Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.     

Investigation towards an efficient synthesis of benzo[g]isoquinoline-1,5,10(2H)-triones

As part of our research on 2-aza analogues of pentalongin, the active principle of Pentas longiflora Oliv., the first synthesis of 2,3-disubstituted benzo[g]isoquinoline-1,5,10(2H)-triones via 3,4-disubstituted 6-hydroxybenzo[g]furo[4,3,2-de]isoquinoline-2,5(4H)-diones as the key intermediates is reported. The latter compounds have been prepared by treating 2-methoxycarbonyl-1,4-naphthoquinone with N-substituted enaminoesters under acidic conditions. These reagents are easily accessible from readily available 1,4-dihydroxy-2-naphthoic acid, β-ketoesters and primary amines. Finally, a short synthesis of substituted benzo[g]isoquinoline-1,5,10(2H)-triones is achieved by an oxidative addition of N-substituted enaminoesters onto methyl 1,4-dihydroxynaphthalene-2-carboxylate.     

Development of SPME on-fiber derivatization for the sampling of formaldehyde and other carbonyl compounds in indoor air

Solid-phase microextraction on-fiber derivatization applied to carbonyl compounds is known, but application to indoor air is poorly developed and the methods deserve to be complemented and optimized. In this work, two derivatization reagents, pentafluorophenylhydrazine and o-2,3,4,5,6-(pentaflurobenzyl)hydroxylamine (PFBHA), and three fiber coatings were tested in order to select the best combination. As Carboxen-based coatings were proven to induce the formation of by-products during the thermal desorption step, a polydimethylsiloxane–divinylbenzene fiber in association with PFBHA was finally chosen. The study of the derivatization kinetics showed that the reaction of PFBHA with carbonyl compounds was instantaneous, except for acetone. Analyses were performed by gas chromatography coupled with flame ionization detection and mass spectrometry. For 5 min fiber exposure, the limits of detection are below 0.5 μg m^-3 in selected ion monitoring mode, the reproducibility was 15 % on average, and the linearity of the calibration curves was satisfactory. For on-site application, the influence of air humidity and the conditions in which the impregnated fibers were stored were studied. It is possible to store the fibers for 3 days before and for at least 2 days after sampling. The relative humidity of air was shown to have no influence on solid-phase microextraction sampling in the range from 0 to 70 %. For formaldehyde, the method was compared with sampling on 2,4-dinitrophenylhydrazine cartridges, and the first results showed good agreement. Finally, the method was applied to three different indoor environments to check its feasibility.     

New and highly efficient synthesis of 3-substituted 1-hydroxybenz[g]isoquinoline-5,10-diones

A new and efficient strategy for the synthesis of 3-substituted 1-hydroxybenz[g]isoquinoline-5,10-diones by reaction of 2-methoxycarbonyl-1,4-naphthoquinone with different pyridinium salts under Kröhnke conditions is disclosed. This one-step reaction was found to be dependent on the substitution pattern of the aromatic nucleus in the pyridinium salts.     

Characterization of the mesostructure of HDPE under “in situ” uniaxial tensile test by incoherent polarized steady‐light transport

This study presents quantitative results related to in situ investigation of the microstructural evolutions of high‐density polyethylene with deformation. These results were obtained thanks to a novel technique (IPSLT) based on the polarized light scattering transport phenomenon. The heterogeneities produced during whitening of the polymer bulk are characterized at the mesoscale level (from hundred of nanometers to a few micrometers). The technique is described as well as the identified parameters it provides, namely: the average size of the scatterers, the anisotropy developed in the medium, and the light transport length, representative of both the volume fraction and size of the heterogeneities. Results obtained during video‐controlled tensile experiments confirm those obtained previously with X‐ray microtomography. They put forward the role of morphological transformations of the amorphous/crystalline phases (especially regarding the creation of fibrillar assemblies) rather than the cavitation phenomenon. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Irreducible Representations of the Quantum Weyl Algebra at Roots of Unity Given by Matrices

To describe the representation theory of the quantum Weyl algebra at an lth primitive root γ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation yx ? γxy = 1, assuming yx ≠ xy. In this note, we complete their result by finding and classifying, up to equivalence, all irreducible matrix solutions (X, Y), where X is singular.     

High oxygen pressures and the stabilization of six-coordinated Ir(VI) in an oxygen lattice

Abstract

During these last twenty five years a great efforts have been made in the Laboratoire de Chimie du Solide du CNRS in order to develop high oxygen pressure for the stabilization of unusual oxidation state of transition elements.

The aims of such research works was to correlate the increase of the Mⁿ⁺-O bond covalency versus the increase of the oxidation state n+ to the physicochemical properties of resulting oxides [1].

Iridium was an interesting element due to its position (5d) in the Periodic Table. In 1980 Ir(V) (d⁴) was stabilized in La₂LiIrO₆ in the perovskite structure [2]. Such a study had underlined the strong value of the spin-orbit coupling associated to Ir(V) [3].

The stabilization of Ir(VI) is interesting from two points of view : (i) its isotropic electronic configuration (d³), (ii) such a high oxidation state could lead to the strongest M-O bond in an oxygen lattice.

Selecting, through a specific methodology, the most appropriate local structural and chemical factors and with the help of high oxygen pressure, Ir(V1) was stabilized in the perovskite Ba₂CaIrO₆. Structural, magnetic and Mössbauer studies have been carried out in order to characterize the physicochemical properties induced by this unusual oxidation state.     

Electron-beam poling in undoped, N- or Ge-doped MDECR H:SiO2 films

Amorphous N- or Ge-doped H:SiO₂ films deposited on silica by the matrix distributed electron cyclotron resonance-PECVD method were irradiated by an electron-beam with different doses in order to pole the material and induce second harmonic generation (SHG). SHG was measured using the Maker-fringe method. When irradiated at an acceleration voltage of 25 kV, an incident current of 5 nA during 480 s, the N-doped H:SiO₂ films exhibited a maximum second harmonic signal in the order of 0.003 pm/V, but when irradiated with an acceleration voltage of 30 kV, at 5 nA during 240 s, the films exhibited a maximum second harmonic signal of 0.006 pm/V. With a smaller current of 0.5 nA during 25 s and 25 kV acceleration voltage, the Ge-doped H:SiO₂ films (3.8 at. % Ge) showed a maximum second-order nonlinearity of 0.0005 pm/V. But an H:SiO₂ films with a smaller Ge content (1.0 at. % Ge), showed a large SHG: d₃₃=0.09 pm/V when irradiated at 25 kV, 0.5 nA during 15 s. PACS 78.66.J; 42.65.K; 68.60.D