Dr. Braiman’s group is developing methods for detecting weak signals in noisy environments using nonlinear equations. These novel techniques based on nonlinear systems of equations in coupled systems are good candidates for detecting signals with low signal-to-noise ratios (SNRs).
Chaos is one class of nonlinear phenomenon described in popular culture as a butterfly flapping its wings in Algeria and causing a hurricane in Florida. A small change in input results in a large change in the evolution of the system. Similarly, stochastic resonance is a phenomenon in which the presence of noise in a nonlinear system enhances the response of the system to an input signal. The small signal produces a very specific effect in the nonlinear system. This is analogous to a system in which only an Algerian butterfly (e.g. not a Nigerian butterfly) creates a tornado in Texas, and the flap of an Algerian butterfly creates a Florida hurricane rather than a New York monsoon.
This research is focused on numerical efforts and takes advantage of the strong computational resources that we have access to, such as GPU units and programming support from experts at Oak Ridge National Laboratory.