A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables.     

Preliminary study of the thermally stimulated blue luminescence of ulexite

In this paper, novel results on the blue thermally stimulated luminescence (TSL) emission of ulexite (NaCaB₅O₆(OH)₆·5H₂O) have been studied. The four maxima appearing at 60, 110, 200 and 240°C on the TSL glow curves of this borate could be respectively associated to: (i) the first dehydration (NaCaB₅O₆(OH)₆·5H₂O→NaCaB₅O₆(OH)₆·3H₂O), (ii) the creation-annihilation of the three-hydrated phase, (iii) the Na-coordinated chains dehydroxylation and the starting point of the alkali self-diffusion through the lattice and (iv) the amorphisation of the lattice. These results are fairly well correlated with the differential thermal analyses (DTA), in situ thermal observations under environmental scanning electron microscope (TESEM) and thermal X-ray diffraction (TXRD) techniques.     

Radical reactions involving esters of fumaric acid—III. Chain transfer processes

Model compounds have been used in studies at 60° in connection with transfer to polymer during the copolymerization of vinyl acetate with esters of fumaric acid. Succinate esters were used to simulate the fumarate ester units and ethyl acetate the vinyl acetate units in the copolymers. The succinate esters are much more reactive than ethyl acetate in transfer reactions with polyvinyl acetate radicals. Methyl isobutyrate and methyl propionate were also examined to assess the difference in reactivity in transfer of tertiary and secondary hydrogen atoms. It is concluded that branching is a very important reaction in the preparation of high conversion copolymers of fumarate esters with vinyl acetate.     

Preparation of Y2Ba4Cu7O15-δ Superconductor without High Oxygen Pressure

The synthesis of bulk Y₂Ba₄Cu₇O_15-δ superconductor at atmospheric oxygen pressure via solid state sintering is reported. Temperature ranging from 860 to 890 °C as well as time interval over 2 to 15 days were used to investigate the formation of the Y₂Ba₄Cu₇O_15-δ phase. A time-temperature profile characterizing the conditions for the preparation of Y₂Ba₄Cu₇O_15-δ phase suggests the optimal condition to be sintering at 890 °C for over 10 days. Detailed results of X-ray diffraction, electrical resistivity, iodometric titration and magnetization measurements are described.     

Effect of orbiting resonance on the elastic differential cross sections

The effects of orbiting resonances on elastic differential cross sections are investigated for the Lennard-Jones (12, 6) model potential. The elastic differential cross section consists of three terms: a resonance term, a potential scattering term and an interference term. The interference term has a significant effect only at small angles of the differential cross section. The importance of the potential scattering term depends proportionally upon the orbiting resonance energy. For the low-lying orbiting resonance states, the resonance term is the dominant term, but at higher energy it appears only in the backward differential cross sections. Generally, by fitting the large angle differential cross sections, the resonance orbital angular momentum can be estimated.     

A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval , and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.