An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Full collocation methods for some boundary integral equations

In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated before. Some numerical experiments, confirming our theoretical results, are given. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Euler-Maclaurin Formula in Presence of a Logarithmic Singularity

In this short note we prove an extension of the Euler-Maclaurin expansion for general rectangular composite quadrature rules in one dimension when the derivative of the integrand has a logarithmic singularity. We show that a correction series has to be added to the formula, but that the asymptotic expansion in powers of the discretization parameter still holds.     

Author Index

Authors Index

Author Index     

Insulating diamond particles as substrate for Pd electrocatalysts

The suitability of insulating highly crystalline diamond particles as support for Pd based electrocatalysts is explored for the first time by evaluating the electrochemical stripping of CO and oxidation of formic acid in acid solutions.     

Periodic Dirac Delta Distributions in the Boundary Element Method

This paper is concerned with the numerical solution of boundary integral equations on smooth curves of the plane with some numerical methods having in common the use of sets of equally spaced periodic Dirac delta distributions as trial functions. In a functional frame of classical periodic pseudodifferential equations of nonpositive order, delta-spline and delta–delta methods are introduced and analysed with the overall aim of obtaining asymptotic expansions of the error in weak and strong norms. As a byproduct we obtain the convergence of the coefficients associated to the discrete delta approximation to pointwise values of the unknown, as well as superconvergent choices of positions of the delta distributions in relation with the discretization grid. Two numerical examples are explored to show nodal errors and the applicability of Richardson extrapolation.     

Surface Activation of Pt Nanoparticles Synthesised by “Hot Injection” in the Presence of Oleylamine

Oleylamine (OA) based “hot injection” colloidal synthesis offers a versatile approach to the synthesis of highly monodisperse metallic and multi‐metallic alloyed nanostructures in the absence of potentially toxic and unstable phosphine compounds. For application in heterogeneous catalysis and electrocatalysis, the adsorbed OA species at the metal surfaces should be effectively removed without compromising the structure and composition of the nanostructures. Herein, we investigate the removal of OA from colloidal Pt nanoparticles through 1) “chemical methods” such as washing in acetic acid or ethanol, and ligand exchange with pyridine; and 2) thermal pre‐treatment between 185 and 400 °C in air, H₂ or Ar atmospheres. The electrochemical reactivity of Pt nanoparticles is acutely affected by the presence of surface organic impurities, making this material ideal for monitoring the effectiveness of OA removal. The results showed that thermal treatment in Ar at temperatures above 400 °C provides highly active particles, with reactivity comparable to the benchmark commercial catalyst, Pt/ETEK. The mechanism involved in thermal desorption of OA was also investigated by thermogravimetric analysis coupled to mass spectrometry (TGA‐MS). Oxidation of HCOOH and adsorbed CO in acidic solution were used as test reactions to assess the Pt electrocatalytic activity.     

Propagation of thermal waves in multilayered cylinders using the thermal quadrupole method

In this work the surface temperature oscillation of multilayered cylindrical samples which are uniformly heated by a modulated light beam is calculated using the thermal quadrupole method. This temperature is compared with that calculated in cylinders with continuously varying in-depth thermal conductivity. Following this theoretical approach, photothermal techniques can be used for the quantitative thermophysical characterization of hardened steel wires, tubes and nails.     

Thermal wave scattering by two overlapping and parallel cylinders

In this paper an analytical solution of the temperature of an opaque material containing two overlapping and parallel subsurface cylinders, illuminated by a modulated light beam, is presented. The method is based on the expansion of plane and cylindrical thermal waves in series of Bessel and Hankel functions. This model is addressed to the study of heat propagation in composite materials with interconnection between inclusions, as is the case of inverse opals and fiber reinforced composites. Measurements on calibrated samples using lock-in infrared thermography confirm the validity of the model.