Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

Random oscillations in the Van der Pol system under the action of a broadband random process

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1517–1521, November, 1998.     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

Adaptive remeshing for ductile fracture prediction in metal formingRemaillage adaptatif pour la prévision de la rupture ductile en mise en forme

The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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Interfacial structure and electrical properties of LaAlO3 gate dielectric films on Si by metalorganic chemical vapor deposition

LaAlO₃ (LAO) gate dielectric films were deposited on Si substrates by low-pressure metalorganic chemical vapor deposition. The interfacial structure and composition distribution were investigated by high-resolution transmission electron microscopy (HRTEM), X-ray photoelectron spectroscopy (XPS), secondary-ion mass spectroscopy (SIMS), and Auger-electron spectroscopy (AES). HRTEM confirms that there exists an interfacial layer between LAO and Si in most samples. AES, SIMS, and XPS analyses indicate that the interfacial layer is compositionally graded La–Al silicate and the Al element is severely deficient close to the Si surface. Electrical properties of LAO films were evaluated. No evident difference in electrical properties between samples with and without native SiO₂ layers was observed. The electrical properties are discussed in terms of LAO growth mechanisms, in relation to the interfacial structure. PACS 73.40.Qv; 81.15.Gh; 77.55.+f; 68.35.-p     

Surface and interfacial properties of PVDF/acrylic copolymer blends before and after UV exposure

Morphological and chemical properties of both the surface and interface of poly(vinylidene fluoride)/poly(methyl methacrylate)-co-poly(ethyl acrylate) (PVDF/PMMA-co-PEA) blend films have been investigated before and after the samples were exposed to ultraviolet (UV) irradiation using a xenon arc lamp at 50 °C and 9% relative humidity (RH) for 7 months. Surface and interfacial morphologies were studied by atomic force microscopy (AFM). Chemical composition information was obtained by confocal Raman microscopy, attenuated total reflection-FTIR spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS), and contact angle measurements. Results show an enrichment of the PVDF material at the air surface, while the acrylic copolymer enriches the interface. Blends having greater than 50% mass fraction of PVDF show little change in the surface morphology after UV exposure for 7 months. However, for a lower PVDF content, blends exhibit significant degradation of PMMA-co-PEA copolymer and a much rougher surface after UV exposure. Microstructural changes in the PVDF spherulites are also observed after UV degradation. It is found that the surface and interfacial morphologies are correlated with the chemical properties.     

Direct measurement of fluid velocity gradients at a wall by PIV image processing with stereo reconstruction

Velocity gradient is typically estimated in Particle Image Velocimetry (PIV) by differentiating a measured velocity field, which amplifies noise in the measured velocities. If gradients near a boundary are sought, such noise is usually greater than in bulk fluid, because of small tracer displacement, uncertainty in the effective positions of velocity vectors, intense deformation of tracer patterns, and laser reflection. We consider here a modified form of the Particle Image Distortion (PID) method todirectly calculate velocity gradients at a fixed wall, and refer it as “PIV/IG” (“Interface Gradiometry”). Results from synthetic 2D PIV images suggest our method achieves higher SNR and accuracy than velocity differentiation. Also, we have developed a procedure to reconstruct three-dimensional velocity gradient at a fixed wall the two non-zero components from PIV/IG data obtained in stereo views; these equations simplify considerably thanks to the no-slip condition. Experimental data from the bottom wall of turbulent open channel flow appear to suffer from a form of pixel locking. As with standard PIV, this underlines the importance of adequate tracer diameter in the images, sufficient seeding density, and of dynamic range of the camera sensor.