Theory of vibronic interactions in D2 and H2: a comparison between multichannel-quantum-defect and coupled-equation approaches

New experimental energy levels for the 2pπC(1)Π(u)(-) state of D(2) are reported extending up to the dissociation limit and including rotational quantum numbers up to N = 10. These data are extracted from recent high resolution optical emission spectra, and they are used for a detailed comparison of two theoretical approaches, both of which are fully ab initio and are based on the same state-of-the-art clamped-nuclei potential energy curves. These are the coupled differential equations (CE) and the multichannel quantum defect theory (MQDT) approaches, each of which accounts for adiabatic corrections and non-adiabatic couplings. Both theoretical approaches reproduce the experimental levels to within a fraction of a wavenumber unit (cm(-1)) for the lower vibrational quantum numbers, with the MQDT surpassing the CE method. As the dissociation limit is approached, the residuals observed-calculated increase up to several cm(-1) and the MQDT method is up to a factor of two less accurate than the CE method. The same analysis is carried out with existing data for the H(2) isotopomer and yields similar results. An analogous comparison is also made for the 3pπD(1)Π(u)(-) and 4pπD('1)Π(u)(-) states for both isotopomers, where the MQDT is found to be superior to the CE approach.     

Molecular dynamics comparative study of methane–nitrogen and methane–nitrogen–ethane systems

This work concerns the site–site interaction study of 256 particles using the Buckingham potential model. We have calculated the new parameters of the Buckingham potential using an iterative algorithm with a mean square method. This adapted model allows determining the characteristics for each state point. We have applied this model to study the liquefied natural gas LNG properties for methane-nitrogen and methane–nitrogen–ethane mixtures by molecular dynamics. We have calculated the thermodynamic, dynamic and structural properties for both the microcanonical NVT and the isothermal-isobaric NPT ensembles of binary and ternary systems from the SP₁ to SP₉ points. Then, we have compared the results between binary and ternary systems. We have obtained a good prediction on transport properties. From the calculated values of self-diffusion coefficient and viscosity, we have confirmed the liquid state of the liquefied natural gas LNG system.     

A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ω^ε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.     

Study of various parameters influencing the fixation of metallic ions Cu2+, Zn2+, and Ni2+ at the catalytic Amberlyst-15 resin in the presence of alcohols

The ionic exchange behavior of Zn²⁺, Ni²⁺, and Cu²⁺ metallic ions on Amberlyst-15 commercial resin was studied as a function of resin solution contact time, initial concentration of metallic ions, nature of the solvent, and the amount of resin. The metallic ions were studied in ternary mixtures using both column and batch experiments. In addition, water, methanol, ethanol, and propan-2-ol were used as solvents for dissolving metallic ions. It was found that the resin behavior depends on the solvent nature and the metallic ion concentration. The analysis of solutions by atomic absorption spectrometry revealed that the affinity of the resin for the studied metallic ions followed the sequence Cu²⁺ > Ni²⁺ > Zn²⁺ in the case of an aqueous medium. Furthermore, uptake increased with increasing amount of resin. A better uptake was observed in the case of the 75:25 % water/methanol compositions when the column technique was used. For the batch technique, we noted a better uptake using 100 % water. The uptake rate decreased with an increase in the number of carbons for the 50 % water–50 % alcohol solvents. The acid–base properties of Amberlyst-15 commercial resin were studied by 2-propanol decomposition test. Propene and acetone are the main expected products and it is believed that they are formed through dehydration or dehydrogenation reaction on acid and base sites, respectively.     

About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half‐space, of which the cross‐section is a local perturbation of a homogeneous half‐plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S‐waves. Thanks to the boundary of the deformed half‐plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright © 2002 John Wiley & Sons, Ltd.     

Hermitean Matrix Ensembles and Orthogonal Polynomials

In this article, we investigate orthogonal polynomials associated with complex Hermitean matrix ensembles using the combination of the methods of Coulomb fluid (or potential theory), chain sequences, and Birkhoff–Trjitzinsky theory. We give a general formula for the largest eigenvalue of the N×N Jacobi matrices (which is equivalent to estimating the largest zero of a sequence of orthogonal polynomials) and the two-level correlation function for the α ensembles (α>0) introduced previously for α>1. In the case of 0<α<1, we give a natural representation for the weight function that is a special case of the general Nevanlinna parametrization. We also discuss Hermitean matrix ensembles associated with general indeterminate moment problems.     

Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations

In this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.     

Ramanujan continued fractions via orthogonal polynomials

Some Ramanujan continued fractions are evaluated using asymptotics of polynomials orthogonal with respect to measures with absolutely continuous components.     

Condensations aryniques d'enolates de cetones—VI: Synthese de phenyl-2 cyclohexanones tricyclo[6,n,0,02,7]trienes-2,4,6 ols-1 diversement substitues

The condensation of benzyne in aprotic medium with the enolates of the 2,2,6-trimethyl, 3,3,5,5-tetramethyl, 4-4-dimethyl, 4-methyl, 4-t-butyl cyclohexanones as well as with those of α-tetralone and α-benzosuberone leads to the corresponding α-phenyl ketones and several tri and tetracyclic benzocyclobutenols.