On the stability and dissipation of wall boundary conditions for compressible flows

Characteristic formulations for boundary conditions have demonstrated their effectiveness to handle inlets and outlets, especially to avoid acoustic wave reflections. At walls, however, most authors use simple Dirichlet or Neumann boundary conditions, where the normal velocity (or pressure gradient) is set to zero. This paper demonstrates that there are significant differences between characteristic and Dirichlet methods at a wall and that simulations are more stable when using walls modelled with a characteristic wave decomposition. The derivation of characteristic methods yields an additional boundary term in the continuity equation, which explains their increased stability. This term also allows to handle the two acoustic waves going towards and away from the wall in a consistent manner. Those observations are confirmed by stability matrix analysis and one‐ and two‐dimensional simulations of acoustic modes in cavities. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear behaviour of the instability of steady natural convection in a vertical air layer

In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method.     

A Wavelet-Balance Method to Investigate the Vibrations of Nonlinear Dynamical Systems

The scope of this paper is to introduce a new wavelet-balanceprocedure allowing to give a genuine time-scale representation ofvibrations of nonlinear dynamical systems by adopting a waveletmultiresolution approach. In a former paper, a wavelet-Galerkinoriented procedure was developed to analyze vibrations of lineartime-periodic systems. The topic is here to extend the process tothe nonlinear case using a perturbation technique. The underlyingidea consists in successively balancing the linearized equationsof motion into wavelet spaces with increasing resolution scales.Here we demonstrate the wavelet-balance procedure may accuratelyexhibit both transient and stationary vibrations of any nonlinearproblem in general, whatever smooth nonlinearity shape or externalforcing may be. In addition, wavelets inherit of fairly goodtime-frequency localization properties that are likely to permitthe investigation of strong nonlinear problems. Numericalexperiments achieved on a well known Duffing oscillator involvinga cubic nonlinearity then illustrate the procedure. Simulationsattest the relevance of the method by comparison with eitherpurely numerical results obtained with a Runge–Kutta integrationscheme or with an analytical study based on the multiple scalesmethod. We demonstrate that this semi-analytical semi-numericalperturbation method permits to capture stable limit cycles of theDuffing oscillator and its related amplitude spectrum response orstill responses to pulse-like excitations. Finally, key propertiesof the method are discussed and future prospective works areoutlined.     

Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment

The present study deals with nonlinear energy pumping which consists in passive irreversible transfer of energy from a linear structure to a nonlinear one. Various results (theoretical, numerical, and experimental) about energy pumping based on recent works are given. Thus, the phenomenon is studied for different excitations: transient and periodical. Moreover, advantages of such a system are carried out in particular efficiency of this phenomenon. That is why the robustness and comparison with classical tuned mass damper are analyzed. An application is considered with physical experiment using a reduced scale building.     

Modulating the photophysical properties of azamacrocyclic europium complexes with charge-transfer antenna chromophores

Two europium complexes with bis(bipyridine) azamacrocyclic ligands featuring pendant arms with or without π-conjugated donor groups are synthesized and fully characterized by theoretical calculations and NMR spectroscopy. Their photophysical properties, including two-photon absorption, are investigated in water and in various organic solvents. The nonfunctionalized ligand gives highly water-stable europium complexes featuring bright luminescence properties but poor two-photon absorption cross sections. On the other hand, the europium complex with an extended conjugated antenna ligand presents a two-photon absorption cross section of 45 GM at 720 nm but is poorly luminescent in water. A detailed solvent-dependent photophysical study indicates that this luminescence quenching is not due to the direct coordination of O-H vibrators to the metal center but to the increase of nonradiative processes in a protic solvent induced by an internal isomerization equilibrium.     

Assignment of the 1H and 13C NMR Chemical Shifts of (3,4-Dihydro-2H-pyran-5-yl)-oxo-acetic Acid Methyl Ester Using the Two Dimensional HMBC Technique

The identification of (3, 4-dihydro-2H-pyran-5-yl)-oxo-acetic acid methyl ester has been realized by combination of two dimensional HETCOR and HMBC techniques. ¹³C and ¹H chemical shifts asignements are described.     

Non smooth dynamics of mechanical systems with history term

Models involving maximal monotone term and history (delay) term are considered in a mathematical and numerical point of view.     

Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.     

Extended complexification method to study nonlinear passive control

Nonlinear Dynamics - The present research work aims to design a passive vibration control based on nonlinear energy pumping. An extended asymptotic approach is introduced based on the invariant...     

Copper catalyzed 1,3-dipolar cycloaddition reaction of azides with N-(2-trifluoroacetylaryl)propargylamines: A mild entry to novel 1,4-disubstituted-[1,2,3]-triazole derivatives

The synthesis of N-(2-trifluoroacetylaryl)propargylamines 10-14 and 17 is presented. The copper(I) catalyzed cycloaddition reaction of these propargylamines (dipolarophiles) with a series of azides (1,3-dipoles) 18-20, 21 and 24 was found to proceed smoothly in dimethylsulfoxide at room temperature, to furnish the corresponding 1,4-disubstituted-[1,2,3]triazole derivatives 26-36 in moderate to good yields.