A posteriori error estimates for mixed finite element approximations of parabolic problems

We derive residual based a posteriori error estimates for parabolic problems on mixed form solved using Raviart–Thomas–Nedelec finite elements in space and backward Euler in time. The error norm considered is the flux part of the energy, i.e. weighted L ²(Ω) norm integrated over time. In order to get an optimal order bound, an elementwise computable post-processed approximation of the scalar variable needs to be used. This is a common technique used for elliptic problems. The final bound consists of terms, capturing the spatial discretization error and the time discretization error and can be used to drive an adaptive algorithm.     

Synthesis of blue imino(pentafluorophenyl)phosphane

The reaction of AgC(6)F(5) with monomeric iminophosphanes of Mes*-N═P-X (X = Cl, I) in CH(2)Cl(2) at ambient temperature gives imino(pentafluorophenyl)phosphane, Mes*N═P(C(6)F(5)) (1), in almost quantitative yield (96%), which could be isolated as a highly viscous blue oil. The same reaction with LiC(6)F(5) results in the formation of imino(amino)phosphane (C(6)F(5))(2)P-N(Mes*)-P═NMes* (2) (yield 93%). In the second series of experiments the analogous reaction of MC(6)F(5) (M = Ag, Li) with dimeric [Cl-P(μ-N-Dipp)](2) was studied, leading to the formation of [R-P(μ-N-Dipp)](2) (R = C(6)F(5)) (3) for M = Ag, while only decomposition products such as P(C(6)F(5))(3) were observed in the reaction with the Li salt. Highly labile Mes*-N═P-C(6)F(5) (1) decomposes at ambient temperatures, forming among other products the diphosphane (C(6)F(5))(2)P-P(C(6)F(5))(2) (4). Reaction of 1 with Fe(2)(CO)(9) yields the iron carbonyl complexes Mes*-N═P(C(6)F(5))·Fe(CO)(4) (5) and [Mes*-N═P(C(6)F(5))](2)·Fe(CO)(3) (6). The structure, bonding, and potential energy surface are discussed on the basis of B3LYP/6-31G(d,p) computations. According to time-dependent B3LYP calculations, the blue color of 1 arises from an n → π* electronic transition.     

Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 2 – Development of an experimental procedure for the determination of the molar mass of silicon using MC-ICP-MS

The isotopic abundances and thus molar mass M(Si) of a silicon crystal material with natural isotopic abundances have been measured for the first time using multicollector-ICP-mass spectrometry (MC-ICP-MS) in combination with a novel concept of a modified isotope dilution mass spectrometry (IDMS)-method. This experimental work is the further development of part 1 of this series of papers. While part 1 describes the theoretical background and the mathematical derivation of the novel concept in detail, the measurements presented here serve to validate the novel concept and give experimental proof of its capability. Moreover, the also new method for the analytical calculation of calibration factors needed in the determination of absolute isotope amount ratios has been tested successfully. Silicon isotopic abundances have been measured directly from an aqueous alkaline matrix following a new sample preparation protocol developed within the framework of this study. A molar mass of M(Si) = 28.08548(13) g/mol with an associated relative uncertainty of u_rel = 4.6 × 10^?6 (k = 1) has been measured. This is in excellent agreement with the current IUPAC value for the molar mass of natural silicon M(Si_nat) = 28.08550(15) g/mol with u_rel = 5.3 × 10^?6 (k = 1). An uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was calculated to assess the presented results and to validate the novel concept with the help of experimental data. The development of a new experimental procedure is presented in detail and the contributions to the uncertainty are discussed in comparison to part 1 of this work.     

Temperature-controlled 'breathing' of carbon dioxide bubbles

We report a microfluidic (MF) approach to studies of temperature mediated carbon dioxide (CO(2)) transfer between the gas and the liquid phases. Micrometre-diameter CO(2) bubbles with a narrow size distribution were generated in an aqueous or organic liquid and subsequently were subjected to temperature changes in the downstream channel. In response to the cooling-heating-cooling cycle the bubbles underwent corresponding contraction-expansion-contraction transitions, which we term 'bubble breathing'. We examined temperature-controlled dissolution of CO(2) in four exemplary liquid systems: deionized water, a 0.7 M aqueous solution of NaCl, ocean water extracted from Bermuda coastal waters, and dimethyl ether of poly(ethylene glycol), a solvent used in industry for absorption of CO(2). The MF approach can be extended to studies of other gases with a distinct, temperature-dependent solubility in liquids.     

Heck and Suzuki–Miyaura couplings catalyzed by nanosized palladium in polyaniline

A novel route to prepare polyaniline (PANI)‐supported Pd(0) nanoparticles by a one‐pot chemical route is presented. Nanosized Pd(0) particles were first prepared by reduction of Pd(OAc)₂ using t‐BuONa activated sodium hydride in refluxing THF. A ligand exchange with aniline on t‐BuONa‐stabilized Pd(0) particles yielded aniline‐stabilized particles. Pd(0)/PANI nanocomposites were finally obtained by polymerizing aniline‐stabilized Pd(0) particles using ammonium persulfate. Nanocomposites were characterized by transmission electron microscopy, X‐ray diffraction and X‐ray photoelectron spectroscopy. Results show that this one‐pot experimental route is successful in producing hybrid materials constituted of Pd(0) nanoparticles stabilized by PANI due to the strong binding of PANI amine groups to Pd(0) particles. TEM images of the nanohybrids show that metal particles with diameters of ca. 4.9 nm are homogeneously dispersed in PANI. The preliminary results indicate that the Pd(0) particles supported on PANI behave as efficient heterogeneous catalysts in the Heck and Suzuki–Miyaura reactions of aryl iodides. Copyright © 2005 John Wiley & Sons, Ltd.     

Flow equations for the relevant part of the pure Yang—Mills action

Wilson’s exact renormalization group equations are derived and integrated for the relevant part of the pure Yang-Mills action. We discuss in detail how modified Slavnov—Taylor identities control the breaking of BRST invariance in the presence of a finite infrared cutoff k through relations among different parameters in the effective action. In particular they imply a nonvanishing gluon mass term for nonvanishing k. The requirement of consistency between the renormalization group flow and the modified Slavnov—Taylor identities allows to control the self—consistency of truncations of the effective action.     

Synthesis and structural characterization of mixed aluminum-gallium-offretites

A new synthesis procedure is reported for the preparation of mixed Al,Ga-offretites over the entire solid solution range 0 ≤ Ga/(Ga + Al) ≤ 1. The resulting materials are characterized by X-ray powder diffraction, adsorption microcalorimetry and multinuclear solid state NMR. The ²⁹Si MAS-NMR data are consistent with statistical occupancy of the T₁ and T₂ sites by aluminum and gallium, and also show no positive evidence for preferential siting effects between both framework metals. Isotropic chemical shifts and nuclear electric quadrupolar coupling constants for ²⁷Al and ⁷¹Ga have been obtained from a field-dependent analysis of the center of gravity in the MAS-NMR spectra. H-Al, Ga-offretites produced by ammonium exchange and subsequent calcination reveal evidence of partial demetallation of the framework with formation of extra-lattice metal species.