On the Second Law of Thermodynamics and the Piston Problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio m/M is a very small parameter, where m is the mass of one particle of the gaz and M is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Une axiomatisation de la substitution

We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Identification of new catalysts for the asymmetric reduction of imines into chiral amines with polymethylhydrosiloxane using high-throughput screening

The use of high-throughput techniques allowed the rapid identification of new catalysts for the enantioselective reduction of imines using polymethylhydrosiloxane (PMHS) as a reducing agent. By a simple modification of the chiral ligand structure that came out of the screening, the enantioselectivity of the reduction was increased from 40% ee to 60% ee.     

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003     

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO₂/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO₂ is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices.     

Numerical solution of the Monge–Ampère equation by a Newton's algorithm

We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations. To cite this article: G. Loeper, F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.