Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

(Mn1−xPbx)Pb10+ySb12−yS26−yCl4+yO, a new oxy-chloro-sulfide with ∼2 nm-spaced (Mn,Pb)Cl4 single chains within a waffle-type crystal structure

The new oxy-chloro-sulfide (Mn_1−xPb_x)Pb_10+ySb_12−yS_26−yCl_4+yO (x ∈ [0.2-0.3]; y ∈ [0.3-1.6]) was synthesized by dry way at 500-600 °C. A single crystal ∼Mn_0.7Pb_11.0Sb_11.3S_25.3Cl_4.7O indicates a monoclinic symmetry, space group C2/m, with a = 37.480(8), b = 4.1178(8), c = 18.167(4) Å, β = 106.37(3)°, V = 2690.2(9) Å³, Z = 2. Its crystal structure was determined by X-ray single crystal diffraction, with a final R = 5.11%. Modular analysis of the crystal structure reveals a “waffle” architecture, where complex rods with lozenge section delimitate an internal channel filled by a single chain of (Mn_0.7Pb_0.3)Cl₆ octahedra connected by opposite edges. Minimal inter-chain distances are close to 18 Å. The rod wall, two-atom thick, presents, in alternation with S atoms, Pb or (Pb,Sb) cations with prismatic coordination in the internal atom layer, while the external atom layer is constituted exclusively by Sb cations with dissymmetric square pyramidal coordination. A (Pb,Sb)₂S₂ fragment connects two successive rods along (2 0 1) to form a waffle-type palissadic layer. The unique O position, half filled, presents the same environment than the isolated O positions in the oxy-sulfide Pb₁₄Sb₃₀S₅₄O₅, or oxy-chloro-sulfides Pb₁₈Sb₂₀S₄₆Cl₂O and (Cu,Ag)₂Pb₂₁Sb₂₃S₅₅ClO. This compound belongs to a pseudo-homologous series of chalcogenides with waffle structure, ordered according to the size of their lozenge shape channel. Such a complex senary compound of the oxy-chloro-sulfide type illustrates the structural competition between three cations, on one hand, and, on the other hand, three anions. This compound is of special interest regarding the 1D distribution of magnetic Mn²⁺ atoms at the ∼2 nm scale.     

Zeeman transitions in deuterium atoms induced by ultra-relativistic electrons

We present data showing hyperfine transitions in an atomic deuterium beam induced by the (476 MHz) radio-frequency field of a 704 MeV electron beam in a storage ring. A polarized deuterium beam, produced in an atomic beam source, was crossed with a stored electron beam and analyzed with a Breit--Rabi polarimeter. Electron-beam induced transitions were singled out by injecting different combinations of hyperfine states. Transition probabilities as high as 70% were measured at large currents (~ 100 mA). All possible deuterium transitions for a radio-frequency of 476 MHz were observed. In addition, a 1--6 transition resulting from the first harmonic (952 MHz) was observed. The effects of these transitions are of general importance for the polarized internal target technique applied in nuclear and particle physics experiments. The data are reasonably described by numerical estimates. The observed mechanism can be exploited to create nuclear polarized atoms when injecting electron polarized atoms with no net nuclear polarization into a storage cell. However, when nuclear polarized atoms are injected, care should be taken to avoid this mechanism, since it would result in depolarization of the atoms. The studies enabled us to choose the magnetic guide field during our spin-dependent electron--deuteron scattering experiments, such that electron-beam induced depolarizing effects were avoided. This revised version was published online in July 2006 with corrections to the Cover Date.     

New polaron effect in magnetooptic phenomena in a quantum well

It is predicted that resonance coupling between two discrete electron energy levels corresponding to different size-quantization quantum numbers and different Landau quantum numbers can occur in a quantum well in a quantizing magnetic field. The resonance coupling is due to the interaction of an electron with LO phonons and results in the formation of polaron states of a new type. It is shown that for a certain value of the magnetic field, which depends on the splitting of the electron size-quantization levels, the absorption peak and the two-phonon resonance Raman scattering peak split into two components, the separation between which is determined by the electron-phonon coupling constant. The resonance coupling between size-quantization levels with the same Landau quantum numbers is also studied. The splitting of the peaks in this case is virtually independent of the magnetic field and can be observed in much weaker fields. The experimental observation of the effect will make it possible to determine the relative position of the electronic levels and the electron-phonon coupling constant. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 511–515 (10 April 1997)     

