First Passage Times in Stochastic Differential Equations of Mathematical Physics and Engineering. Final Report April 1, 1983 - March 30, 1985

摘要

The goal of our study was to develop new asymptotic and singular perturbation methods for the analysis of random phenomena, and their application in various areas of science and engineering. We have studied the problems of 1) atomic migration in crystals, 2) ionic and superionic conductivity, 3) chemical reaction rates, surface desorption rates, and more general activated rate processes, 4) noise effects on the hysteretic Josephson junction, D.C.-SQUID, and other tunnel junction devices, 5) stability and reliability of randomly loaded elastic structures, 6) relative stability of various multi-stable systems, among others. Considerable success has been achieved, not only in developing new mathematical methods, but in solving a number of problems whose solution has long been outstanding. These include the Kolmogorov Exit Problem and the Kramers nonlinear diffusion problem, among others.