Soft X-ray spectromicroscopy of phase-change microcapsules

A synchrotron-based scanning transmission X-ray microscope (STXM) is used to investigate Micronal^® phase-change microcapsules. Prolonged X-ray illumination of the specimen leads to the breaking of the microcapsules’ protective polymer shell and a partial separation of the core–shell species occurs. The paraffin wax and acrylic polymer components are characterized by carbon K-edge near X-ray edge absorption fine structure (NEXAFS) spectroscopy and components distribution mapping of the beam-damaged specimen is performed.     

properties for Gaussian random series

Let be an arbitrary sequence of and let be a random series of the type

where is a sequence of independent Gaussian random variables and an orthonormal basis of (the finite measure space being arbitrary). By using the equivalence of Gaussian moments and an integrability theorem due to Fernique, we show that a necessary and sufficient condition for to belong to , for any almost surely is that . One of the main motivations behind this result is the construction of a nontrivial Gibbs measure invariant under the flow of the cubic defocusing nonlinear Schrödinger equation posed on the open unit disc of .

     

Quantitative analysis of scanning transmission X-ray microscopy images of gas-filled PVA-based microballoons

We report on the quantitative analysis of scanning transmission X-ray microscopy (STXM) images of gas-filled, poly(vinyl alcohol) (PVA)-based microballoons (MB) in a water environment. A model for the transmitted intensity is proposed on the basis of a perfect spherical shell stabilizing the microballoon. An extension of this model to take into account the deformation of the MBs is also presented. Taking into consideration a density gradient of the shell and the STXM resolution, we were able to explain very precisely two types of experimental STXM profiles observed on gas-filled MBs. This enables the detailed characterization of MB properties such as radius and wall thickness and the determination of their wall density with unprecedented high resolution.     

Photoinduced radical reactions of α-alkylated ethyl 2-oxo-1-cyclopentanecarboxylate derivatives: α-cleavage and cyclization to the skeleton of linear cyclohexano diquinanes

The tricyclic core of linear cyclohexano diquinanes was synthesized using photoinduced electron transfer (PET) as a key step. The reaction proceeded in high regioselective manner via ketyl radical anions leading to distonic δ-keto radical anion as reactive intermediates. The irradiation was carried out at a wavelength of 254 nm with triethylamine (TEA) as a strong reducing reagent in acetonitrile. We also showed that the photolysis of the α-alkylated 2-oxocyclopentanecarboxylate derivatives does not lead to any cyclization products via a δ-hydrogen abstraction process. In this case α-C-C bond cleavage as a predominant process was observed.     

Surface chemistry of ultrathin films of histidine on gold as probed by high-resolution synchrotron photoemission

Procedures for the vacuum deposition of thin histidine films on polycrystalline Au(111) and their characterization with high-resolution synchrotron-radiation-based photoelectron spectroscopy are reported. The chemical form of histidine (anionic vs zwitterionic) and the nature of its interactions with the substrate (strong ionic-covalent vs weak van der Waals bonding) in mono- and multilayer films are analyzed. It is shown that water adsorption on a pre-prepared histidine film at 100 K results in protonation of histidine molecules and partial formation of hydroxyl anions. These chemical effects are carefully differentiated from spectral changes associated with radiation damage of the histidine films.     

Reactivity of V2O3(0001) surfaces: molecular vs dissociative adsorption of water

The adsorption of water on V2O3(0001) surfaces has been investigated by thermal desorption spectroscopy, high-resolution electron energy loss spectroscopy, and X-ray photoelectron spectroscopy with use of synchrotron radiation. The V2O3(0001) surfaces have been generated in epitaxial thin film form on a Rh(111) substrate with three different surface terminations according to the particular preparation conditions. The stable surface in thermodynamic equilibrium with the bulk is formed by a vanadyl (VO) (1x1) surface layer, but an oxygen-rich (radical3xradical3)R30 degrees reconstruction can be prepared under a higher chemical potential of oxygen (microO), whereas a V-terminated surface consisting of a vanadium surface layer requires a low microO, which can be achieved experimentally by the deposition of V atoms onto the (1x1) VO surface. The latter two surfaces have been used to model, in a controlled way, oxygen and vanadium containing defect centres on V2O3. On the (1x1) V=O and (radical3xradical3)R30 degrees surfaces, which expose only oxygen surface sites, the experimental results indicate consistently that the molecular adsorption of water provides the predominant adsorption channel. In contrast, on the V-terminated (1/radical3x1/radical3)R30 degrees surface the dissociation of water and the formation of surface hydroxyl species at 100 K is readily observed. Besides the dissociative adsorption a molecular adsorption channel exists also on the V-terminated V2O3(0001) surface, so that the water monolayer consists of both OH and molecular H2O species. The V surface layer on V2O3 is very reactive and is reoxidised by adsorbed water at 250 K, yielding surface vanadyl species. The results of this study indicate that V surface centres are necessary for the dissociation of water on V2O3 surfaces.     

The effect of the electric field on the kinetics of dichlorosilane oxidation in the absence of discharge

A constant electric field incapable of discharge generation affects the kinetics of the ignition and combustion of dichlorosilane-oxygen mixtures: near the lower self-ignition limit, the induction period decreases and the region of the oscillating combustion regimes is enlarged. These phenomena depend on the material and state of the reactor surface. The lower self-ignition limitP ₁ over the CuSO₄ and ZnSO⁴ surfaces abruptly increases with an increase in the voltage of the constant electric field.     

Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin–Ono equation, posed on the circle, on the first N, N ≥ 1 modes in the trigonometric bases.     

Multilinear estimates for the Laplace spectral projectors on compact manifolds

The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension 2. We also give some related trilinear estimates. To cite this article: N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Ill-posedness of nonlocal Burgers equations

Nonlocal generalizations of Burgers equation were derived in earlier work by Hunter [J.K. Hunter, Nonlinear surface waves, in: Current Progress in Hyberbolic Systems: Riemann Problems and Computations, Brunswick, ME, 1988, in: Contemp. Math., vol. 100, Amer. Math. Soc., 1989, pp. 185–202], and more recently by Benzoni-Gavage and Rosini [S. Benzoni-Gavage, M. Rosini, Weakly nonlinear surface waves and subsonic phase boundaries, Comput. Math. Appl. 57 (3–4) (2009) 1463–1484], as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage [S. Benzoni-Gavage, Local well-posedness of nonlocal Burgers equations, Differential Integral Equations 22 (3–4) (2009) 303–320] under an appropriate stability condition originally pointed out by Hunter. In this article, it is shown that the latter condition is not only sufficient for well-posedness in Sobolev spaces but also necessary. The main point of the analysis is to show that when the stability condition is violated, nonlocal Burgers equations reduce to second order elliptic PDEs. The resulting ill-posedness result encompasses various cases previously studied in the literature.