Polarization imaging for 3D inspection of highly reflective metallic objects

In the field of industrial vision, the 3D inspection of highly reflective metallic objects is still a delicate task. The specular reflections prevent the use of a 3D laser scanner, whereas the phase shifting-based 3D systems are more adapted to inspect surfaces with low curvature. This paper deals with a new automated 3D inspection system based on polarization analysis. Studying the state of polarization of the reflected light is very useful for obtaining information on the normals of the surface. An extension of the shape from polarization method from dielectric to metallic surfaces is demonstrated. Then, an improved relaxation algorithm is provided in order to reconstruct the shape from the normal field given by the polarization analysis. Finally, applications to shape defect detection are discussed and the efficiency of the system in discriminating defects on highly reflective metallic objects made by stamping and polishing is presented. The text was submitted by the authors in English.     

Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

Effect of structure on glass transition temperature of amine crosslinked epoxies

About 40 epoxide-amine network polymers with glass transition temperatures ranging from 0 to 232°C were investigated, about one-third being reported for the first time. The glass transition temperature T_gl of the corresponding linear copolymers was first calculated by use of an additivity law whose physical validity was carefully checked. Then the contribution of crosslink mers was determined, and various physical and empirical approaches of the effect of crosslinking on T_g were compared. The results gave evidence in favor of the DiMarzio approach. A predictive relationship based on these considerations is proposed.     

Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed in Hainzl (Ann. H. Poincaré, in press). We fix an arbitrary cut-off parameter Λ and recover the α²-term of the self-energy, where α is the coupling parameter representing the fine structure constant. Thereby we develop a method which allows to expand the self-energy up to any power of α. This implies that perturbation theory in α is correct if Λ is fix. As an immediate consequence we obtain enhanced binding for electrons.     

Courants caractéristiques et analyse de SEREigen currents and RCS analysis

In this Note, we return to the theory of characteristic modes which was introduced 30 years ago for electromagnetic scattering problems. A simple mathematical framework is proposed and complete definitions are given. The potential interest of this theory in terms of Radar Cross Section (RCS) analysis is then discussed, especially in the low frequency case. Finally, a 3-D example is presented to illustrate the efficiency of this decomposition. To cite this article: Y. Morel et al., C. R. Mecanique 332 (2004).     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.