Noise-Induced Escape in Multistable Systems

点击翻译按钮获取中文摘要

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.