Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels

This paper experimentally investigates the holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound levels. The theoretical formulations are based on a semi-empirical approach and the use of Fok’s function to model the acoustic surface impedance. For the high sound level regime, an empirical power law involving three coefficients is adapted. It is shown theoretically and experimentally that these coefficients can lead to optimized absorption performance and particularly, a formula relating the critical Reynolds number (Reynolds number value after which the absorption coefficient decreases with the increase of sound level) and the center-to-center distance between the perforations is derived. It is demonstrated that the first coefficient of the nonlinear acoustic resistance strongly depends on the separation distance between the apertures and decreases with a decrease of this latter distance. Analysis of the data reveals the fact that even with Holes Interaction Effect (HIE), the nonlinear reactance dependence on velocity is still very low compared to the resistance-velocity dependence. Four perforated panels of 1.5 mm thickness with different separation distances between the holes (from widely to closely separation) were built and tested. Experimental results performed with an impedance tube are compared with the described model for HIE. To test the dependence of the coefficients on frequency, the experiments are carried out for two different excitation frequencies (292 Hz and 506 Hz). The results can be used for designing optimal perforated panels for ducts, silencers and for the automotive industry.     

Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations

An analysis of the discrete shallow‐water equations using the Raviart–Thomas and Brezzi–Douglas–Marini finite elements is presented. For inertia–gravity waves, the discrete formulations are obtained and the dispersion relations are computed in order to quantify the dispersive nature of the schemes on two meshes made up of equilateral and biased triangles. A linear algebra approach is also used to ascertain the possible presence of spurious modes arising from the discretization. The geostrophic balance is examined and the smallest representable vortices are characterized on both structured and unstructured meshes. Numerical solutions of two test problems to simulate gravity and Rossby modes are in good agreement with the analytical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Countability via capacity

Abstract. Let K be a compact subset of {\bf C}, and let c denote logarithmic capacity. We prove that if and only if K is countable. As an application, we obtain a short proof of the scarcity theorem for countable analytic multifunctions. Received: 13 November 2000 / Published online: 18 January 2002     

Computation of capacity

This article introduces a method for computing upper and lower bounds for the logarithmic capacity of a compact plane set. If the set has the Hölder continuity property, then these bounds converge to the value of the capacity. A number of examples are discussed in detail, including the Cantor middle-third set, for which we estimate .

     

On two-dimensional supergravity and the quantum super-Möbius group

We describe the quantum-group structure of two-dimensionalN=1 supergravity in the conformal gauge. The operator-algebra of this (super-Liouville) theory is shown to correspond to a quantum deformation of the super-Möbius group, which provides a new solution of Yang and Baxter's equation. This structure is used to investigate the strong-coupling regime of the theory (1d9). Ford=5, a unitary truncation theorem-similar to the one of the bosonic case-is derived for the fundamental representation.Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud     

Computation of weighted capacity

We introduce a method for computing the weighted capacity of a closed plane set. The method automatically yields upper and lower bounds for the capacity, and, for compact sets, these bounds converge to the true value of the capacity. No prior knowledge of the support of the equilibrium measure is required, and indeed the method can be used to determine this support. We discuss a number of examples in detail.     

Impact of mass lumping on gravity and Rossby waves in 2D finite‐element shallow‐water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite‐element velocity/surface‐elevation pairs that are used to approximate the linear shallow‐water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P₀?P₁, RT₀ and P?P₁ pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results. Copyright © 2008 John Wiley & Sons, Ltd.     

On the variations of acoustic absorption peak with particle velocity in micro-perforated panels at high level of excitation

The acoustic behavior of micro-perforated panels (MPP) is studied theoretically and experimentally at high level of pressure excitation. A model based on Forchheimer's regime of flow velocity in the perforations is proposed. This model is valid at relatively high Reynolds numbers and low Mach numbers. The experimental method consists in measuring the acoustical pressure at three different positions in an impedance tube, the two measurement positions usually considered in an impedance tube and one measurement in the vicinity of the rear surface of the MPP. The impedance tube is equipped with a pressure driver instead of the usual loudspeaker and capable of delivering a high sound pressure level up to 160 dB. MPP specimens made out of steel, dural and polypropylene were tested. Measurements using random noise or sinusoidal excitation in a frequency range between 200 and 1600 Hz were carried out on MPPs backed by air cavities. It was observed that the maximum of absorption can be a positive or a negative function of the flow velocity in the perforations. This suggests the existence of a maximum of absorption as a function of flow velocity. This behavior was predicted by the model and confirmed experimentally.     

Automated capillary liquid chromatography for simultaneous determination of neuroactive amines and amino acids

A method for the separation and quantitative determination of neuroactive amino acids (aspartate, glutamate, citrulline, arginine, glycine, taurine, gamma-aminobutyric acid) and neuroactive amines (noradrenaline, dopamine and serotonin) in a single chromatographic analysis is presented. The method is based on pre-column derivatization with o-phthalaldehyde and tert.-butyl thiol, on-column preconcentration and separation using 50 microns I.D. packed capillary columns, and detection by amperometry. Mass limits of detection are 80-900 amol for all neurotransmitters with RSDs of 0.71 and 4.6% or better for retention time and peak area, respectively. The method was demonstrated by application to the determination of neurotransmitters in microdialysis samples collected from striatum of live rats and tissue samples extracted from butterfly brains.