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.     

An Exact Solution for the Optical Absorbance of Thin Films

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in their sample program for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.     

Aligned magnetic effects through varying permeable bed

The aligned magnetic effects on a steady laminar, viscous, incompressible, conducting fluid down an open inclined channel bounded below by a bed of varying permeability has been studied when the free surface is exposed to atmospheric pressure. Beavers and Joseph slip condition at the interface of the free flow region and the fluid flow in the porous bed and the Darcy’s law in the porous medium have been used. The expressions for velocity, magnetic strength and the mass flow across the cross-section of the channel are obtained.     

Unusual contributions of molecular architecture to rheology and flow birefringence in hyperbranched polystyrene melts

With the increase in sophisticated synthesis methods, it appears that polymer architecture may be a tunable property. Therefore, the role of architecture in rheological and processing properties has received renewed attention, mainly because of dendrimer synthesis and metallocene‐catalyst technology. Linear polymers and hyperbranched polymers represent two ends of branching complexity. Some previous studies have suggested that hyperbranched polymers may behave like unentangled polymers, whereas others have proposed that they exhibit the properties of soft colloids. In an effort to compare the responses of linear and hyperbranched polymers, we synthesized starlike hyperbranched polystyrenes (HBPSs) of various branch lengths and numbers of branches. The HBPSs used in this study were unentangled or weakly entangled, allowing us to study the effect of branch density more readily. Two linear polystyrene (L‐PS) melts and two HBPSs were studied. Using a custom‐built rheooptical apparatus, we characterized the rheology and flow birefringence of these materials. To our knowledge, these are the first flow birefringence measurements on highly branched polymer melts. Our results suggest that the flow behavior of HBPS is significantly different from that of L‐PS: (1) HBPS shows nonterminal behavior in the low‐frequency rheological response; (2) when the stress‐optical rule (SOR) holds, the stress‐optical coefficient of HBPS is much lower than those of analogous linear polymers; and (3) when the branch density is high and the branch length is sufficiently low, the SOR fails for these homopolymer melts. A significant increase in the birefringence for a given amount of stress in the low‐frequency region suggests that there may be a soft core in these materials due to the strong preferential radial orientation of chain segments near the center of a molecule versus those near the periphery. The predominantly elastic response of the soft structures may be responsible for the enhanced form birefringence. Our preliminary results indicate that these materials may exhibit both polymeric and soft‐colloid natures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2562–2571, 2001     

A facile one-pot synthesis of N-substituted tetrahydroquinolines

An uncatalyzed one-pot synthesis of N-substituted tetrahydroquinolines was achieved in good yields by the reaction of quinoline and alkyl/acyl halides with Hantzsch dihydropyridine ester under mild reaction conditions.