Tuesday, May 20

3:00 PM-5:00 PM Ballroom I - Level B

Model Reduction, Analysis, and Control of Spatio-Temporal Dynamics Using KL Methods

Understanding the dynamics of spatio-temporal (ST) phenomena is important in many areas of research, such as turbulent flow, reaction-diffusion systems, and coupled oscillators. Because ST dynamics exhibits both low and and high dimensional behavior, it is important to characterize the behavior in a practical way, since many methods from low dimensional dynamics do not carry over to ST systems. One recent methodology for understanding ST dynamics is that of Karhunen-Loeve (KL) decomposition. One of the main advantages in using KL methods is that an orthogonal basis can be constructed from measured data, and then used to project out low dimensional dynamic models. In this minisympoium, the speakers will address areas of application of KL methods to both continuous and discrete applied areas in dynamics. Projected low dimensional behavior of fluid mechanics, analysis and control of bursting in reaction-diffusion, singularly perturbed structural mechanics, and large arrays of coupled oscillators will be discussed using a KL point of view.

Organizer: Ira B. Schwartz
U.S. Naval Research Laboratory

3:00 Analysis of Extensive Chaos by the Karhunen-Loeve Decomposition and by a Hierarchy of Unstable Periodic Orbits
Henry Greenside, Duke University
3:30 Analysis and Control of Spatio-Temporal Chaos in Reaction-Diffusion Processes
Ioana Triandaf, Science Applications International Corporation
4:00 New Measures of Coherence in Disordered and Noisy Arrays of Coupled Phase Oscillators
Thomas W. Carr, Southern Methodist University; and Ira B. Schwartz, Organizer
4:30 Modeling the Dynamics of Wall Bounded Turbulence
Larry Sirovich, Brown University and Mount Sinai School of Medicine

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TMP, 4/4/97