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.     

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.

     

Synthesis of PrBa2Cu4O8 by Solution Method under Ambient Oxygen Pressure

A highly homogeneous and nearly monophasic PrBa₂Cu₄O₈ compound has been synthesized at 1 atm of oxygen via a route employing polymeric ethylenediamine/citric acid precursors. The PrBa₂Cu₄O₈ compound with a trace amount of BaCuO₂ was synthesized for the first time by sintering the pellets at the temperature of 875 °C under ambient oxygen pressure. The temperature coefficient of the resistivity is positive below 190 K while above 190 K is negative. The superconducting transition was not detected down to 4.2 K. Samples were characterized by X-ray diffraction, scanning electron microscopy, thermal analysis, and transport and magnetic measurements.     

Period-doubling route to chaos for a swirling flow in an open cylindrical container with a rotating disk

Conclusion The period-doubling route to chaos for a swirling vortex flow in an open cylindrical container, at an aspect ratio of 2, driven by a rotating bottom disk was recognized by using laser-Doppler velocimetry. The onset of periodic motion for the flow was found when Re was in the range between 1850 and 1900. The flow was subharmonically bifurcated into a double-period motion when Re was about 2150. When the Reynolds number was in the range from 2300 to 2400, the flow bifurcated again through the period-doubling mode. When the Reynolds number was further increased, the flow eventually showed chaotic motion. The existence of a free surface promotes the onset of periodicity, and the difference of the critical Reynolds number with and without a free surface was estimated to be about 600.This work was supported by the National Science Council of the Republic of China under grant No. NSC-82-0410-E-002-191     

Coprecipitation Synthesis of a Superconductor via Multi‐Precipitants

A precipitation process has been developed to prepare precursor powders, which can be calcined and sintered to form high‐Tc superconductors such as YBa₂Cu₃O_y. Precursor powders are prepared using a mixed‐precipitants system in which a solution contains precipitating anions such as hydroxide, oxinate and oxalate ions. A theoretical study on the conditions of mixed‐precipitants coprecipitation is performed. The solution pH of complete precipitation of the title system is extended and is maintained between 4.46 and 12.0. A series of experiments were conducted to confirm the as‐derived optimal condition. Finally, characterization of the properties of the YBa₂Cu₃O_y obtained after high temperature treatment is reported.     

Correlation of swirl number for a radial-type swirl generator

An experimental investigation was undertaken to derive a new correlation for the swirl number of a radial-type swirl generator under various Reynolds numbers and various vane angle conditions. A radial-type swirl generator with 16 rotary guide vanes was used to generate an annular swirling jet flow. The Reynolds numbers ranged from 60 to 6000, and the vane angles from 0° to 56°. Quantitative measurements for the velocities were made by using an optical method of laser-Doppler anemometry (LDA). Three-component velocity profiles of axial, radial, and azimuthal components at the swirling jet exit were measured for various flow conditions. A flow visualization method using smoke-wire and still photography was also applied to observe the flow patterns of the recirculation region behind the circular bluff body. Under low Reynolds number conditions, the swirl strength was found to be strongly dependent on the Reynolds number as well as on the guide vane angle. Based on the experimental results, a modified swirl number S is derived to characterize the swirling flow, which is useful for the design of a swirl generator.