CPM Seminar

Spatio-Temporal Chaos and Defects in Pattern-Forming Systems

Hermann Riecke

Northwestern University

Many spatially extended dynamical systems exhibit patterns that are chaotic in space and time. Various kinds of defects are often striking features of these patterns. A tantalizing question is to what extent the defects can be used to characterize and describe the patterns and their dynamics. I will discuss a few types of defect-dominated spatio-temporal chaos and how we characterize them in terms of their defects. In rotating non-Boussinesq convection in water we find ordered and chaotic hexagonal patterns far into the nonlinear regime. Through an interaction with the whirling motion of the hexagons the defects in the chaotic state exhibit statistics that differ noticeably from the squared Poisson distribution commonly found in defect chaos. In a Ginzburg-Landau model for parametrically driven waves we find a transition from a disordered to a spatially ordered chaotic state. We characterize it in terms of the statistics of the defects' space-time trajectories. This approach, which we also apply to the classic complex Ginzburg-Landau equation, provides a somewhat intuitive picture of the role of the defects in the break-down of the spatial order.