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
Example of Spatiotemporal Chaos: The Spiral-Defect
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
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
Centers and Groups:
- Guenter Ahlers,
experimental pattern formation in fluids and liquid crystals.
Dwight Barkley, theory, simulation of excitable
Eshel Ben-Jacob's Bacterial Pattern-Formation Group
- Bob Behringer
(granular flow, convection experiments).
Eberhard Bodenschatz, experimental pattern formation in
convecting flows, turbulence.
- Michael Cross,
theoretical pattern formation.
Bob Ecke, experimental pattern formation, chaos in
Jerry Gollub, pattern formation and chaos in
convection, capillary waves, granular media.
Michael Gorman, experimental pattern formation and
chaos in combustion.
Alain Karma, theory of excitable media and cardiac
Eugenia Kalnay, numerical weather forecasting.
Ray Kapral, theoretical studies of chemical spatiotemporal
Levine, theoretical/computational pattern formation and
Ron Lifshitz (Caltech)
Losert's Pattern Formation Laboratory at UMD.
Peter Lucas, visualization of cryogenic convecting
Alexander S. Mikhailov, analysis, control of
Stephen Morris, experimental patterns in fluids,
liquid crystals, and granular media.
James D. Murray, mathematical biology, pattern
Hermann Riecke, theoretical/computational pattern
Scholl, spatiotemporal dynamics of semiconductor systems.
Harry Swinney, experimental pattern formation in many systems.
- Cliff Surko,
experimental pattern formation, chaos in convecting flows.
- Lev Tsimring,
theoretical pattern formation, biological physics.
Vinals, theoretical pattern formation in capillary waves.
Henry Greenside's home page
| Department of Physics