Preparing polymer brushes on polytetrafluoroethylene films by free radical polymerization

Films of polytetrafluoroethylene (PTFE) were exposed to sodium naphthalenide (Na/naphtha) etchant so as to defluorinate the surface for obtaining hydroxyl functionality. Surface-initiators were immobilized on the PTFE films by esterification of 4,4′-azobis(4-cyanopentanoic acid) (ACP) and the hydroxyl groups covalently linked to the surface. Grafting of polymer brushes on the PTFE films was carried out by the surface-initiated free radical polymerization. Homopolymers brushes of methyl methacrylate (MMA) were prepared by free radical polymerization from the azo-functionalized PTFE surface. The chemical composition and topography of the graft-functionalized PTFE surfaces were characterized by X-ray photoelectron spectroscopy (XPS), attenuated total reflectance (ATR) FT-IR spectroscopy and atomic force microscopy (AFM). Water contact angles on PTFE films were reduced by surface grafting of MMA.     

Working Methods Paper: Critical considerations with respect to the identification of tin species in the environment

Biogeochemical pathways of tin species in the environment are still controversial, e.g. with regard to methylation and transmethylation phenomena, owing to the fact that the identification of methylated tin-compounds is often difficult. The previous tentative identification of a mixed methylbutyltin compound in sediment and biological samples by GC/AAS after hydride generation gave an illustration of this problem. This compound was previously identified in sediments by other authors and also suspected to occur in a contaminated sediment sample from the Boyardville Marina, France. The retention time obtained by GC/AAS corresponded to the actual retention time of a mixed methylbutyltin calibrant. However, additional checks demonstrated that the compound detected was actually monophenyltin. This evidence was produced by a thorough analysis of a selected sediment sample by alternative techniques such as GC/AAS and GC/AES after pentylation, GC/FPD and GC/MS. The results presented highlight the need for a full identification of compounds to avoid mis-interpretation.     

Sur l'existence des opérateurs d'onde pour l'équation de Wigner dans les espaces L2,pExistence of wave operators for the Wigner equation in L2,p spaces

Basing on the formalism established by Markovich, we show the completeness of wave operators for the Wigner equation in L². In the second part, using estimations proved by Castella and Perthame on the one hand, and the L^p→L^q estimations for the Schrödinger group on the other hand, we prove the existence of the wave operators in L^2,p spaces. To cite this article: H. Emamirad, P. Rogeon, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 811–816.     

Local-moment and itinerant antiferromagnetism in the heavy-fermion system Ce(Cu1−xNix)2Ge2

Elastic and inelastic neutron-scattering studies on the system Ce(Cu_1?xNi_x)₂Ge₂ are reported. These measurements are complemented by measurements of the magnetic susceptibility, high-field magnetization, heat capacity, thermal expansion, electrical resistivity and thermopower. The results reveal an interesting T-x phase diagram consisting of two different antiferromagnetic phases for x < 0.2 and 0.2 < x < 0.75, respectively, and a heavy-Fermi-liquid regime at higher Ni concentrations. The experimental results are interpreted in terms of an alloying-induced transition from local-moment to itinerant heavy-fermion magnetism. Fingerprints of this latter phase are a strongly reduced ordered moment and a short incommensurate ordering wave vector, in accord with theoretical predictions. A surprisingly good agreement between theory and experiment is found for x > 0.5. Further experimental evidence for different types of antiferromagnetic ordering derives from a line-shape analysis of the quasielastic neutron-scattering intensity, from magnetization and thermopower experiments.     

Complex polymer architectures through dimethoxymethyl 1,1‐diphenylethylene derivatives

The reactions of polystyryllithium and potassium on dimethoxymethyl 1,1‐diphenylethylene derivatives were studied in different solvents. In a polar medium, A₃ and A₆ star types were formed according to the stoichiometry, whereas in a nonpolar medium, hyperbranched structures were synthesized. Extensions of an already proposed mechanism in polar and nonpolar media were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3329–3335, 2003