的数学技术，大大拓宽了各种系统和情况下访问分析;这些技术的应用，以解决物理，化学和工程系统中的突出问题;和测试，实验和数值，所产生的理论预测。因此，整个研究计划的目标是在我们对受弱噪声扰动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，这些系统在各种科学领域中具有根本重要性，同时具有广阔的未来技术应用前景。这些包括液晶中的电对流图案形成、小体积中的振荡化学反应、周期性驱动的成核、纳米磁体中的磁化反转以及单价金属纳米线的稳定性。培训将提供给毕业生，如果可能的话，来自不同背景的本科生。例如，该提案包括在研究威尔斯之间的传输在周期性调制的电位，采用光学陷阱的实验/理论合作。该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，他的博士学位是论文将包括这些研究。此外，还应开展一些外联活动，包括在当地K-12学校举办讲座，以及在多学科暑期学校为其他领域的研究生举办讲座。PI多年来经常参与这些活动。PI长期以来一直是大波动和噪声诱导的逃离局部稳定状态的积极贡献者。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的一些激动人心的基本问题，广泛适用于速率过程理论和非平衡系统动力学。

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.