On optimal triangular meshes for minimizing the gradient error

Summary Construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed. Using an appropriate linear coordinate transformation, rigorously optimal meshes for controlling the error in quadratic data functions are constructed. It is shown that the transformation can be generated as a curvilinear coordinate transformation for anyC data function with nonsingular Hessian matrix. Using this transformation, a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed. In particular, it is shown that equilibration of errors is not a sufficient condition for optimality. A comparison of meshes generated under several different criteria is made, and their equilibrating properties illustrated.This work was supported by the Natural Sciences and Engineering Research Council of Canada, by the Information Technology Research Centre, which is funded by the Province of Ontario, by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc., and through an appointment to the U.S. Department of Energy Postgraduate Research Program administered by Oak Ridge Associated Universities     

Chemical repercussions of orbital interactions through bond and through space The reactivity of the double bond in unsaturated cyclic sulphones towards aziridine formation and epoxidation

The ease of formation of aziridine and/or epoxides from a series of bicyclic olefins, where distant sulphonyl groups are present, is very variable. There is some correlation between reactivity of the vinyl group and its π-ionisation potential which is high in the present molecules relative to comparison olefins. This increase is thought to be due to the presence of orbital interactions through bonds and/or through space between the sulphone group and the double bond, making the latter electron deficient. The ionisation potentials were determined by UV-photoelectron spectroscopy and the assignments made by recourse to ab initio configuration interaction methods.     

A two time scale analysis of gyroscopic motion with friction

The motion of a symmetric rigid body having one fixed point and subject to frictional forces is considered. The frictional forces are due to a surrounding dissipative medium and are accounted for by a model wherein the frictional torque is proportional to the angular velocity. A two time scale perturbation technique is used to analyze and characterize possible motions. The results of calculations which illustrate some of these motions are provided. These results show full agreement with qualitative observations.

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Résumé On considère le mouvement d'un corps rigide symétrique ayant un point fixe et sujet à des forces de friction. Les forces de friction sont dues à un milieu dissipatif et sont représentées par un modèle où le moment de friction est proportionnel à la vitesse angulaire. On utilise une technique de perturbations à double échelle pour l'analyse et la charactérisation des mouvements possibles. On donne des résultats numériques illustrant certains de ces mouvements. Ces résultats sont en accord complet avec les observations qualitatives.

     

The use of thermal and spectroscopic methods to study chemically modified materials

The application of thermal and spectroscopic techniques in the characterisation of chemically modified materials is illustrated with several examples: ethylene vinyl acetate (EVA) copolymers which had been hydrolysed under alkaline conditions, amosite asbestos fibres which had been reacted with alkyldimethylchlorosilanes, and a polymeric composite material which had been affected by moisture.The authors acknowledge the following for assistance in the project: Rhona MacBeth, Conservator, Courtauld Institute of Art and presently at the Boston Museum of Fine Arts, for the TMA measurements, conditioning of composite samples, and useful discussions. PL-Thermal Sciences (John Gearing for the DETA measurements on EVA). PL-Thermal Sciences (Epsom Laboratories) for the use of Dynamic Mechanical Thermal Analysis equipment.     

Loss of alignment gain in the πh 9/2[541 1/2−] ⊗ (νi 13/2)2 band in 167Tm and neighbouring odd-Z N = 98 nuclei

Theπh_9/2[541 1/2^?] band in ¹⁶⁷Tm has been studied through the ¹²⁴Sn(⁴⁸Ca, p4n)¹⁶⁷Tm reaction at E _beam = 210 MeV. The favoured signature of the πh_9/2[541 1/2^?] band is observed to spin 61/2h?. A remarkable small gain in aligned angular momentum at the AB-band crossing has been found. The crossing frequency and the gain in aligned angular momentum for ¹⁶⁷Tm are compared with data for the N = 98 isotones of Lu, Ta and Re, and contrasted with Cranked Shell Model predictions, based on frequency diabatic configurations. Large deviations are found for the gain in aligned angular momentum.     

The Euroball Spectrometer

Euroball is a European project to build a highly efficient and powerful gamma-ray spectrometer for nuclear spectroscopy. The project represents an amalgamation of recent technical advances in detectors, electronics and data acquisition. These developments and the status of the project will be discussed.     

Evidence for an i13/2 neutron band in133Sm

A rotational band of nine γ-rays has been observed in¹³³Sm. The moment of inertia of the band indicates that it has a higher deformation than expected for states in nuclei in this region. The properties are such that it can be interpreted as being due to the odd neutron occupying the ν i2/13 nn intruder orbital. This is the first evidence for the occupation of this orbital in nuclei with neutron number N<73.