An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

Semiclassical Orthogonal Polynomials, Matrix Models and Isomonodromic Tau Functions

The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-2 rational covariant derivative operators. The corresponding matrix models, consisting of unitarily diagonalizable matrices with spectra supported on these contours are analyzed, and it is shown that all coefficients of the associated spectral curves are given by logarithmic derivatives of the partition function or, more generally, the gap probabilities. The associated isomonodromic tau functions are shown to coincide, within an explicitly computed factor, with these partition functions. Research supported in part by the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR du Québec and EC ITH Network HPRN-CT-1999-000161.     

Cusp catastrophe in slowly varying equilibriums

Solutions of the equations v _x+v ³?tv+x=0 and v _xx=v ³? tv+x, which describe the nucleation of domain walls occurring in the neighborhood of cusps of slowly varying equilibriums, are analyzed. Examples related to the diffusion in smoothly inhomogeneous media are considered.     

Multiplicité des solutions d'équilibre d'une coque de Marguerre–von Kármán membranaireMultiplicity of solutions to the Marguerre–von Kármán membrane equations

We build explicitly an infinite number of equilibrium solutions of unloaded Marguerre–von Kármán membrane shells. This construction is based upon the existence of three elementary solutions, together with the solution of a Monge–Ampère equation associated with a partition of the reference configuration of the shell. To cite this article: A. Léger, B. Miara, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 649–654.     

Characterization of phospho-olivines as materials for Li-ion cell cathodes

Solid State Reaction was employed to prepare phospho-olivines LiMPO₄ (where M=Fe, Co) as pure phase and LiNiPO₄ in presence of foreign phases, as cathodic materials for lithiumions batteries. The relationship between structural, morphological and electrochemical properties were investigated in the case of LiFePO₄. Structural investigation has been carried out by means of X-ray powder diffraction (XRPD) and Rietveld refinement. The influence on the morphology of annealing temperature, different flowing gas mixture and addition of ascorbic acid during the synthesis, has been analysed via scanning electron microscopy. The electrochemical cycling performances on LiFePO₄ showed to be positively affected by the modifications of the experimental conditions. Cyclic voltammetry showed a good reversibility during insertion-extraction mechanism, in particular in presence of additives. LiCoPO₄ and LiNiPO₄ are interesting as high voltage cathode materials for Li-ion batteries and have been taken into account, but their electrochemical operating conditions are still to be optimised. In the case of LiNiPO₄ it is very difficult to obtain, by solid state synthesis, suitable purity powders, having a grain size small enough to exploit it usefully as cathodic material for Li-ion cells. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16 – 22, 2000.     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

Change in the energy of a charged particle moving in the field of a slow electromagnetic wave

A differential equation is obtained that describes the change in the energy of a charged particle in the field of a slow wave (with phase velocity not equal to unity) as a function of the distance traversed. Analysis of this equation yields the amplitude and period of the change in the particle's energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 97–102, February, 1981.