with Glen Granzow, Lander University
Phys. Rev. Lett. 87 (2001) 174502

Parametrically Excited Waves

·  Coupled Ginzburg-Landau equations

¶t A + s ¶x A = dx ¶x2A + dy ¶y2A + a A + b B + c |A|2 A + g |B|2 A ¶t B - s ¶x B = d*x ¶x2B + d*y ¶y2B + a* B + b A + c* |B|2 B + g* |A|2B

these equations are, e.g., relevant for parametrically forced waves in electroconvection and with some restrictions also for surface waves on a vibrated fluid   
·   Typical phase diagram

Ordered and Disordered Chaos

·  Pattern

A brief movie clip (300kB) shows the creation and annihilation of defect pairs (break-up of rolls).

Defect Loops in Space-Time

Defect motion
climb Þ local change in wavelength
glide  Þ local rotation of pattern

Statistics of Loops in Space-Time

ordered: exponential decay
disordered: power-law decay