Nonlinear time-series analysis. Search for low-dimensional dynamics in physical processes and the development of empirical models (based directly on experimental measurements) for process identification, prediction, and control. Current projects include data analysis and modeling from mechanical systems (strings), lasers, and fluid flows.
Development of a physically useful topological theory of chaos and a normal form theory of nonlinear dynamical systems. This work includes the application of knot theory to low-dimensional dynamical systems.
Application of Karhunen-Loeve procedure (aka, principal component analysis, proper orthogonal decomposition, empirical orthogonal functions) to the analysis and modeling of spatial-temporal complex system (aka, weak and hard turbulence). Current projects include data analysis from Taylor-Couette flow, Rayleigh-Benard convection with rotation, and the self interaction of laser beams in sodium vapor.
Pattern formation in marine geology and ocean physics. In particular, the interaction of flows with a sandy bottom, and problems concerned with sediment transport, ripple and dune formation.