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

Normalizations with exponentially small remainders for nonautonomous analytic periodic vector fields

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordinates in E1 allowing to eliminate up to a finite polynomial order all terms depending only on the coordinate u0 of E0 in the E1 component of the vector field. We moreover show that, optimizing the choice of the degree of the polynomial change of coordinates, we get an exponentially small remainder. In the second part, we prove a normal form theorem with exponentially small remainder. Similar theorems have been proved before in the autonomous case : this paper generalizes those results to the nonautonomous periodic case

Study of the air-formed oxide layer at the copper surface and its impact on the copper corrosion in an aggressive chloride medium

The electrochemical behaviour of pre-oxidized copper surfaces prepared by heating in air at 90°C was studied to evaluate the impact of the air-formed oxide layer at the copper surface on the corrosion in an aggressive chloride medium. In a first part, the evolution of the chemical composition and the structure of the air-formed oxide layer with the heating time were investigated by cyclic voltammetry in an alkaline medium in which the different oxide species can be discriminated, X-ray photoelectrons spectroscopy experiments (XPS) and water contact angle measurements. It was demonstrated that short heating times produce Cu2O-rich films, while CuO-rich films were obtained after long heating-time periods. Furthermore, cyclic voltammetric data strongly support a stratification of the corrosion products in the mature oxide layer. In a second part, the protection efficiency of air-formed films, aged from 1 to 22 days, against the copper corrosion was study using a potentiodynamic technique and the electrochemical impedance spectroscopy (EIS) in an aerated 0.2 M NaCl aqueous electrolyte. Results demonstrate that the chemical composition of the air-formed oxide layer has an important impact in the overall corrosion process. Results are tentatively explained in terms of composition and structure of the oxide layer

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

Observation of wave turbulence in vibrating plates

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small lengthscales. Here, wave turbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of D{\"u}ring et al. [Phys. Rev. Lett. 97, 025503 (2006)]. Alternative scenarios are suggested to account for this discrepancy -- in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior

ε^2-Order normal form analysis for a two-degree-of-freedom nonlinear coupled oscillator

In this paper, we describe an ε^2-order normal form decomposition for a two-degree-of-freedom oscillator system that has a mass supported with horizontal and vertical support springs. This system has nonlinear terms that are not necessarily ε^1-order small when compared to the linear terms. As a result, analytical approximate methods based on an ε expansion would typically need to include higher-order components in order to capture the nonlinear dynamic behaviour. In this paper we show how this can be achieved using a direct normal form transformation up to order ε^2. However, we will show that the requirement for including ε^2 components is primarily due to the way the direct normal form method deals with quadratic coupling terms rather than the relative size of the coefficients

Sur le calcul numérique des modes non-linéaires

Nos travaux portent sur le calcul numérique de modes non linéaires. L'approche adoptée consiste à résoudre par différence finie l'équation différentielle décrivant un mode, s'exprimant comme un problème de transport dont on recherche les conditions initiales donnant des solutions périodiques. Les algorithmes de résolution et d'optimisation sont testés sur un système à deux degrés de liberté et à non linéarités cubiques. Cet exemple nous permet de discuter de la convergence des algorithmes et des problèmes d'implémentation. Les résultats sont également comparés à des calculs par continuation

Tyrosyl-tRNA synthetase: the first crystallization of a human mitochondrial aminoacyl-tRNA synthetase.

Human mitochondrial tyrosyl-tRNA synthetase and a truncated version with its C-terminal S4-like domain deleted were purified and crystallized. Only the truncated version, which is active in tyrosine activation and Escherichia coli tRNA(Tyr) charging, yielded crystals suitable for structure determination. These tetragonal crystals, belonging to space group P4(3)2(1)2, were obtained in the presence of PEG 4000 as a crystallizing agent and diffracted X-rays to 2.7 A resolution. Complete data sets could be collected and led to structure solution by molecular replacement.journal articleresearch support, non-u.s. gov't2007 Apr 012007 03 30importe

Characterizing convection schemes using their responses to imposed tendency perturbations

Convection is usually parameterized in global climate models, and there are often large discrepancies between results obtained with different convection schemes. Conventional methods of comparing convection schemes using observational cases or directly in 3D models do not always clearly identify parameterization strengths and weaknesses. In this paper we evaluate the response of parameterizations to various perturbations rather than their behavior under particular strong forcing. We use the linear response function method proposed by Kuang (2010) to compare twelve physical packages in five atmospheric models using single-column model (SCM) simulations under idealized radiative-convective equilibrium conditions. The models are forced with anomalous temperature and moisture tendencies. The temperature and moisture departures from equilibrium are compared with published results from a cloud-resolving model (CRM). Results show that the procedure is capable of isolating the behavior of a convection scheme from other physics schemes. We identify areas of agreement but also substantial differences between convection schemes, some of which can be related to scheme design. Some aspects of the model linear responses are related to their RCE profiles (the relative humidity profile in particular), while others constitute independent diagnostics. All the SCMs show irregularities or discontinuities in behavior that are likely related to switches or thresholds built into the convection schemes, and which do not appear in the CRM. Our results highlight potential flaws in convection schemes and suggest possible new directions to explore for parameterization evaluation