Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Sulfur adsorption on Fe(1 1 0): a DFT study

The adsorption of atomic S on the Fe(1 1 0) surface is examined using density functional theory (DFT). Three different adsorption sites are considered, including the atop, hollow and bridge sites and the S is adsorbed at a quarter monolayer coverage in a p(2 × 2) arrangement. The hollow site is found to be the most stable, followed by the bridge and atop sites. At all three sites, S adsorption results in relatively minor surface reconstruction, with the most significant being that for the hollow site, with lateral displacements of 0.09 Å. Comparisons between S-adsorbed and pure Fe surfaces revealed reductions in the magnetic moments of surface-layer Fe atoms in the vicinity of the S. At the hollow site, the presence of S causes an increase in the surface Fe d-orbital density of states between 4 and 5 eV. However, S adsorption has no significant effect on the structure and magnetic properties of the lower substrate layers.     

On the Smoothness of a Generalized Solution of the First Initial Boundary-Value Problem for Strongly Parabolic Systems in a Cylinder with Nonsmooth Base with Respect to Time Variable

We consider the first initial boundary-value problem for strongly parabolic systems in an infinite cylinder with nonsmooth boundary. We establish conditions for the existence of generalized solutions, an estimate for this solutions, and an estimate for the derivative of the solution.     

Spectral Domain Analysis of Coaxial Cavities

Coaxial cavities are used in high power gyrotrons as the beam-wave interaction structure. Much research has been devoted to their mode selective properties. A coaxial cavity lacks a sharp boundary at its open end, so it has some physical features that can only be observed using a spectral model, such as frequency-dependent field profiles and mode overlapping effects. These properties are important since cold tests are usually conducted in the frequency domain. This study applies the incident/reflected wave boundary condition to the wave equation of a weakly irregular coaxial waveguide. The resistivity of the wall is considered in the analysis. Calculations reveal that the fixed-position spectrum yields an uncertain resonant frequency and quality factor. Although the maximum-field spectrum can uniquely determine the properties of the coaxial cavity, the resonant frequency obtained using the maximum-field spectral model is inconsistent with that obtained using the temporal model. The field-energy spectrum explains the low Q nature of the coaxial cavity. Moreover, resonant frequencies evaluated using the field-energy spectrum agree precisely with those evaluated using the temporal model.     

Synthesis and characterization of wholly aromatic poly(azomethine)s containing donor–acceptor triphenylamine moieties

N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine was synthesized from N‐(4‐nitrophenyl)‐diphenylamine by the Vilsmeier‐Haack reaction. Soluble aromatic poly(azomethine)s (PAMs) were prepared by the solution polycondensation of N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine and aromatic diamine in N‐methyl‐2‐pyrrolidone (NMP) at room temperature under reduced pressure. All the PAMs are highly soluble in various organic solvents, such as N,N‐dimethylacetamide (DMAc), chloroform (CHCl₃), and tetrahydrofuran (THF). Differential scanning calorimetry (DSC) indicated that these PAMs had glass‐transition temperatures (T_gs) in the range of 170–230 °C, and a 10% weight‐loss temperatures in excess of 490 °C with char yield at 800 °C in nitrogen higher than 60%. These PAMs in NMP solution showed UV‐Vis charge‐transfer (CT) absorption at 405–421 nm and photoluminescence peaks around 462–466 nm with fluorescence quantum efficiency (Φ_F) 0.10–0.99%. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of these PAMs can be determined from cyclic voltammograms as 4.86–5.43 and 3.31–3.34 eV, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4921–4932, 2007     

Synthesis of poly(arylene disulfide)-vermiculite nanocomposites via in situ ring-opening reaction of cyclic oligomers

An exfoliated poly(4,4^′-oxybis(benzene)disulfide) (POBDS)/vermiculite (VMT) nanocomposite was prepared by using cyclo(4,4^′-oxybis(benzene)disulfide) (COBDS) oligomers and cetyltrimethyl ammonium bromide exchanged VMT. The POBDS/VMT nanocomposites were fabricated in two steps. First, the COBDS oligomers were used to swell and exfoliate organo VMT to afford COBDS-VMT nanocomposite precursor. Subsequently, the exfoliated POBDS-VMT nanocomposite can be made via in situ and instant melt ring-opening polymerization of the COBDS-VMT nanocomposite precursor. High molecular weight POBDS polymer can be formed in a few minutes. The nano scale dispersion of VMT layers within POBDS polymer was confirmed by both the X-ray diffraction patterns and TEM examinations. This methodology provides a potential approach to synthesize high performance polymer nanocomposite.     

Analysis of nine rhubarb anthraquinones and bianthrones by micellar electrokinetic chromatography using experimental design

An efficient micellar electrokinetic chromatography (MEKC) method has been developed for the analysis of nine anthraquinones and bianthrones in rhubarb. A chemometric approach was used to search for the optimum conditions of separation. Those factors which were found to be significant with a screening design were further optimized with a central composite face-centered (CCF) design. Acetonitrile concentration was found to be the most influential, not only in resolution, but also in analysis time and peak asymmetry. With the optimized conditions: 15 mM sodium tetraborate/15 mM sodium dihydrogenphosphate buffer, 30 mM sodium deoxycholate, pH 8.6, 17 vol.% acetonitrile and 28 kV, nine tested analytes were baseline-separated within 14 min. The method was validated to analyze the rhubarb material. Solid-phase extraction (SPE) was manipulated to remove interfering substances. Five anthraquinones and two glycosidic bianthrones were detected and quantificated. The method should be suitable for determining these major active principles in rhubarb crude drugs.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.     

Synthesis of 5‐Radioiodoarabinosyl Uridine Analog for Probing the HSV‐1 Thymidine Kinase Gene

Tumor cells transduced with herpes simplex virus thymidine kinase gene have been intensively applied to the field of positron emission tomography via imaging of its substrate. As a pilot synthesis approach, a facile preparation of 5‐[¹²⁵I] iodoarabinosyl uridine starting from commercially available uridine is reported herein.