Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

Stereoselectivity in Reactions of Metal Complexes. Part XI. 2,6-Bis(pyrrolidin-2-yl)pyridine: Synthesis and resolution of the meso and the optically active isomers. Complex formation with copper(II) ion in aqueous solution

The new linear triamine 2,6-bis(pyrrolidin-2-yl)pyridine ( II ) has been synthesized, and the (R, S)-, (R, R)-, and (S, S)-isomers have been separated. Compared to other triamines showing a similar structure, these new ligands form very stable Cu²⁺ complexes. No significant difference is observed between the meso and the racemic forms for their binary or ternary mixed-ligand complexes with the amino acids alanine and proline.     

From gas dynamics to pressureless gas dynamics

This paper is devoted to the convergence of solutions of the compressible Euler equations towards solutions of the pressureless gas dynamics system, when the pressure tends to 0. The goal is to prove accurate uniform bounds for particular solutions of the Euler equations.

     

Laser heating and ablation at high repetition rate in thermal confinement regime

Laser heating and ablation of materials with low absorption and thermal conductivity (paint and cement) were under experimental and theoretical investigations. The experiments were made with a high repetition rate Q-switched Nd:YAG laser (10 kHz, 90 ns pulse duration and λ = 532 nm). High repetition rate laser heating resulted in pulse per pulse heat accumulation. A theoretical model of laser heating was developed and demonstrated a good agreement between the experimental temperatures measured with the infrared pyrometer and the calculated ones. With the fixed wavelength and laser pulse duration, the ablation threshold fluence of paint was found to depend on the repetition rate and the number of applied pulses. With a high repetition rate, the threshold fluence decreased significantly when the number of applied pulses was increasing. The experimentally obtained thresholds were well described by the developed theoretical model. Some specific features of paint heating and ablation with high repetition rate lasers are discussed.     

Polarized light and X-ray precession study of the ferroelastic domains of YBa2Cu3O7-δ

The ferroelastic domains of the orthorhombic phase of YBa₂Cu₃O_7- have been observed in polarized light on ceramics and single crystals. By combining polarized light microscopy with the X-ray precession technique, the correlation of the orientation of the orthorhombica- andb-axes with that of thea-b-plane bireflectance, reflection dichroism, transmission dichroism (at a thickness of about 1m), reflection tints generated with compensators and upon uncrossing of polars, as well as the orientation of etch pits has been realized on ferroelastic single domains, bi-domains and more complicated domain patterns. Four ferroelastic orthorhombic domain states have been identified, at variance with former group theoretical considerations, predicting only two states. Ensembles of lamellar domains beyond optical resolution generate strong bireflectance with principal axes rotated by 45° relative to the truea, b-directions.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Direct quantitative determination of surface Brønsted acidity of solids by H/D exchange using D2O

A highly flexible method for direct and quantitative determination of surface Br?nsted acidity of solids in terms of number, type and strength of the acid sites based on quantitative H/D exchange kinetics between the acid solid and gaseous D2O has been developed and applied to materials covering the whole range of acidity.     

Voltammetric sizing of a sphere.

The size of a glass sphere positioned in the center of a microdisk electrode is determined by using a simple electrochemical procedure and is confirmed, additionally, by a microscopical measurement of the sphere at the time of the electrochemical measurement. The cyclic voltammetric response of the naked electrode and of the electrode with the sphere positioned in its center is recorded over a wide range of scan rates (0.002-1.5 V s(-1)). The size of the sphere is then determined by comparison of the experimental voltammogram with simulations for each individual scan rate.