This research is supported by NASA's Fluid Physics Program

Control of Spatially Extended Systems

The desire to improve performance of many practically important systems and devices (semiconductor lasers, chemical reactors, internal combustion engines, etc.) often calls for shifting their operating range into a highly nonlinear regime, which after a series of bifurcations typically leads to irregular chaotic behavior. This side effect is usually undesirable, while substantial benefits could be obtained by making the dynamics regular (e.g., by creating patterns). This goal can be achieved by applying feedback to steer the system towards a state with desired properties, which is broadly referred to as chaos control. Numerous experiments suggest that spatially extended systems present additional difficulties. It turns out that that the primary reason for these difficulties is rooted in the geometry: spatial uniformity and isotropy cause degeneracies in the spectrum of the evolution operator, leading to failure of conventional control techniques. Efficient control algorithms applicable to experimental extended systems are the subject of my group's current research.

Most of our research in this area is directed at control of instabilities arising in fluid systems. One particular example is the contact line instability in spreading thin liquid films driven by a thermally imposed gradient is surface tension. In the figure below (click here to see a movie) the liquid spreads in the upward direction and undergoes a fingering instability without control. As the images shows, applying feedback effectively quenches the instability. The left (uncontrolled) half of the contact line develops "fingers", while the right (controlled) half remains straight. In the experiments control is applied by radiatively heating or cooling the capillary ridge behind the contact line by an amount proportional to the local deviation of the contact line from the mean position.

Experiment by M. Schatz