9501077 Armbruster The apparent spatial coherence of many large-scale systems with complex dynamics implies that the underlying behavior can be described mathematically with relatively few degrees of freedom. The goal of this research project is to elucidate the dynamical mechanisms that underlie such spatio-temporal behavior by using a qtandard mathematical tool, sometimes called Karhunen-Loeve (K-L) analysis. In addition it is planned to apply some of the methods used so successfully for chaotic time series data to spatio- temporal data. By using K-L analysis to find an approximate low dimensional model of some of the spatio-temporal behavior, methods that have been developed for chaotic time series data may be applicable to spatially extended data. In addition, it is planned to investigate control strategies for spatio-temporally chaotic dynamics by developing appropriate control mechanisms for suitable low-dimensional approximations. The apparent spatial coherence of many large-scale systems with complex dynamics implies that the underlying behavior can be described mathematically with relatively few degrees of freedom. The goal of this research project is to elucidate the dynamical mechanisms that underlie such spatio-temporal behavior. Examples currently under investigation include the analysis of the onset of turbulence in 2-dimensional fluid flow and the analysis of the dynamics of cellular flames that is complicated in space and time. This study is intended to characterize the spatio-temporally complex motion of the flame cells in order to develop a phenomenological model as a prerequisite for systematically controlling the behavior of such cellular flames. The long term potential of this research is considerable. The experiments on flames are typical of many spatio-temporally complex problems. As a result of this research, fundamental mathematical insights into the processes that generate and drive spatio-temporal structures are expe cted. Such insight is a prerequisite for any advanced technological use of nonlinear dynamics, for example, to control combustion processes or to suppress and control boundary layer turbulence along airfoils. ***
