Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybrid Electrodes Used in Polymer Electro-Optic Modulator with Ultra-Broadband

Hybrid electrode combined coplanar waveguide (CPW) and microstrip lines in ultra-broadband electro-optic modulators. The characteristics of the modulators with hybrid electrode is like that of the modulator with the microstrip lines, in which the microstrip electrode is loaded above only one arm of Mach-Zehnder (M-Z) optical waveguide, besides the problem of microstrip line to coaxial transition and corona polarization in polymer modulators have been best solved at the same time. By using finite element method (FEM), the characteristic parameters such as half-wave voltage, modulation bandwidth characteristic impedance, effective microwave refractive index of polymer modulators with microstrip line and hybrid electrode are analysed and compared in this paper. The results present that velocity match, impendence match and lower microwave propagating loss is easily realized in modulators with hybrid electrode.     

An efficient one‐pot synthesis of novel pyrimidoquinoline derivatives under microwave irradiation without catalyst

A series of pyrimidoquinoline derivatives were synthesized through one‐pot condensation of 2,6‐diaminopyrimidin‐4‐one, aldehyde and cyclic a 1,3‐dicarbonyl compound in glycol under microwave irradiation without catalyst. The protocol in the absence of catalyst has the advantage of good yield (87‐95%), short reaction time (4‐7 min) and an environmentally friendly technique.     

Evidences of phase separation in moisture‐cured poly(urethane urea)s by means of temperature modulated differential scanning calorimetry

The degree of phase separation in several moisture‐cured poly(urethane urea)s (PUUs) was studied by FTIR spectroscopy, wide angle X‐ray diffraction (WAXD), and temperature‐modulated differential scanning calorimetry (TMDSC). This latter technique was shown to be particularly useful in analysing the degree of phase separation in PUU polymers. Both phase mixing and phase segregation coexisted in the PUUs and the degree of phase separation increased as the urea hard segment (HS) content in the PUU increased. The maximum solubility of urea HSs into the polyol soft segments (SSs) was achieved for 50 wt % urea HS content in diol‐based PUUs, whereas for triol‐based PUUs the highest solubility between HS and SS was reached for lower urea HS amount. Finally, the higher the urea HS content the higher the extent of phase separation in the PUU. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3034–3045, 2007     

Effect of short glass fiber on structure and viscoelastic behavior of olefinic polymers synthesized with metallocene catalyst

Several composites were prepared on the basis of an ethylene homopolymer and different copolymers of ethylene and 1‐hexene, synthesized with a metallocene catalyst, as matrices and a content of a 5 wt % of short glass fiber. The effect of the fiber incorporation on the structure and mechanical and viscoelastic behaviors was analyzed for the different samples. The glass fibers induced a slightly higher crystallinity, and the crystallite morphology significantly changed (long spacings and crystal orientation). The incorporation of fibers did not reinforce the different matrices under study at this low content; consequently, the mechanical parameters, such as Young's modulus, yielding stress, and microhardness, were lower in the composites as compared with those values found in the neat polyolefins. The location and apparent activation energies of distinct relaxation processes are also discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1244–1255, 2003     

A case of concomitant polymorphism and spontaneous resolution: the tetragonal phase of 5‐hydroxymethyl‐7,7,N‐trimethyl‐6‐oxabicyclo[3.2.1]octane‐1‐carboxamide

The title compound, C₁₂H₂₁NO₃, crystallizes in two polymorphic forms, viz. the tetragonal form described here and the monoclinic form described previously [Foces‐Foces, López‐Rodríguez, Pérez, Martín & Pérez‐Hernández (2007). Cryst. Growth Des. 7 , 905–911]. The differences in the conformations of the hydroxymethyl and methylaminocarbonyl substituents have important consequences in the hydrogen‐bond interaction motifs and, therefore, in the packing arrangements. These forms are concomitant polymorphs with melting points differing by 3 K.     

A generalized quasi-sum relations for oscillator strengths in transition arrays: theoretical study of the opacity of Ge plasmas

We present a simplified relativistic configuration interaction method (SRCI), by which all the energy levels and oscillator strengths in each transition array can be calculated. There exist generalized quasi-sum relations for the calculated oscillator strengths in the relevant transition arrays by the SRCI and by an unresolved transition array model (UTA). Based on UTA and the detailed configuration accounting (DCA), with a fully relativistic treatment incorporated with the quantum defect theory, the X-ray absorption spectra for any middle- and high-Z plasmas or composite plasmas can be calculated with much less computational efforts. The gross features of calculated spectra by DCA-UTA are in agreement with the relevant experimental measurements, except some detailed structures in some narrow spectral ranges. Such detailed structures can be calculated by SRCI incorporated with DCA-UTA. As an illustrative example, the absorption spectra of Ge plasmas are calculated by DCA-UTA-SRCI and are in agreement with the experimental opacity data. Therefore, the theoretical method (DCA-UTA-SRCI) verified by experimental measurements will not only be a basic tool to provide “precision” opacity data for the inertial confinement fusion research (ICF) and studies in stellar physics but also can be used to analyze the relevant diagnostic measurements for ICF plasmas.     

Effects of diamines and their fluorinated groups on the color lightness and preparation of organosoluble aromatic polyimides from 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]‐hexafluoropropane

To investigate the position and amount of the CF₃ group affecting the coloration of polyimides (PIs), we prepared 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]hexafluoropropane ( 2 ) with four CF₃ groups with 2‐chloro‐5‐nitrobenzotrifluoride and 2,2‐bis(4‐hydroxyphenol)hexafluoropropane. A series of soluble and light‐colored fluorinated PIs ( 5 ) were synthesized from 2 and various aromatic dianhydrides ( 3a – 3f ). 5a – 5f had inherent viscosities ranging from 0.80 to 1.19 dL/g and were soluble in amide polar solvents and even in less polar solvents. The glass‐transition temperatures of 5 were 221–265 °C, and the 10% weight‐loss temperatures were above 493 °C. Their films had cutoff wavelengths between 343 and 390 nm, b* values (a yellowness index) ranging from 5 to 41, dielectric constants of 2.68–3.01 (1 MHz), and moisture absorptions of 0.03–0.29 wt %. In a comparison of the PI series 6 – 8 based on 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane, 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]propane, and 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane, we found that the CF₃ group close to the imide group was more effective in lowering the color; this means that CF₃ of 5 , 7 , and 8f was more effective than that of 6c . The color intensity of the four PI series was lowered in the following order: 5 > 7 > 6 > 8 . The PI 5f , synthesized from diamine 2 and 4,4′‐hexafluoroisopropylidenediphthalic anhydride, had six CF₃ groups in a repeated segment, so it exhibited the lightest color among the four series. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 922–938, 2003     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

Blind Channel Identification Based on Noisy Observation by Stochastic Approximation Method

A stochastic approximation algorithm for estimating multichannel coefficients is proposed, and the estimate is proved to converge to the true parameters a.s. up-to a constant scaling factor. The estimate is updated after receiving each new observation, so the output data need not be collected in advance. The input signal is allowed to be dependent and the observation is allowed to be corrupted by noise, but no noise statistics are used in the estimation algorithm.