Analysis of finite element methods for second order boundary value problems using mesh dependent norms

This paper presents a new approach to the analysis of finite element methods based onC ⁰-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely ralated to theL ₂ norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in theL ₂ norm and in the 2nd order Sobolev norm — the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform.     

The finite element method with Lagrangian multipliers

Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.This paper was supported by the Atomic Energy Commission under Contract No. AEC AT (40-1) 3443/4.     

Measurement of multiplet intensities and noble gas-broadened line widths in the V3-fundamental of methane

Integrated intensity data at 300°K for J-multiplets between P(11)and R(11) in the _{V3-fundamental of ¹²CH4} are presented, along with the intensity of the entire Q-branch, which also encompasses the Q-branch of the _{V3-fundamental of ¹³CH4}. These data, together with theoretical estimates for the intensities of J-multiplets of J > 11, sum up to a value of S_band= 284±14cm^?2atm^?1 at 300°K. This results is in excellent agreement with most of the previously published values for this parameter. Within experimental error, the intensities of the J-multiplets in the _{V3-fundamental do not seem to exhibit the strong anamolies that were characteristic of lines in the 2V3}-band.Line widths have been measured at 100°K, 130°K, 190°K, 250°K, and 300°K for R(0), R(1), and R(2) broadened by He, Ne and Ar. The temperature dependence of the line width is discussed for the three cases of broadening. In neon broadening at 300°K, the ‘effective mean line widths’ for multiplets R(3) through R(11) have also been obtained experimentally; their J-dependence is interpreted using Gordon's theory of line shapes in multiplet spectra.     

Electrothermal AAS studies of Sm, Eu, Dy, and Er separated from uranium

Summary Studies were conducted on the assay of Sm, Eu, Dy and Er separated from uranium using aqueous standards by electrothermal AAS with Massmann type graphite furnace. The working curves were found to be linear in the ranges Sm (1–10 g/ml), Eu (0.05–0.6 g/ml), Dy (0.1–0.8 g/ml) and Er (0.1–1.0 g/ml). The values obtained for synthetic samples agreed favourably with those obtained by emission spectrographic method. Experiments using pyrolytic carbon coated tubes with and without pretreatment by La, Ta and Y have shown an enhancement with treatment upto a maximum of 15% and improve the memory effect marginally. The effect of Ta treatment was found to be singularly useful in improving the general behaviour of Sm. The interference effects of lanthanides, other than the analyte, were found to be negligible. However, the presence of uranium was found to affect the absorbance. The absorbance of Eu was found to be nearly independent of uranium after an initial increase. On the other hand, the absorbance of other elements studied was found to drastically decrease after an initial enhancement. Detailed investigations of temperature dependence of absorbance were carried out using Eu, Dy and Er. The differences in the behaviour of these elements is attributed to probable differences in the modes of their atomization.

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Untersuchung von aus Uran abgetrenntem Samarium, Europium, Dysprosium und Erbium durch elektrothermische Atomabsorptions-Spektralphotometrie

Zusammenfassung Die Untersuchungen wurden mit Hilfe des Graphitrohrofens nach Maßmann durchgeführt. In folgenden Bereichen ergaben sich lineare Eichkurven: Sm 1–10 g/ml, Eu 0,05–0,6 g/ml, Dy 0,1–0,8 g/ml, Er 0,1-1,0 g/ml. Die aus synthetischen Proben erhaltenen Ergebnisse stimmten gut mit den durch Emissionsspektrographie erhaltenen überein. Versuche wurden mit Röhren mit pyrolytischen Kohlenstoffüberzug mit und ohne Vorbehandlung durch La, Ta und Y durchgeführt und ergaben eine bis 15%ige Steigerung durch die Behandlung sowie eine mäßige Besserung des Memoryeffektes. Eine Behandlung mit Ta war besonders für Sm vorteilhaft. Störungen durch andere Lanthanide waren vernachlässigbar. Uran beeinflußte jedoch die Absorption. Im Falle von Eu zeigte sich nach anfänglicher Zunahme fast eine Unabhängigkeit, während bei den anderen untersuchten Elementen nach anfänglicher Zunahme eine beträchtliche Abnahme auftrat. Mit Eu, Dy und Er wurde ebenfalls die Temperaturabhängigkeit der Absorption untersucht. Festgestellte Unterschiede im Verhalten werden auf unterschiedliche Atomisierung zurückgeführt.

