The overall goal of our investigations has been to formulate and develop methods of analysis for complex interactions between noise and inherent nonlinearities in mechanical and structural systems, and to suppress undesirable vibrations which can lead to failure. Practical applications of these new fundamental results are beginning to appear across the entire spectrum of mechanics; for example, stability of aircraft at high angles of attack, wave propagation in random media, mixing and transport phenomena in fluid mechanics. Some of the results are even contrary to intuition, such as stabilization by noise and stochastic resonance.

Multi-scale phenomena, dimensional reduction, and stability and bifurcations of invariant measures that arise in the study of nonlinear and stochastic systems are the focus of several projects.