European Space Agency experiments on thermodiffusion of fluid mixtures in space.

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

Dynamics of weakly coupled parametrically forced oscillators.

The dynamics of two weakly coupled parametric oscillators are studied in the neighborhood of the primary subharmonic instability. The nature of both primary and secondary instabilities depends in a critical way on the permutation symmetries, if any, that remain after coupling is considered, and this depends on the relative phases of the parametric forcing terms. Detailed bifurcation sets, revealing a complex series of transitions organized in part by Bogdanov-Takens points, are calculated for representative sets of parameters. In the particular case of out-of-phase forcing the predictions of the coupled oscillator model are compared with direct numerical simulations and with recent experiments on modulated cross waves. Both the initial Hopf bifurcation and the subsequent saddle-node heteroclinic bifurcation are confirmed.

Onset patterns in a simple model of localized parametric forcing.

We investigate pattern selection at onset in a parametrically and inhomogeneously forced partial differential equation obtained by generalizing Mathieu's equation to include spatial interactions. No separation of scales is assumed. The proposed model is directly relevant to the case of parametrically forced surface waves, such as cross-waves, excited by the horizontal vibration of a fluid, where the forcing is localized to a finite region near the endwall or wavemaker. The availability of analytical solutions in the limit of piecewise constant forcing allows us investigate in detail the dependence of selected eigenfunctions on spatial detuning, forcing width, damping, boundary conditions, and container size. A wide range of onset patterns are located and described, many of which are rotated, modulated, or both, and deviate far from simple crosswise oriented standing waves. The linear selection mechanisms governing this multiplicity of potential onset patterns are discussed.