     

Voice responses to changes in pitch of voice or tone auditory feedback

The present study was undertaken to examine if a subject's voice F0 responded not only to perturbations in pitch of voice feedback but also to changes in pitch of a side tone presented congruent with voice feedback. Small magnitude brief duration perturbations in pitch of voice or tone auditory feedback were randomly introduced during sustained vowel phonations. Results demonstrated a higher rate and larger magnitude of voice F0 responses to changes in pitch of the voice compared with a triangular-shaped tone (experiment 1) or a pure tone (experiment 2). However, response latencies did not differ across voice or tone conditions. Data suggest that subjects responded to the change in F0 rather than harmonic frequencies of auditory feedback because voice F0 response prevalence, magnitude, or latency did not statistically differ across triangular-shaped tone or pure-tone feedback. Results indicate the audio-vocal system is sensitive to the change in pitch of a variety of sounds, which may represent a flexible system capable of adapting to changes in the subject's voice. However, lower prevalence and smaller responses to tone pitch-shifted signals suggest that the audio-vocal system may resist changes to the pitch of other environmental sounds when voice feedback is present.     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Optical absorption and photoluminescence studies of Eu-doped phosphate and fluorophosphate glasses

Phosphate (P₂O₅+K₂O+BaO+Al₂O₃+Eu₂O₃) and fluorophosphate (P₂O₅+K₂O+BaO+BaF₂+Al₂O₃+Eu₂O₃) glasses with different Eu³⁺ ion concentrations have been prepared and characterized through optical absorption, photoluminescence and decay times. An intense red luminescence is observed from the ⁵D₀ emitting level of Eu³⁺ ions in these glasses. The relative luminescence intensity ratio of ⁵D₀→⁷F₂→⁵D₀→⁷F₁ transitions has been evaluated to estimate the local site symmetry around the Eu³⁺ ions. The emission spectra of these glasses show a complete removal of degeneracy for the ⁵D₀→⁷F₁ and ⁵D₀→⁷F₂ transitions. Second and fourth rank crystal-field (CF) parameters have been calculated together with the CF strength parameter by assuming the C_2v symmetry for the Eu³⁺ ions in both the phosphate and fluorophosphate glasses. Judd-Ofelt parameters have been evaluated from the luminescence intensity ratios of ⁵D₀→⁷F_J (J=2, 4 and 6) to ⁵D₀→⁷F₁ transitions. These parameters have been used to derive radiative properties such as transition probabilities, branching ratios, radiative lifetimes and peak stimulated emission cross-sections for the ⁵D₀→⁷F_J transitions. Decay curves of the ⁵D₀ level of Eu³⁺ ions in these two Eu³⁺:glass systems have been measured by monitoring the ⁵D₀→⁷F₂ transition (611 nm) at room temperature. The experimental lifetime of the ⁵D₀ level in the title glasses is found to be higher than Eu³⁺-doped niobium phosphate glasses. The analysis indicates that the lifetime of the ⁵D₀ level is found to be less sensitive to the Eu³⁺ ion concentration and addition of BaF₂ has no significant effect on the optical properties of Eu³⁺-doped phosphate glasses.     

Fabrication of high performance Gd–Ba–Cu–O single grains in air using a practical melt processing technique

A practical processing route for the fabrication of LRE-Ba–Cu–O single grain superconductors has been developed at the University of Cambridge based on a generic, Mg-doped Nd-123 melt textured seed and suppression of the formation of the solid solution phase in air by enriching the precursors with higher Ba concentration. The processing of high performance Gd–Ba–Cu–O single grains using this processing route is described. The Mg-doped generic seed crystal has been used effectively to promote heterogeneous nucleation via a cold-seeding process. The Gd/Ba solid solution has been suppressed by enriching Gd–Ba–Cu–O precursor powders with two different Ba-rich compositions. This involved adding BaO₂ and GdBa₆Cu₃O_y (Gd-163) (a novel Ba-rich second phase) to the precursor powders, respectively. The Gd-163 phase has been observed not only to suppress formation of the solid solution phase, but also to promote increased heterogeneous grain size. A detailed further study has been carried out with an initial aim of optimizing the BaO₂ and Gd-163 phase content of the precursor composition to produce a single grain almost free of solid solution. Based on the optimized parameters, large single grain Gd–Ba–Cu–O superconductors have been fabricated in an air atmosphere and demonstrated to exhibit record trapped magnetic fields for this material melt processed in air in relatively small single grain samples. The trapped fields of samples produced in air atmosphere are at least comparable to those processed under reduced oxygen partial pressure.