A phenomenological model for predicting the effect of damping on wave turbulence spectra in vibrating plates

International audienceThin plates vibrating at large amplitudes may exhibit a strongly nonlinear regime that has to be studied within the framework of wave turbulence. Experimental studies have revealed the importance of the damping on the spectra of wave turbulence , which precludes for a direct comparison with the theoretical results, that assumes a Hamiltonian dynamics. A phenomenological model is here introduced so as to predict the effect of the damping on the turbulence spectra. Self-similar solutions are found and the cutoff frequency is expressed as function of the damping rate and the injected power

On the three-dimensional temporal spectrum of stretched vortices

The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.Comment: 4 pages, RevTeX, submitted to PR

Wave turbulence in vibrating plates

International audienceTurbulence is a general term used for describing the erratic motions displayed by nonlinearsystems that are driven far from their equilibrium position and thus display complicatedmotions involving different time and length scales. Wave turbulence (WT) share many common ideas with turbulence, in particular asbeing a statistical theory for out-of-equilibrium systems. A main difference resides in thefact that the persistence of waves is assumed.The application of WT to vibrating plates started with the theoretical derivation ofthe kinetic equation from the dynamical von Karman equations thatdescribe large-amplitude motions of thin plates. Since this date, numerous papershave been published covering experimental, theoretical and numerical materials. In fact,it appears that the vibrating plate is a perfect candidate for a thorough comparison ofexperiments with theoretical predictions. As compared to other physical systems such ascapillary or gravity waves for example, an experimental set-up with a fine control of energyinjection and a confortable range of wavelength is not too difficult to put in place. Secondly,the available measurement techniques allow one to get a complete and precise picture of thedynamics through the scales, both in the space and frequency domains. Finally, numericalcodes with good accuracy have been developed so that all the underlying assumptions ofthe theory as well as its predictions have been tested, both on the experimental and thenumerical levels

Building block libraries and structural considerations in the self-assembly of polyoxometalate and polyoxothiometalate systems

Inorganic metal-oxide clusters form a class of compounds that are unique in their topological and electronic versatility and are becoming increasingly more important in a variety of applications. Namely, Polyoxometalates (POMs) have shown an unmatched range of physical properties and the ability to form structures that can bridge several length scales. The formation of these molecular clusters is often ambiguous and is governed by self-assembly processes that limit our ability to rationally design such molecules. However, recent years have shown that by considering new building block principles the design and discovery of novel complex clusters is aiding our understanding of this process. Now with current progress in thiometalate chemistry, specifically polyoxothiometalates (POTM), the field of inorganic molecular clusters has further diversified allowing for the targeted development of molecules with specific functionality. This chapter discusses the main differences between POM and POTM systems and how this affects synthetic methodologies and reactivities. We will illustrate how careful structural considerations can lead to the generation of novel building blocks and further deepen our understanding of complex systems

Experimental test of the Gallavotti-Cohen fluctuation theorem in turbulent flows

We test the fluctuation theorem from measurements in turbulent flows. We study the time fluctuations of the force acting on an obstacle, and we consider two experimental situations: the case of a von K\'arm\'an swirling flow between counter-rotating disks (VK) and the case of a wind tunnel jet. We first study the symmetries implied by the Gallavotti-Cohen fluctuation theorem (FT) on the probability density distributions of the force fluctuations; we then test the Sinai scaling. We observe that in both experiments the symmetries implied by the FT are well verified, whereas the Sinai scaling is established, as expected, only for long times