On-off intermittency at the onset of the ion-acoustic instability in a laboratory plasma

The ion-ion beam instability is experimentally studied just above threshold in a laboratory double-plasma device. Intermittent bursts of unstable waves are recorded in the target plasma and the distribution of the recurrence times of the bursts is estimated. At the onset of instability, the measurements are in agreement with the expected evolution deduced from a theoretical model that combines the normal form of a supercritical Hopf-Andronov bifurcation and the parametric noisy deviations from threshold typical of on-off intermittency. In both the experiment and the model, the distribution of the recurrence times of the bursts decays as an inverse power law and the evolution of the mean laminar length when the control parameter is increased beyond threshold exhibits a power law of exponent -1.

Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation.

The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield with the complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of the Ginzburg-Landau equation in terms of the kernels of the Volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics. (c) 2000 American Institute of Physics.

Statistics of return times in a self-similar model.

In this paper, we propose a model for the hyperbolic part of the phase space of a Hamiltonian system that is located near a hierarchical islands around islands structure. We study the statistics of Poincare recurrences, the type of orbits that are mainly responsible for slowly decaying correlations, and thus the mechanisms generating power law tails. (c) 1999 American Institute of Physics.