Characterization of the transition from defect- to phase-turbulence
  For the complex Ginzburg-Landau equation on a large periodic interval, we show that the transition from defect- to phase-turbulence is more accurately described as a smooth crossover rather than as a sharp continuous transition. We obtain this conclusion by using a powerful parallel computer to calculate various order parameters, especially the density of space-time defects, the Lyapunov dimension density, and the correlation lengths of the field phase and amplitude. Remarkably, the correlation length of the field amplitude is, within a constant factor, equal to the length scale defined by the dimension density. This suggests that a correlation measurement may suffice to estimate the fractal dimension of some large homogeneous chaotic systems. 
David A. Egolf (Department of Physics and Center for Nonlinear and   Complex Systems, Duke University) and Henry S. Greensid...