On the concentration and determination of plutonium in natural waters by adsorption on MnO2 filters

A new method of analysis of the efficiency of four filters of MnO₂ in series which takes into account the reactions induced in plutonium by the sorbent is described. The system of differential equations describing the behaviour of plutonium in water as it passes through the filters is solved and the parameters of the filters are determined for a best fitting of the solutions corresponding to the experimental uncertainties. The method is checked by numerical simulation and then applied to water solutions with a known plutonium concentration and to some experimental results given by other authors. In all occassions the results are consistent with the possibility of determining the contents of plutonium in sea and continental waters with uncertainties of the order of 10%.     

Quasi-genericity of bifurcations to high dimensional invariant tori for maps

We consider a family of maps in a Banach spaceE near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle, the other part of the spectrum being strictly inside the unit disc. We focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantT ¹-circles into a family of invariantT ²-tori. We show that this problem needs a 3 dimensional parameter unfolding and that, for the complete maps, bifurcation occurs at points _,, where is the rotation number on the non-normally hyperbolicT ¹-circle, ande ^±2i are the eigenvalues of the constant matrix conjugated to the non-contracting part of the linearization on the normal fiber bundle overT ¹. Making some non-resonance and diophantine assumptions on (, ) leading to a positive measure Cantor set inT ², we show that in paraboloïdal regions of the 3 dim. parameter space we have clean bifurcations as for the truncated normal form. The complement of these regions forms a set of bubbles such as the ones obtained by Chenciner in [Chen] for a codimension 2 problem for maps in ². The main tool here is a generalization for a matrix function onT ¹, close to a constant, of the quasi-conjugacy to a constant, modulo a minimum of additional parameters (moved quasi-conjugacy). For the infinite dimensional case we use aC decoupling result on the angular dependent linear parts into a contraction, still angular dependent, and another part quasi-conjugated to a constant matrix. This type of analysis applies for a wide range of problems, where truncated normal forms of the maps give bifurcations fromT ⁿ toT ⁿ⁺¹ tori, and this needs a (n+1)-dimensional parameter unfolding.We gratefully acknowledge the DRET (contrat 86/1445) who supported one of the authors (J.L.) during this work. This research has been also supported by the E.E.C. contract No. ST 2J-0316-C (EDB) on Mathematical problems in nonlinear Mechanics     

Impedance studies of porous lanthanum-phosphate-bonded nickel electrodes in concentrated sodium hydroxide solution

The hydrogen evolution reaction (HER) was investigated on a lanthanum-phosphate-bonded nickel (LPBN) powder electrode in 30 wt.% NaOH at 70°C using ac impedance and steady-state polarization techniques. Circuits containing one or two constant-phase elements (CPEs) in parallel with a resistance and corresponding to fractal and porous electrode models were tested in order to interpret the ac impedance data. The experimental impedance spectra were well described by the porous electrode model and the circuit containing two CPEs. The results obtained from the ac impedance and steady-state measurements allowed the mechanism and kinetics of the HER to be evaluated. Comparison of these parameters with those obtained on the polycrystalline nickel electrode in 1 M alkaline solution at 25°C indicates that an increase in activity is principally due to an increase in the real surface area.     

Differential double-layer capacitance of a mercury-drop electrode attached to a platinum wire: Frequency dispersion due to the measuring bridge and to the geometry at pendant and sessile electrodes

