Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Magnetic resonance imaging: a new window into industrial processing.

Although the most important use of nuclear magnetic resonance imaging (MRI) continues to be for diagnostic medicine, recognition is being gained for many nonmedical applications. Examples include the following areas: petrogeology, food, agriculture, polymers and polymer-composites, and pharmaceuticals. These areas all involve studies of species that have short spin-spin relaxation times, and consequently need far fast gradient switching. These technical details are discussed and typical applications given.     

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

Quantitative electron probe microanalysis for the characterization of thin carbon-boron layers in fusion devices

Summary The first wall of the fusion device TEXTOR at the Forschungszentrum Jülich has been coated in situ with an amorphous hydrogen rich carbon/boron film (a-C/B:H) which reduces plasma impurities caused by the plasma surface interaction. The results of the coating process of the 35 m² large inner wall surface have been controlled by a recently developed modification of the quantitative electron probe microanalysis, which has been applied to 12 samples from specified positions inside the tokamak. The quantification itself is based on a Monte Carlo simulation of electron trajectories providing very accurate results for X-ray intensities emitted by elements present in the electron bombarded sample. The Monte Carlo results are used in the present work to calibrate the measured X-ray intensities emitted by boron and carbon from the a-C/B:H layers deposited on pure silicon substrates. As a result the total deposited mass of the layer per area unit as well as the composition of the layers (except hydrogen) could be determined very accurately. The relative errors were less than 7%. The limit of detectability were found to be in the range of one monolayer for boron as well as for carbon.     

The epitaxial growth of gaas using alkylarsine: Part 2. molecular orbital calculation

Semi-empirical molecular orbital calculations were carried out for the compounds (C₂H₅)₃As, (C₂H₅)₃Ga and RAsH₂ (R = C₂H₅, i-C₃H₇, i-C₄H₉, and t-C₄H₉) by using the CNDO/2-U program, and their capability of β-elimination reaction is compared on the basis of the torsion energy to the transition state, electrostatic interactions and orbital overlapping between the central atom and the β-hydrogen, and bond order of the metal-carbon, and carbon-hydrogen bond. In the comparison of (C₂H₅)₃As with (C₂H₅)₃Ga, we found that the β-elimination of (C₂H₅)₃As could hardly be expected to take place in the thermal decomposition. The capability of β-elimination would be smaller in C₂H₅AsH₂ than that in (C₂H₅)₃As. Moreover when the ethyl group is replaced by a t-butyl group in RAsH₂, the β-elimination reaction appears to become more difficult and a large possibility for a radical process is suggested.     

Silver nitrate-acetonitrile and iodine-benzene complexes as studied by NMR in thermotropic liquid crystals

Silver nitrate-acetonitrile and π iodine-benzene complexes in thermotropic liquid crystals have been studied by ¹H, ²H, and ¹³C NMR spectroscopy and by optical microscopy. Evidence for at least two silver complexes in each liquid crystal is presented.     

THE USE OF THERMOELASTICITY TO EVALUATE STRESS REDISTRIBUTION AND NOTCH SENSITIVITY IN CERAMIC MATRIX COMPOSITES

Thermoelastic stress analysis was used to document the effect of composite damage on the stress distribution in three ceramic matrix composites. Composite damage was found to significantly alter the thermoelastic response of each material, with the greatest effect noted in SiC/CAS. Thermoelastic imaging of these materials affords a more complete picture of how the various damage mechanisms affect the stress distribution. In particular, a stress concentration factor computed from thermoelastic images, serves as an indicator of stress redistribution. The stress concentration factors were computed by comparing notch root to far field temperatures, and monitored after the introduction of various amounts of damage. In each material, the stress concentration factor diminished as the damaging load approached the ultimate stress. Reduction in the stress concentration is associated with local changes in modulus, mechanistically arising from combinations of fiber, matrix and interface fracture. Stress redistribution occurs as a consequence of modulus changes, leading to lower notch sensitivity in each of the tested composites.