The Slow Erosion Limit in a Model of Granular Flow

We study a 2 × 2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill. The original model was proposed by Hadeler and Kuttler (Granul Matter 2:9–18, 1999). The Cauchy problem for this system has been studied by the authors in recent papers (Amadori and Shen in Commun Partial Differ Equ 34:1003–1040, 2009; Shen in J Math Anal Appl 339:828–838, 2008). In this paper, we first consider an initial-boundary value problem. The boundary condition is given by the flow of the incoming material. For this problem we prove the global existence of BV solutions for a suitable class of data, with bounded but possibly large total variations. We then study the “slow erosion (or deposition) limit”. We show that, if the thickness of the moving layer remains small, then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill, not on the time-law describing the rate at which the material slides down. More precisely, in the limit as the thickness of the moving layer tends to zero, the slope of the mountain is provided by an entropy solution to a scalar integro-differential conservation law.     

Organo-Polyoxometalate-Based Hydrogen-Bond Catalysis

Several urea-inserted organo-polyoxometalates (POMs) derived from polyoxotungstovanadate [P₂V₃W₁₅O₆₁]⁹⁻ were prepared. The insertion of the carbonyl into the polyoxometallic framework activates the urea toward Hydrogen-bond catalysis. This was shown on the Friedel-Crafts arylation of trans-β-nitrostyrene. Modelling shows that the most stable form of the organo-POMs features a cis-trans arrangement of the two N−H bonds, but that the likely catalytically active trans-trans form is accessible at room temperature. Finally, it is possible that the oxo substituents next to the vanadium atoms may help the approach of the nucleophile via H-bonding.     

The synthesis and application of polyamino polycarboxylic bifunctional chelating agents

Bifunctional chelating agents (BFCAs) are molecules which contain two different moieties: a strong metal chelating unit and a reactive functional group. The latter is directed to react with amines, thiols, alcohols or other reactive molecules to form stable covalent bonds while the chelating moiety is able to strongly coordinate a metal ion. In this way, it is possible to label a molecule of interest (e.g. an antibody or a peptide) with a metal or a radioactive metal ion. Of all the ligands reported so far, those based on a polyamino polycarboxylic structure are most efficient and are widely employed for the chelation of metal ions. The resulting metal complexes have found a broad range of applications in chemistry, biology and medicine. Diagnostic imaging (MRI, SPECT, PET), molecular imaging, tumour therapy and luminescent materials are only a few examples. The present critical review gives an overview of the syntheses and most important applications of polyamino polycarboxylic BFCAs (334 references).     

White CsPbBr3: Characterizing the One-Dimensional Cesium Lead Bromide Polymorph

Inorganic lead halide perovskites have gained immense scientific interest for optoelectronic applications. In this work, we present a one-dimensional polymorph of cesium lead bromide (δ-CsPbBr₃) synthesized through a simple anion-exchange reaction, wherein distorted edge-sharing PbBr₆ octahedra form 1D chains isolated by Cs ions. δ-CsPbBr₃ was characterized by Raman spectroscopy, X-ray diffraction, ²⁰⁷Pb and ¹³³Cs solid-state NMR, and by optical emission and absorption spectroscopies. This non-perovskite material irreversibly transforms into the well-known three-dimensional perovskite phase (γ-CsPbBr₃) upon heating to above 151 °C. The indirect bandgap was determined by absorption measurements and calculation to be 2.9 eV. δ-CsPbBr₃ exhibits broadband yellow photoluminescence with a quantum yield of 3.2 %±0.2 % at room temperature and 95 %±5 % at 77 K, and this emission is attributed to the recombination of self-trapped excitons. This study emphasizes that the metastable δ-CsPbBr₃ may be a persistent, concomitant phase in Cs−Pb-Br-containing materials systems, such as those used in solar cells and LEDs, and it showcases the characterization tools used for its detection.     

Efficient Verification Tools for Reduced Derivatives Computed by a First-Optimize-Then-Discretize Approach for Optimal Control Problems

We give an overview about several verification tools to study consistency between discrete optimization problem and discrete derivatives when using independent discretization schemes for state and adjoint systems within the context of optimal control problems. We present strategies that detect impreciseness within a considered quantity without any additional effort. They are therefore a suitable tool to control the grid refinement within a multilevel setting. More detailed tools are useful to verify the problem implementation and to analyze the quantities discretization error order. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global existence of BV solutions and relaxation limit for a model of multiphase reactive flow

We consider a strictly hyperbolic system of balance laws in one space variable, that represents a simple model for a fluid flow in the presence of phase transitions. The state variables are specific volume, velocity and mass-density fraction λ of the vapor in the fluid. A reactive source term drives the dynamics of the phase mixtures; such a term depends on a relaxation parameter and involves an equilibrium pressure, allowing for metastable states.First we prove the global existence of weak solutions to the Cauchy problem, where the initial datum for λ is close either to 0 or 1 (the pure phases) and has small total variation, while the initial variations of pressure and velocity are not necessarily small. Then we consider the relaxation limit and prove that the weak solutions of the full system converge to those of the reduced system.     

