Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Determination of certain trace impurities in uranium concentrates by activation analysis

A method is presented for the simultaneous determination of chromium, iron, cobalt and zinc in samples of uranium concentrates, oxides and metallic uranium by neutron-activation analysis. The method involves adequate decontamination of gross fission product activities by adsorption on silica gel, removal of uranium by solvent extraction, separation of most carrier-free rare-earth activities by coprecipitation with aluminium chloride, and, finally, fractional separation of the elements concerned by ion-exchange chromatography. The method can assay ppm of such elements in limited quantities of samples by scintillation gamma-ray spectrometric analysis with a reproducibility of 10-15%.     

Studies with polyfunctionally substituted heteroaromatics: 2-Phenyl-4-p-tolylhydrazono-2-oxazoline-5-one as a precursor for the synthesis of substituted 1,2,4-triazoles and pyridines

2-Phenyl-4-p-tolylhydrazono-2-oxazoline-5-one ( 3 ) was rearranged by the action of phenols and naphthols into 1,2,4-triazole-5-carboxylic esters ( 5 ) that were rearranged further on reflux in AcOH-ZnCl₂ into triazolyl ketones ( 7 ). Rearrangement of 3 into 1,2,4-triazole derivatives could also be effected by the action of heterocyclic amines and 1-naphthylamine. © John Wiley & Sons, Inc.     

Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform

Convergence properties of a class of least-squares methods for finding approximate inverses of the Laplace transform are obtained by using reproducing kernel Hilbert space techniques (or, alternatively, related minimization techniques) and some classical interpolation results.     

Pressures inside a room subjected to simulated sonic booms

The pressure variations inside a room of plaster-wood construction subjected to sonic boom loadings were investigated both analytically and experimentally to study the problems of dynamic structural response. The N-wave pressure signatures were generated in the UTIAS (University of Toronto Institute for Aerospace Studies) Travelling Wave Horn-Type Sonic Boom Simulator. The room overpressures in some cases were found to be twice as great as that in the incident sonic boom. The analysis and experimental data can be useful in assessing structural damage caused by supersonic aircraft overfligths.     

Photogenerated defects in shape-controlled TiO2 anatase nanocrystals: a probe to evaluate the role of crystal facets in photocatalytic processes

The promising properties of anatase TiO(2) nanocrystals exposing specific surfaces have been investigated in depth both theoretically and experimentally. However, a clear assessment of the role of the crystal faces in photocatalytic processes is still under debate. In order to clarify this issue, we have comprehensively explored the properties of the photogenerated defects and in particular their dependence on the exposed crystal faces in shape-controlled anatase. Nanocrystals were synthesized by solvothermal reaction of titanium butoxide in the presence of oleic acid and oleylamine as morphology-directing agents, and their photocatalytic performances were evaluated in the phenol mineralization in aqueous media, using O(2) as the oxidizing agent. The charge-trapping centers, Ti(3+), O(-), and O(2)(-), formed by UV irradiation of the catalyst were detected by electron spin resonance, and their abundance and reactivity were related to the exposed crystal faces and to the photoefficiency of the nanocrystals. In vacuum conditions, the concentration of trapped holes (O(-) centers) increases with increasing {001} surface area and photoactivity, while the amount of Ti(3+) centers increases with the specific surface area of {101} facets, and the highest value occurs for the sample with the worst photooxidative efficacy. These results suggest that {001} surfaces can be considered essentially as oxidation sites with a key role in the photoxidation, while {101} surfaces provide reductive sites which do not directly assist the oxidative processes. Photoexcitation experiments in O(2) atmosphere led to the formation of Ti(4+)-O(2)(-) oxidant species mainly located on {101} faces, confirming the indirect contribution of these surfaces to the photooxidative processes. Although this work focuses on the properties of TiO(2), we expect that the presented quantitative investigation may provide a new methodological tool for a more effective evaluation of the role of metal oxide crystal faces in photocatalytic processes.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.