The frequency dependence of the double-layer capacitance has been studied at the interface Hg/0.116 M KCl in water at ?1.200 V vs. a reversible calomel electrode at 25°C. Two drop electrodes attached to 0.1-mm platinum wire have been used, one sessile with a narrow wedge, the other pendant with a widely open wedge between drop surface and support. The operation of the a.c. resistor-ratio arms bridge has been analysed in a manner generally applicable to series-R, C measurements. On that basis the effect of stray capacitances could be compensated and the frequency dispersion due to the measuring system reduced to a minimum. Both electrodes show a low-frequency dispersion of the measured series capacitance C(ω) and resistance R(ω), ω being the angular frequency. This dispersion has been analysed with a simple R, C network. In series with the bulk resistance R₃ this network has two mutually parallel series R, C's: R₁, C₁ of the drop itself and R₂, C₂ of its edge (neck). From the actual C(ω), R(ω) data follow correct capacitance data C₁, while R₂ and C₂ show a relatively stronger dependence on frequency and kind of electrode (pendant or sessile). Moreover, a sessile electrode exhibits a wedge or shielding effect above a much smaller ω (=ω_h >ω₁, the frequency above which the edge effect becomes insignificant) than a pendant electrode. Conclusions drawn from this information are: in the frequency domain (ω_h?ω₁) diffusive mass transport may be studied without interference from any geometric effect, which is probably also true at small electrolyte concentrations. This study should be performed with a pendant electrode, since it has the largest (ω_h?ω₁) domain.     

Ion pair formation in alkali-SF6 collisions: Dependence on collisional and vibrational energy

The dependence of ion pair formation in collisions of fast alkali atoms (K, Na and Li) with SF₆ on the initial relative kinetic energy and the internal energy of the target molecule has been studied by the crossed molecular beam method. Using a mass spectrometer we have measured total cross sections for negative ion formation as a function of translational and internal energy. Collision energies ranged from threshold up to 35 eV and SF₆ source temperatures were varied from 300 K to 850 K.By means of an inverse Laplace transform of the measured cross sections, we have determined total specific cross sections for each negative ion depending on the SF₆ vibrational energy and at fixed relative kinetic energy.The relative importance of both collisional and internal energy in promoting the electron transfer process is discussed for the various reaction channels in terms of a collision model. An essential feature of this model is the stretching of the S-F molecular ion bond during the collision. The product show complete relaxation in the threshold region, i.e., vibrational and collisional energy are equivalent: This holds for the SF⁻₆ formation only near threshold and for the SF⁻₅ and F⁻ formation up to about 2 eV above threshold. In the post-threshold region the effect of the internal energy on the cross section dominates over that of the translational energy.From these measurements the adiabatic electron affinity of SF₆ is inferred to be 0.32 ± 0.15 eV, T = 0 K. Some other thermodynamic data are deduced: EA(SF₅) > 2.9 ± 0.1 eV (T = 300 K) and D₀(SF⁻₅-F) = 1.0 ± 0.1 eV.     

Spectral coarse graining of complex networks

Reducing the complexity of large systems described as complex networks is key to understanding them and a crucial issue is to know which properties of the initial system are preserved in the reduced one. Here we use random walks to design a coarse graining scheme for complex networks. By construction the coarse graining preserves the slow modes of the walk, while reducing significantly the size and the complexity of the network. In this sense our coarse graining allows us to approximate large networks by smaller ones, keeping most of their relevant spectral properties.     

Excited levels of 233Pa by alpha decay of 237Np

α-spectrometry using Si(Au) detectors has been performed with thin samples of ²³⁷Np; αγ bi-parametric coincidences have permitted an analysis and unfolding of the spectrum and give data about the level scheme. Direct and α-coincident γ-spectra have been measured using Ge(Li) and Si(Li) detectors, obtaining the characteristic electromagnetic transitions in ²³³Pa. Nine new γ-transitions are found, relative to the most recent compilation made by Ellis. In the level scheme, the existence of a level at 306.1 keV is confirmed. A level at 257.1 keV, previously suggested, is evidenced. The level at 300.5 keV is proposed as the $\text{7}\text{2}{}^{\mathrm{?}}$ component of the $\text{5}\text{2}\text{(523)}$ band, hence proposing the 306.1 keV level as the $\text{7}\text{2}{}^{\mathrm{+}}$ term of the $\text{5}\text{2}\text{(642)}$ band.