High-performance liquid chromatography coupled to ultraviolet diode array detection and electrospray ionization mass spectrometry for the analysis of intermediates produced in the initial steps of the photocatalytic degradation of sulfonated azo dyes

High-performance liquid chromatography coupled to ultraviolet diode array detection and electrospray ionization mass spectrometry was applied to monitor the photocatalytic degradation mediated by TiO2 of three sulfonated monoazo dyes (Orange I, Orange II, and Ethylorange) present in aqueous solution. Photobleaching, organic carbon, nitrogen and sulfur evolution were also followed during the process. Delayed carbon mineralization was observed with respect to both dyes disappearance and photobleaching, due to the formation of transient intermediate compounds which were in turn completely degraded. Among the intermediates produced during the initial degradation steps the formation of several hydroxylated derivatives, mostly coloured, was evidenced. The MS(2) spectra allowed one to formulate hypothesis about the OH attack positions; a peculiar reactivity of the azo moiety was shown by Orange I and Orange II.     

Theoretical elastic moduli for disordered packings of interconnected spheres

A theoretical model has been developed which provides analytical expressions for the elastic moduli of disordered isotropic ensembles of spheres interconnected by physical bonds. Young's and shear moduli have been derived assuming an ideal random isotropic network and the radial distribution function for disordered packings of spheres. The interparticle interactions are accounted for in terms of surface forces for the two distinct cases of perfectly rigid spheres and spheres deformable at contact. A theoretical expression is also derived in a similar way for the bulk or compressibility modulus. In this case, an atomistic approach has been followed based on the analogy with noble gas solids and colloidal crystals. Also in this case, disordered spatial distribution of the spheres is described statistically. For the case of colloidal aggregates, a total two-body mean-field interaction potential is used which includes the Born repulsion energy. This latter contribution plays an essential role in determining the compression behavior of systems of particles aggregated in the primary minimum of the potential well and, therefore, must not be neglected. Both the expression of the Young's modulus and that of the compressibility modulus derived in this work are found to be consistent with two distinct sets of experimental data which recently appeared in the literature.     

Decay modes of 24Mg excited at 46.4 MeV

⁸Be_gs coincidences with ¹²C, ⁸Be_gs and α-particles produced in the ¹²C +¹²C interaction at 65 MeV have been measured in a wide in-plane angular range. The 3 −⁸Be_gs final state is found to be produced, even if poor statistics prevent any identification of the ¹⁶O states involved in the first stage of the process. The ⁸Be_gs−α and ⁸Be_gs−¹²C coincidence yields are found to be due to ¹²C and ¹⁶O excited states, decaying into the ⁸Be_gs+α and ¹²C +α systems, respectively. Received: 15 June 1998 / Revised version: 4 December 1998     

Molecular Complexes of Simple Anions with Electron‐Deficient Arenes: Spectroscopic Evidence for Two Types of Structural Motifs for Anion–Arene Interactions

Anion–π interactions between a π‐acidic aromatic system and an anion are gaining increasing recognition in chemistry and biology. Herein, the binding features of an electron‐deficient aromatic system (1,3,5‐trinitrobenzene (TNB)) and selected anions (OH^?, Br^?, and I^?) are examined in the gas phase by using the combined information derived from collision‐induced dissociation experiments at variable energy, infrared multiple‐photon dissociation spectroscopy, and quantum chemical calculations. We provide spectroscopic evidence for two different structural motifs of anion–arene complexes depending on the nature of the anion. The TNB–OR^? complexes (R=H, or alkyl groups which were studied earlier) adopt an anionic σ‐complex structure whereby RO^? attacks the aromatic ring with covalent bond formation, and develops a tetrahedral ring carbon bound to H and OR. The halide complexes rather conform to a structure in which the TNB moiety is hardly altered, and the halogen is placed on an unsubstituted carbon atom over the periphery of the ring at a C–X distance that is appreciably longer than a typical covalent bond length. The ensuing structural motif, previously characterized in the solid state and named weak σ interaction, is now confirmed by an IR spectroscopic assay in the gas phase, in which the sampled species are unperturbed by crystal packing or solvation effects.