Research Professor Fox's research includes stochastic processes, nonlinear dynamics, quantum chaos, and biophysics.
Stochastic processes arise from the study of fluctuations in physical systems.
Applications include magnetic relaxation, the theory of spectra, noise in lasers, and hydrodynamic turbulence. The primary focus of Professor Fox's work in nonlinear dynamics has been on the exponential amplification of intrinsic, molecular fluctuations by chaotic dynamics. Amplification by several orders of magnitude has been predicted for fluid systems, and in laser systems the expectation is that amplification will be over many orders of magnitude. This effect has repercussions for the physical reality of fractal attractors and for the feasibility of control of chaos by feedback. It also forces a rethinking of the relationship between the microscopic description of physical processes and macroscopic descriptions of the same.