On Nonlinearly Elastic Membranes under Compression

The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo (1993) and Pantz (2000). We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini (1995). We generalize the application of their result from plane elasticity to three-dimensional plane membranes.     

On metric properties of stratified sets

 We study the class of those locally radial stratified spaces which are (C)–regular for standard control functions. These spaces generalise Whitney stratified spaces, but are shown to have the same topological and metric properties. The weakly Whitney stratified spaces that we have introduced recently form an intermediate class between Whitney stratified spaces and these locally radial (C)–regular spaces. Received: 14 January 2000 / Revised version: 27 November 2002 Published online: 20 March 2003 Mathematics Subject Classification (2000): 58A35, 58C35, 26B20     

On Some Properties of Bilinear Maps of Order Bounded Variation

In this paper we study properties of bilinear maps of order bounded variation. Theorems of preservation of properties in passage to the triadjoint and the tensor product are presented.     

Linear systems subject to input saturation and time delay: Global asymptotic and Lp-stabilization

This Note deals with two problems on stabilization of linear systems by static feedbacks which are bounded and time-delayed, namely global asymptotic stabilization and finite gain $L^p$-stabilization, $p\in [1,\infty ]$. Regarding the first issue, we provide, under standard necessary conditions, two types of solutions for arbitrary small bound on the control and large (constant) delay. The first solution is based on the knowledge of a static stabilizing feedback in the zero-delay case and the second solution is of nested saturation type, which extends results of Mazenc et al. [IEEE Trans. Automat. Contr. 48 (1) (2003) 57–63]. For the finite-gain $L^p$-stabilization issue, we assume that the system is neutrally stable. We show the existence of a linear feedback such that, for arbitrary small bound on the control and large (constant) delay, finite gain $L^p$-stability holds with respect to every $L^p$-norm, $p\in [1,\infty ]$. Moreover, the corresponding $L^p$-gain is delay-independent. To cite this article: K. Yakoubi, Y. Chitour, C. R. Acad. Sci. Paris, Ser. I 340 2005).     

Methane production in a 100-L upflow bioreactor by anaerobic digestion of farm waste

Manure waste from dairy farms has been used for methane production for decades, however, problems such as digester failure are routine. The problem has been investigated in small scale (1–2 L) digesters in the laboratory; however, very little scale-up to intermediate scales are available. We report production of methane in a 100-L digester and the results of an investigation into the effect of partial mixing induced by gas upflow/recirculation in the digester. The digester was operated for a period of about 70 d (with 16-d hydraulic retention time) with and without the mixing induced by gas recirculation through an internal draft tube. The results show a clear effect of mixing on digester operation. Without any mixing, the digester performance deteriorated within 30–50 d, whereas with mixing continuous production of methane was observed. This study demonstrates the importance of mixing and its critical role in design of large scale anaerobic digesters.     

Structure and Electrical Properties of Potassium-Doped Siloxane-Poly(oxypropylene) Ormolytes

The structure and the ionic conduction properties of siloxane-poly(oxypropylene) (PPO) hybrids doped with different potassium salts (KCF₃SO₃, KI, KClO₄ and KNO₂) are reported for two polymer molecular weights (300 and 4000 g/mol), labelled PPO₃₀₀ and PPO₄₀₀₀, respectively. The doping concentration, related to the concentration of the ether type oxygen of the PPO chain, is the same whatever the salt and verifies [O]/[K] = 20. Ionic room temperature conductivity shows the highest value for the KCF₃SO₃ doped PPO₄₀₀₀ hybrid (4 × 10^{–7 –1} cm^–1). The structure of these hybrids was investigated by X-ray powder diffraction (XRPD) and X-ray absorption spectroscopy (EXAFS and XANES) at the potassium K-edge (3607 eV). XRPD results show that the hybrid matrix is always amorphous and the formation of secondary potassium phases is observed for all the samples, except for the KCF₃SO₃ doped PPO₄₀₀₀ hybrid. EXAFS results evidence a good correlation between the ionic conductivity and the presence of oxygen atoms as first neighbours around potassium.     

Growth and characterization of high purity single crystals of barium ferrite

High purity single crystals of barium ferrite have been grown with the use of a BaO flux. The detected residual impurities have a total concentration of 130 ppm (wt), of which 100ppm is due to platinum. While the crystals exhibit occassional inclusions of a barium rich phase, the predominant microstructural defects are voids, which exhibit two geometries; one spherical and one hexagonal. Magnetic and resistivity measurements have yielded values which are comparable to those reported in the literature. Room temperature effective linewidth measurements at 10 GHz indicate that eddy current losses are dominant for disk shaped samples thicker than ≈0.3 mm. Room temperature FMR linewidth measurementson a sample 0.04 mm thick exhibit a linear frequency response between 55 and 90 GHz, which is consistent with a Landau-Lifshitz damping mechanism.