Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates

We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.     

A hybrid method for hydrodynamic-kinetic flow Part I: A particle-grid method for reducing stochastic noise in kinetic regimes

In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime.     

A novel use of Ti‐POSS as initiator of L‐lactide ring‐opening polymerization

The efficacy of a metal‐silsesquioxane, namely, heptaisobutyl (isopropoxyde)titanium‐polyhedral oligomeric silsesquioxanes (Ti‐POSS), as initiator of the ring‐opening polymerization of L ‐lactide (LLA) has been assessed. Indeed, as demonstrated by proton nuclear magnetic resonance (¹H NMR) spectroscopy and gel permeation chromatography (GPC) measurements, a well‐controlled polymerization occurs via a coordination‐insertion mechanism. Moreover, the above reaction leads to the direct insertion of the silsesquioxane molecule into the polymer backbone, thus producing a hybrid system. Differential scanning calorimetry measurements demonstrated that in comparison with a commercial poly‐L ‐lactide (PLLA), the polymers prepared with Ti‐POSS exhibit a higher crystallinity. Indeed, the presence of silsesquioxane molecules, attached to one end of the polymer chains, has been found to appreciably affect the crystal nucleation density. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Incorporation of Ce3+ in crystalline Gd-silicate nanoclusters formed in silica

Structural and optical properties of sol–gel silica based glassceramics doped with 0.1 mol% Ce and codoped with Gd at high concentrations, from 5 mol% up to 40 mol%, are investigated and compared to those of analogous samples doped only with Ce. Raman scattering, transmission electron microscopy, and x-ray diffraction reveal the formation of Gd apatite-like silicate (Gd_4.67O(SiO₄)₃) and of Gd pyrosilicate (Gd₂Si₂O₇) nanophases whose morphology and crystallinity depend on the Gd concentration and thermal treatments. Optical absorption measurements demonstrate the role of the densification atmosphere in modifying the charge state of Ce ions. The incorporation of Ce³⁺ ions in the nanophases is put in evidence by photo- and radio-luminescence results.     

Pd(II) complexes of monodentate deoxycholic acid derived binaphthyl diamido phosphites as chiral catalysts in the asymmetric Suzuki-Miyaura cross-coupling

Chiral binaphthyl diamidophosphites derived from deoxycholic acid were synthesized and used as ligands for the preparation of mononuclear Pd(II) complexes, which were employed as catalysts in the asymmetric Suzuki-Miyaura cross-coupling of arylboronic acids with aryl bromides. Among the different reaction parameters, the substrate concentration emerged as being crucial for the outcome of the reaction: the reaction was faster in a concentrated reaction mixture, and could be performed at 0 °C, where the reaction promoted by the Pd-complexes was more enantioselective affording cross-coupling products with ee up to 70%.     

Corrigendum to “A Morse–Smale index theorem for indefinite elliptic systems and bifurcation” [J. Differential Equations 258 (5) (2015) 1715–1748]

We discussed in a previous paper elliptic systems of partial differential equations on star-shaped domains and introduced the notions of conjugate radius and bifurcation radius. We proved that every bifurcation radius is a conjugate radius, and believed to have shown by an example that on the other hand not every conjugate radius is a bifurcation radius. This note reveals that our previous example was wrong, but it also introduces an improved example that shows the assertion that we claimed before.     

Enantioselective Aza‐Michael Addition of Imides by Using an Integrated Strategy Involving the Synthesis of a Family of Multifunctional Catalysts,Usage of Multiple Catalysis,and Rational Design of Experiment

A challenging asymmetric reaction (aza‐Michael addition of imides to enones) has been optimized through an integrated approach involving the synthesis of a family of organocatalysts, multiple catalysis (usage of additives), and finally with rational exploration of the chemical space by the application of the experiment design.