A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.     

Complete Carton-13 Assignments of the Sesquiterpene Lactone 11,13,-Dihydroparthenolide Using 2D-Inadequate

The complete ¹³C NMR resonances for the sesquiterpene lactone 11,13-dihydroparthenolide were established by the application of 2D-INADEQUATE.     

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.     

Interatomic electronic decay driven by nuclear motion

The interatomic electronic decay after inner-valence ionization of a neon atom by a single photon in a neon-helium dimer is investigated. The excited neon atom relaxes via interatomic Coulombic decay and the excess energy is transferred to the helium atom and ionizes it. We show that the decay process is only possible if the dimer's bond stretches up to 6.2 ?, i.e., to more than twice the equilibrium interatomic distance of the neutral dimer. Thus, it is demonstrated that the electronic decay, taking place at such long distances, is driven by the nuclear motion.     

Monitoring of NO2 in the ambient air with passive samplers before and after a road reconstruction event

Nitrogen dioxide (NO₂) concentrations were used to evaluate the air quality before and after the infrastructural change of an important traffic artery in Mortsel, Antwerp (Belgium). During the reconstruction works two pairs of traffic lanes were reduced to one in each direction. Two sampling campaigns were conducted: the first one before the works in 2003 and the second one in 2005, after the road works were finished. Sampling was performed on a weekly base with the use of passive diffusion tubes on the streets, and also indoors in nearby houses. The samples were analyzed by ion chromatography, from which data the NO₂ concentrations in air could be calculated. These results were compared with NO₂ values from the air monitoring station 42R801 of the Flemish Environment Agency in Borgerhout, Antwerp. On the base of different NO₂ concentrations, correlated well with the traffic density, sampling locations were classified into three groups as follows: 1) ‘heavily polluted’ (heavy traffic); 2) ‘moderately polluted’ (medium traffic); or 3) ‘less polluted’ (low traffic density). Sampling sites located further from the road works, enclosed to the group ‘less polluted’, showed the lowest NO₂ concentrations. The highest NO₂ level was found for the locations close to reconstruction works, which belonged to the group ‘heavily polluted’. The contribution of NO₂ was at the same level before and after the road works. During the first campaign it ranged from 30 ± 7 µg/m³ to 71 ± 11 µg/m³ and during the second sampling it was between 36 ± 17 µg/m³ and 73 ± 17 µg/m³. These modernization works had no impact on preventing the traffic-related pollutant as NO₂ and as a consequence no significant effect on the air quality in the studied region. It has been proven that the impact of traffic on the air quality is unmistakably high and simply reduction of the number of the traffic lanes, intended to discourage the traffic flow, had apparently no environmentally advantageous effect.     

Spectroscopic characterization of molybdenum dinitrogen complexes containing a combination of di- and triphosphine coligands: 31P NMR analysis of five-spin systems

The three molybdenum-N2 complexes [Mo(N2)(dpepp)(depe)] (1), [Mo(N2)(dpepp)(dppe)] (2), and [Mo(N2)(dpepp)(1,2-dppp)] (3), all of which contain a combination of a bi- and a tridentate phosphine ligand, were prepared and investigated by vibrational and (31)P NMR spectroscopy. As a tridentate ligand bis(2-diphenylphosphinoethyl)phenylphosphine (dpepp) has been employed. The three different bidentate ligands are 1,2-bis(diethylphosphino)ethane (depe), 1,2-bis(diphenylphosphino)ethane (dppe), and R-(+)-1,2-bis(diphenylphosphino)propane (1,2-dppp). N-N as well as metal-N vibrations of 1-3 are identified and interpreted in terms of the geometric and electronic structures of the complexes. (31)P NMR spectra are recorded and fully analyzed. Moreover, correlation spectroscopy (COSY)-45 measurements are performed to determine the relative signs of coupling constants. Special attention is directed to a detection of different isomers and their (31)P NMR, as well as vibrational spectroscopic properties. The implications of the results for the area of synthetic nitrogen fixation with phosphine complexes are discussed.