Research

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.

Characterization of Complex Patterns

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-Benard 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.

Pattern Control and Forecasting

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.

 
Turbulence in Taylor-Couette Flow

In shear flows, the transition to turbulence typically occurs through a subcritical bifurcation where a finite amplitude perturbation is required to take the system from the laminar state to a turbulent one. Some experiments suggest that the lifetime diverges at a finite Reynolds number; others suggest that the lifetime diverges only at infinite Reynolds number.  We measure turbulent state lifetimes for the flow between concentric, rotating cylinders in the regime where the transition to turbulence is subcritical.  Our study also allows us to test whether the transient nature of the turbulence observed in previous experiments is specific to those flow geometries or is present in a more general class of shear flows.  We also investigate the effects of various boundary conditions and weak counter/co-rotation on the observed lifetimes.

Two-Dimensional Turbulence

Recent theoretical advances suggest ways to find unstable exact Navier Stokes solutions that capture many features of coherent structures, which have long been observed in turbulent flow. It remains unknown whether these solutions, termed Exact Coherent States, can describe observations of turbulent flow in laboratory experiments. Our experimental and numerical investigations search for unstable solutions in quasi-2D flows driven by electromagnetic forces. In the experiments, time series of velocity fields are obtained from images of the visualized flow. In the simulations, long time series of velocity fields are calculated for flows with forcing similar to that in the experiments. Recurrence plots constructed from velocity field data provide evidence for the existence of unstable periodic orbits.

People

Michael Schatz (PI)	Daniel Borrero	Huseyin Kurtuldu	Adam Perkins
Reuven Ballaban	Jon Paprocki

Publications

A complete list of publications can be viewed here.

Links

Center for Nonlinear Science		  

School of Physics

Georgia Institute of Technology

Physics Education Research Group

Contact Us

Our labs are located on the third floor of the Howey Physics Building, rooms W301 and W303.
   
Lab Phone: 404-894-5094
Contact the Webmaster: adam.perkins@gatech.edu