This proposal is for the support of work to study a broad class of stochastic processes, both classical and quantum, involving noise-induced escape from the basin of attraction of a locally stable state. The proposed research involves the development of new mathematical techniques for analyzing these processes, and their application to a variety of open problems in condensed matter and nuclear physics associated with nucleation 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 techniques that broaden the variety of systems and situations accessible to theoretical analysis; application of these techniques to the solution of open problems in physical systems; and testing, both experimentally and numerically, of the resulting predictions. The overall research program 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 scientific importance in a variety of scientific fields, and at the same time have promising future technological applications. These include magnetization reversal in nanomagnets, stability and lifetimes of monovalent metallic nanowires, decay of high-angular momentum superdeformed nuclear states, the thermal activation$quantum tunneling transition, and electroconvective pattern formation in liquid crystals. These problems are accessible through a unified mathematical approach resulting from the work of PI and collaborators. Training will be provided to postdoctoral researchers, graduate students, and, if possible, undergraduate students from diverse backgrounds. For example, the proposal includes an experimental/numerical/theoretical collaboration in the study of thermally induced magnetization reversal in submicron-scale ferromagnetic annuli. The experiment, already in its initial stages, is designed to test theoretical predictions of the PI and others, and is largely being carried out by a graduate student towards a Ph.D. thesis. There should also be several resulting outreach activities, including presentations to classes at local K-12 schools, science projects for NYC high school students participating in science competitions for scholarships, and lectures to graduate students in other fields at multidisciplinary summer schools. Finally, the applicability of the PI?s work to areas of potential technological importance has already led to one patent application, and is likely to lead to more. NATIONAL SCIENCE FOUNDATION Diary Note Proposal:0651077 PI Name:Stein, Daniel Printed
