Olivier Vallée

An integral representation for the product of Airy functions

Abstract.An integral representation for the product of Airy functions is given. Particular cases are examined and applications to integrals involving such products are performed.

On the use of linear CCD image sensors in optics experiments

The use of linear CCD (coupled charge devices) photodiode arrays is presented through a quantitative study of Fraunhofer diffraction. Other optics experiments easily realized when using CCD photodiode arrays, i.e., spectroscopy and a mirage effect investigation, are also suggested.

Analytical results and feedback circuit analysis for simple chaotic flows

Simple jerk systems are very useful for combining analytical computations and dynamical analysis in phase space. This is particularly relevant since there is still no direct link between the algebraic structure of ordinary differential equations and the topology of the chaotic attractors which they generate. In this paper, particular analytical solutions are identified for three simple chaotic flows. It is shown that these solutions have varying effects on the bifurcation diagrams. Moreover, a feedback circuit analysis is used to exhibit the similarities between the three simple systems. Such analysis also exhibits the relevant role of double nullcline in the topology of the attractor.

Assessment of the blast wave generated by a low-energy plasma igniter and spectroscopic measurements

Assessment of the output of plasma devices and comparison with thermodynamic calculations makes it possible to improve the efficiency of these devices. The experiment is based on two capacitor banks (1 and 20 kJ) and on a small plasma torch used in electrothermal-chemical (ETC) basic studies. The behavior of a plasma igniter is studied using spectroscopic measurements to obtain the electronic density from H/sub /spl alpha// line Stark width. The temperature is obtained from Boltzmann plots on copper and iron atomic lines. Under the local thermodynamic equilibrium assumption, the electron density (N/sub e/) depends on the electron temperature (T/sub e/) via Sahas law (N/sub e//spl prop/T/sub e//sup 3/4/). A check on this behavior permits validation of the thermodynamic equilibrium assumption, and the pressure of the emitting area is obtained by using Daltons law. The flight time and the overpressure generated by the plasma igniter can be compared at the Sedov-Taylor blast wave theory. Finally, we give a comparison of the pressure of the emitting area found using Daltons law and also by applying the Sedov-Taylor blast wave model.

TRANSITION FROM THE SEDOV–TAYLOR BLAST WAVE SOLUTION UP TO THE SOUND WAVE

In the case of a spherical blast wave described by the Sedov–Taylor model in an ideal gas, we apply the Vashy–Buckingham theorem (Pi theorem) to take into account the pressure of the medium at rest, and consequently the internal energy of the gas at rest. We obtain a single formula which contains the full time behavior of the explosion from the very beginning (Sedov–Taylor solution) up to the sound wave, therefore describing analytically the transition phase from t = 0 until t → ∞.

Computation of the Whittaker functions W k,m (Z) with series expansions and Pade´ approximants

Different mathematical representations of the Whittaker functions W k,μ(z) are investigated, allowing to compute them numerically with high precision for various values of the argument z and of the parameters k and μ. Application of Pade Approximants with Wynn’s algorithm on an asymptotic series expansion appears to be a powerful numerical method.

A MODEL FOR COAXIAL ABLATION BY PLASMA AT THE HEAT FLUX THRESHOLD

The purpose of this paper is to present a model for ablation due to a plasma flash in cylindrical symmetry. The model of ablation speed of the coaxial material is based on the integral method of the heat equation which basically involves the idea of a thermal layer. It is first shown that an important step in the process is the heating of the material. When the material comes up to melt, it is found that the mass ablated by the plasma flux appears only beyond a threshold.

A quantum method for the inversion of bound - free Franck - Condon factors

An exact quantum method is introduced for the inversion of the bound - free continuum spectrum originating in a single discrete vibrational level. It allows one to obtain an unknown bound-state potential and the transition operator from two observed continuum spectra originating on different vibrational levels of that state and a knowledge of the repulsive final-state potential. This procedure is tested numerically with a couple of well known potentials: an exponential and a Morse potential. A comparison of the exact and the reconstructed potentials is discussed in order to illustrate the numerical limitations of this method.

Anomalous Ar I 430.01 nm line profile distortion in an arc plasma

Abstract A strong asymmetry of the Ar I 430.01 nm line profile is investigated for high electron densities (Ne > 1017 cm-3) in an arc plasma operating in pure argon. This asymmetry may be explained by considering the presence of the forbidden 429.9 nm line of Ar I.

A visual thermodynamical effect

This paper deals with a simple experiment carried out with a pressurized can containing a foam (a can of shaving foam, for example) that readily demonstrates the concepts of both adiabatic and isobaric thermodynamic processes.