Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Pseudo-symplectic Runge-Kutta methods

Apart from specific methods amenable to specific problems, symplectic Runge-Kutta methods are necessarily implicit. The aim of this paper is to construct explicit Runge-Kutta methods which mimic symplectic ones as far as the linear growth of the global error is concerned. Such method of orderp have to bepseudo-symplectic of pseudosymplecticness order2p, i.e. to preserve the symplectic form to within ⊗(h ^2p )-terms. Pseudo-symplecticness conditions are then derived and the effective construction of methods discussed. Finally, the performances of the new methods are illustrated on several test problems.     

Purification of a 166mHo solution by successive high-performance liquid chromatography and gravitational chromatography for half-life determination

A methodology to purify a ^166mHo solution has been developed by a combination of activity and mass concentration measurements in order to further determine the ^166mHo half-life. The isobaric interference at m/q ? 166 requires Ho purification from non-natural Er with a high purification degree due to the large amount of Ho as opposed to Er. The Ho/Er separation was achieved using high-performance liquid chromatography on a semi-preparative column followed by purification on gravitational chromatography. The efficiency of the separation was evaluated after precise determination of the Er isotopic composition. The purification methodology enabled to separate Ho from Er.     

Two-proton radioactivity of 45Fe

In an experiment at the SISSI-LISE3 facility of GANIL, the decay of the proton drip line nucleus 45Fe has been studied. Fragment-implantation events have been correlated with radioactive decay events in a 16x16 pixel silicon-strip detector. The decay-energy spectrum of 45Fe implants shows a distinct peak at (1.14+/-0.04) MeV with a half-life of T(1/2)=(4.7(+3.4)(-1.4)) ms. None of the events in this peak is in coincidence with beta particles. For a longer correlation interval, daughter decays of the two-proton daughter 43Cr can be observed after 45Fe implantation. The decay energy for 45Fe agrees nicely with several theoretical predictions for two-proton radioactivity.     

A composition law for Runge-Kutta methods applied to index-2 differential-algebraic equations

This paper presents a new composition law for Runge-Kutta methods when applied to index-2 differential-algebraic systems. Applications of this result to the study of the order of composite methods and of symmetric methods are given.     

Molecular dynamic simulation of disorder induced amorphization in pyrochlore

The defect accumulation mechanism of amorphization has been studied for the La2Zr2O7 pyrochlore by means of classical molecular dynamic simulations. Present calculations show that the accumulation of cation Frenkel pairs is the main driving parameter for the amorphization process, while the oxygen atoms simply rearrange around cations. Under Frenkel pair accumulation, the structure follows the pyrochlore-fluorite-amorphous sequence. Present results consequently provide atomic-level interpretation to previous experimental irradiation observations of the two-step phase transition.     

Characterization of an ytterbium-doped double-clad fiber laser passively mode-locked by nonlinear polarization rotation

The properties of an ytterbium-doped double-clad fiber laser, passively mode-locked by nonlinear polarization rotation are investigated in this work. Cartographies of mode-locking regime versus halfwave plates orientations are presented for several values of the total cavity dispersion and for different pump powers. Bistability between the continuous and the mode-locking regimes is pointed out. The effect of the total group velocity dispersion is described with a master mode-locking equation. PACS 42.55.Wd; 42.65.Re     

Comparison of thermal ionization mass spectrometry and Multiple Collector Inductively Coupled Plasma Mass Spectrometry for cesium isotope ratio measurements

In the nuclear domain, precise and accurate isotopic composition determination of elements in spent nuclear fuels is mandatory to validate neutron calculation codes and for nuclear waste disposal. The present study presents the results obtained on Cs isotope ratio by mass spectrometric measurements. Natural cesium is monoisotopic (¹³³Cs) whereas cesium in spent fuels has 4 isotopes (¹³³Cs, ¹³⁴Cs, ¹³⁵Cs, and ¹³⁷Cs). As no standard reference material is available to evaluate the accuracy of Cs isotopic measurements, a comparison of cesium isotopic composition in spent nuclear fuels has been performed between Thermal Ionization Mass Spectrometry (TIMS) and a new method involving Multiple Collector Inductively Coupled Plasma Mass Spectrometry (MC-ICPMS) measurements. For TIMS measurements, isotopic fractionation has been evaluated by studying the behavior of cesium isotope ratios (¹³³Cs/¹³⁷Cs and ¹³⁵Cs/¹³⁷Cs) during the analyses. For MC-ICPMS measurements, the mass bias effects have been corrected with an external mass bias correction using elements (Eu and Sb) close to cesium masses. The results obtained by the two techniques show good agreement: relative difference on ¹³³Cs/¹³⁷Cs and ¹³⁵Cs/¹³⁷Cs ratios for two nuclear samples, analyzed after chemical separation, ranges from 0.2% to 0.5% depending on the choice of reference value for mass bias correction by MC-ICPMS. Finally the quantification of the ¹³⁵Cs/²³⁸U ratio by the isotope dilution technique is presented in the case of a MOx (mixed oxide) spent fuel sample. Evaluation of the global uncertainties shows that this ratio could be defined at an uncertainty of 0.5% (k = 2). The intercomparison between two independent mass spectrometric techniques is fundamental for the evaluation of uncertainty when no isotopic standard is available.