Research
Overview
Our research focuses primarily on the interdisciplinary field of pattern formation, a major branch of nonlinear science. Studies of pattern formation use a common set of fundamental concepts to describe how non-equilibrium processes cause structure to appear in a wide variety of complex systems in nature and in technology. While much progress toward understanding pattern dynamics has been made in recent years, fundamental challenges remain. Below are brief descriptions of our current experimental research projects addressing some of these outstanding issues; click on a link to learn more.
Extracting information from the complex structures created by physical systems driven out of equilibrium is a huge challenge. We address this challenge by applying different characterization techniques to Rayleigh-Bénard convection, a system well-known for exhibiting spatiotemporally chaotic dynamics. These techniques include the established Karhunen-Loeve decomposition (KLD) as well as a novel characterization tool, computational homology. This new method exposes a symmetry breaking not observable using conventional statistical measures. A system dimension, related to the number of degrees of freedom present in the system, can be defined for both methods. The constraining effect of the physical boundaries is revealed by this measure.
Forecasting is a central goal in the study of many physical systems, and chaos can be a limiting factor to this goal. One well-known example is weather, illustrated by the so-called butterfly effect: the idea that a small disturbance can be amplified to create large-scale changes to a system. We are using a novel experimental technique to probe system dynamics near instability in a paradigm of pattern forming systems, Rayleigh-Bénard convection (RBC). This procedure extracts the structure and growth rates of modes governing the instability. We are also using this tool to investigate the role of instability in limiting predictive ability through the application of a state and parameter estimation algorithm (LETKF) to prepared patterns.
© 2013 Schatz Pattern Formation and Control Lab | Last updated: 12-10-2013