Construction of Equilibrium Magnetic Vector Potentials

In [9] we introduced the notion of equilibrium surface current JdS_x on the closed C smooth surfaces in R ³ as a generalization of electric solenoid, and proved their existence. We here show an algorithm for JdS_x starting from a given surface current J dS_x on .     

Wavelet bases in

Some years ago, compactly supported divergence-free wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of . These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier-Stokes equations. In this paper, we construct stable wavelet bases for the stream function spaces . Moreover, -free vector wavelets are constructed and analysed. The relationship between and are expressed in terms of these wavelets. We obtain discrete (orthogonal) Hodge decompositions.

Our construction works independently of the space dimension, but in terms of general assumptions on the underlying wavelet systems in that are used as building blocks. We give concrete examples of such bases for tensor product and certain more general domains . As an application, we obtain wavelet multilevel preconditioners in and .

     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

Chemical kinetics at high pressure

Abstract

Numerous studies have demonstrated the importance to include pressure as a kinetic parameter in the elucidation of inorganic reaction mechanisms. These studies have specially led to a better understanding and a systematic classification of solvent exchange and ligand substitution reactions of octahedral complexes of transition metal elements. The mechanistic picture for substution reactions on square planar complexes is well established and involves a concurrent bimolecular attack by solvent and the nucleophile on the substrate with a considerable discrimination among different entering groups. The search for factor promoting the conversion of the normal associative mode of activation into a dissociative process has then attracted much attention. Two attempts to induce dissociation, as studied by high-pressure NMR, are presented: one is to prevent the formation by means of sterically hindered ligands, the other one is to promote bond weakening at the leaving group.     

THE EFFECT OF POLYMER COMPOSITION ON THE MOLECULAR ADSORPTION AREA OF THE EMULSIFIER

Conductometric coap titration and Maron's³ method of plotting polymer concentration vs. soap concentration is used to determine the molecular adsorption area (MAA) of potassium oleate in a number of polymer and copolymer latex systems. It is demonstrated that the MAA of potassium oleate increases in the series polystyrene→ polybutadiene→polystyrene-coacrylonitrile as well as in a series of polystyrene-coacrylonitrile systems with increasing acrylonitrile content in the polymer composition

It is further demonstrated that the MAA increases with temperature at rates dependent on the chemical nature of the polymer systems. The composition induced increases in the MAA correlate as well with the polar nature of the polymer and are attributed to decreasing solubility of the lyophilic segment of the emulsifier chain in the polymer. Temperature induced MAA increases are attributed to Increasing mobility of the hydrophylic emulsifier segment in the aqueous phase.     

Zur affinen Differentialgeometrie zweier komplexer Veränderlicher: Flächen im vierdimensionalen Raume

Ohne Zusammenfassung     

Synthesis of dendritic macromolecules through divergent iterative thio‐bromo “Click” chemistry and SET‐LRP

The development of a novel nucleophilic thio‐bromo “Click” reaction, specifically base‐mediated thioetherification of thioglycerol with α‐bromoesters was reported in an earlier article. The combination of this thio‐bromo click reaction with subsequent acylation with 2‐bromopropionyl bromide provides an iterative two‐step divergent growth approach to the synthesis of a new class of poly(thioglycerol‐2‐ propionate) (PTP) dendrimers. In this article, the addition of a third step, the single‐electron transfer living radical polymerization (SET‐LRP) of methyl acrylate (MA), was shown to provides access to a three‐step “branch” and “grow” divergent approach to dendritic macromolecules wherein poly(methyl acrylate) (PMA) connects the branching subunits. This facile methodology can provide a diversity of dendritic macromolecular topologies and will ultimately provide the means to the development of self‐organizable dendritic macromolecules. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3940–3948, 2009     

Treanor pumping of CO initiated by CO laser excitation

An experiment is discussed in which CO can be excited up to energies of several electronvolts by the absorption of infrared radiation from a relatively low-power CO laser. Furthermore, experimental results are examined through kinetic modelling. In the experiment, the beam of an intracavity-chopped CO laser operating on all lines at 500 mW and containing a few milliwatts of the fundamental ν= 1→0 band component, is focused into an absorption cell containing a mixture of CO and Ar. The absorption of this infrared radiation is monitored by the optoacoustic effect. A second CO laser operating cw and capable of providing 8 W on all lines but not lasing on the ν= 1→0 band component, is then focused into the same volume in the absorption cell. With both lasers simultaneously focused into the absorption cell, strong fluorescence from the irradiated region is detected by a photomultiplier tube. Modulation of the signal intensity with time is observed, and indicates chemical destruction of the CO in the cell. An analysis and kinetic modelling calculation of this experiment shows that it is possible to excite CO up to high vibrational quantum numbers (ν40) at gas temperatures up to 800 K. by means of CO laser irradiation at the fundamental ν= 1→0 band component. One source responsible for the fluorescence signal observed in the experiment is identified as the 4th positive A ¹Π→X ¹Σ⁺ spontaneous emission. Although the present kinetic model does not incorporate the chemical processes that may lead to the production of additional fluorescing species such as C₂, good agreement is obtained with the observed fluorescence signal characteristics.     

X‐ray photoelectron spectroscopic chemical state quantification of mixed nickel metal,oxide and hydroxide systems

Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)₂, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O₂ and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd.