Defect Chaos

Null Results: Our Model for Bodenschatz's Defect Chaos Doesn't Correlate. (Roberts; 72)

2.5M mpeg

Just before his arrival at Cornell, I was watching Eberhard Bodenschatz's spiral defect chaos movie. I became convinced that there should be a hydrodynamic description of the motion, where each defect should be like an atom and the atom density (plus defects minus minus defects) should have a long-wavelength description like gases and liquids. Bruce Roberts, Eberhard and I looked hard at this question: Bruce extracted 1/r^2 predictions from a likely theoretical starting point (Generic Scale Invariance, which begins by writing the most general local equation of motion allowed by symmetry, violating detailed balance ...) and ran extensive simulations of a likely model (the Complex Ginzburg-Landau Equation). We found very little in the way of long-range correlations (they certainly decay faster than 1/r^2). Bruce wouldn't write it up, though, until he had proven a bound (using the topological nature of the defects) that ruled out the predicted scaling.

More Information

Eberhard Bodenschatz's Experiment

This research was paid for by THE US GOVERNMENT through the National Science Foundation (NSF #DMR-9419506). Currently, we are also receiving support from the Cornell Theory Center.

Links Back

Sethna's Research 90-94
Entertaining Science done at

Last modified: April 13, 1995

James P. Sethna,

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).