Synthesis and photoinitiated radical cyclization of allyl- and propynyloxymethyl substituted cyclopentanones to tetrahydrocyclopenta[c]furanols

Bicyclic cyclopentafuranols were formed by photoinitiated radical cyclization of allyl- and propinyloxymethyl substituted cyclopentanones with high regioselectivity. The irradiations were carried out at a wavelength of 300 nm in aprotic solvents such as benzene and acetonitrile. We could also show that reductive photoinduced electron transfer (PET) of the propynyloxymethyl substituted cyclopentanone 5 does not lead to any cyclization. The starting materials were synthesized in good yields following known procedures.     

Glycine-ice nanolayers: morphology and surface energetics

Ultrathin glycine-ice films (nanolayers) have been prepared in ultrahigh vacuum by condensation of H(2)O and glycine at 110 K and 150 K on single crystalline Al(2)O(3) surfaces and have been investigated by temperature programed thermal desorption, x-ray photoelectron spectroscopy, and work function measurements. Various layer architectures have been considered, including glycine-on-ice, ice-on-glycine, and mixed glycine-ice nanolayers. Low coverages of adsorbed glycine molecules on amorphous ice surfaces suppress the amorphous-to-crystalline phase transition in the temperature range 140-160 K in near-surface regions and consequently lead to a lower desorption temperature of H(2)O molecules than from pure ice layers. Thicker glycine overlayers on ice provide a kinetic restriction to H(2)O desorption from the underlying ice layers until the glycine molecules become mobile and develop pathways for water desorption at higher temperature (>170 K). Ice overlayers do not wet glycine film surfaces, but the glycine molecules on ice are sufficiently immobile at 110 K, so that continuous glycine overlayers form. In mixed glycine-ice nanolayers the glycine phase displays hydrophobic behavior and a phase separation takes place, with the accumulation of glycine near the surfaces of the films.     

On the Propagation of Weakly Nonlinear Random Dispersive Waves

We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast physics literature on related topics, we then study how much the Fourier modes of the solution at later times remain decorrelated. Our results are sensitive to the resonances associated with the dispersive relation and to the particular choice of the initial data.     

Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊³ × 𝕊³.     

Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).     

Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

We present a general result of transverse nonlinear instability of 1d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1-d model and the transverse perturbation “have the same sign”. Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Boussinesq system and the Zakharov–Kuznetsov equation and we hope that it may be useful in other contexts.     

In Situ Synchrotron Radiation X‐Ray Microspectroscopy of Polymer Microcontainers

Direct, real‐time analytical techniques that provide high‐resolution information on the chemical composition and submicrometer structure of various polymer micro‐ and nanoparticles are in high demand in a range of life science disciplines. Synchrotron‐based scanning transmission X‐ray microspectroscopy (STXM) combines both local‐spot chemical information (assessed via near‐edge X‐ray absorption fine structure spectroscopy) and imaging with resolution of several tens of nanometers, and thus can yield new insights into the nanoscale properties of these materials. Furthermore, this method allows in situ examination of soft‐matter samples in aqueous/gaseous environments and under external stimuli, such as temperature, pressure, ultrasound, and light irradiation. This Minireview highlights some recent progress in the application of the STXM technique to study the temperature‐dependent behavior of polymer core–shell microcapsules and to characterize the physicochemical properties of the supporting shells of gas‐filled microbubbles in their natural hydrated state.     

Bilinear eigenfunction estimates and the nonlinear Schr?dinger equation on surfaces

We study the cubic non linear Schrödinger equation (NLS) on compact surfaces. On the sphere and more generally on Zoll surfaces, we prove that, for s>1/4, NLS is uniformly well-posed in H^s, which is sharp on the sphere. The main ingredient in our proof is a sharp bilinear estimate for Laplace spectral projectors on compact surfaces.

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Résumé On étudie léquation de Schrödinger non linéaire (NLS) sur une surface compacte. Sur la sphère et plus généralement sur toute surface de Zoll, on démontre que pour s>1/4, NLS est uniformément bien posée dans H^s, ce qui est optimal sur la sphère. Le principal ingrédient de notre démonstration est une estimation bilinéaire pour les projecteurs spectraux du laplacien sur une surface compacte.

     

Helical cyclogenesis

The model for the formation of basic structures in the atmosphere, such as cloud clusters and hurricane type phenomena, is formulated on the basis of the inverse cascade in three-dimensional turbulence.