Research In Spatiotemporal Chaos

One of the more fascinating aspects of sustained nonequilibrium systems is that they often enter into time-dependent dynamical states that are disordered both in time and in space. While a precise definition of spatiotemporal chaos has not yet been agreed upon (there are several proposed definitions and they don't always agree with each other), the essential fact seems to be that fluctuations in space play a significant role in the dynamics. Such fluctuations arise typically when a system is strongly driven out of equilibrium (e.g., high Reynolds number fluid flow) or simply made large (e.g., large-aspect-ratio Benard convection). Researchers would then like to understand what kinds of dynamical states exist, how they vary with parameters, what kinds of bifurcations separate different states and how various physical properties such as heat or matter transport depend on details of the dynamical state.

The DOE supported research is summarized at the web page http://www.cmp.caltech.edu/~stchaos/index.html.


Example of Spatiotemporal Chaos: The Spiral-Defect Chaos State

MPEG example (3.2 MB) of spatiotemporal chaos, the spiral defect chaos state, which is found in experiments (and simulations of experiments) in large convection cells just beyond the primary bifurcation of a motionless conducting fluid to a convecting fluid. The movie is actually a numerical simulation of the two-dimensional Generalized Swift-Hohenberg equations, a reduced dynamical model that reproduces many of the complex dynamics observed in actual convection experiments near onset. The stripes of alternating color represent rising warm fluid and descending cold fluid respectively in some plane of a three-dimensional convection cell.

This spiral defect chaos state is especially interesting on two accounts. One is that all boundary conditions are static in time and uniform in space so that the intrinsic structure emerges spontaneously from the dynamics. Second, the range of wavenumbers lies within the region of linearly stable straight convection rolls and so the spiral defect chaotic attractor coexists in phase space with attractors of straight time-independent parallel rolls. It is not yet known how to predict the appearance of the spiral defect chaos state, how it varies with parameters, or its statistical properties.


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