Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory

It is well known that apparently similar discretization schemes of Maxwell's equations in Fourier series may provide very different convergence performances because of truncation. We argue that this work performed in grating theory can be applied to other electromagnetic theories relying on expansions over series different from Fourier series. This generalization is supported by an intuitive argument and by a simple numerical example with Hermite–Gauss functions.     

International Symposium on 'Nanoparticles: Technology and Sustainable Development,' Taipei,Taiwan, September 9–10, 2002

Journal of Nanoparticle Research -     

Aerosol Charge Neutralization by a Radioactive Alpha Source

The performance of a Po-210 radioactive ionizer for aerosol charge neutralization and bipolar charging has been evaluated. Monodisperse neutral and singly charged aerosols have been passed through the ionizer and their approach to the steady-state Boltzmann charge measured by measuring the fraction of particles that are electrically charged. The result shows that an Nt of approximately 2.5 × 10⁵ cm^?3 s is needed for the development of a steady-state charge fraction equal to that given by the Boltzmann' s law where N is the ion concentration and t is the residence time of the aerosol in the neutralizer. In addition, the performance of the ionizer for particle charge neutralization in a vibrating-orifice aerosol generator has been evaluated and the result shows that the source is less effective for this application and the residual charge on the particles is considerably higher than that given by the Boltzmann's law.     

Transport with a Very Low Density Contrast in Hele–Shaw Cell and Porous Medium: Evolution of the Mixing Zone

The optimal concentration of a blue dye solution with 'tracer' properties, enabling a pollutant to be marked was determined by the use of numerical, theoretical and experimental approaches. Experimental investigations were performed on a transparent Hele–Shaw cell and the concentration distribution was analyzed using an optical technique based on dye light absorption properties. The injected optimal concentration was established thanks to a theoretical and experimental study carried out on the output signal dynamics. Using the same experimental conditions, numerical simulations were performed. The very good agreement between the data (experimental and numerical) clarified that: (i) the choice of the blue dye optimal concentration was valid and (ii) the concentration-dependent density should not be neglected in flow and transport equations even if it concerns a so-called 'tracer'. Following this remark, a theoretical aspect was developed in order to determine the analogous conditions between a Hele–Shaw cell and a porous medium for the variable density transport phenomenon. The structure of the concentration-dependent dispersion tensor used in the numerical code was obtained by homogenizing the Stokes flow of a bi-component mixture. The numerical results show that, as long as the tracer density does not exceed a certain value, it is not necessary to take into account a density contrast in terms of the dispersion tensor. The classical form of the Taylor dispersion tensor can be used successfully.     

A mild and efficient palladium-catalyzed cyanation of aryl chlorides with K4[Fe(CN)6

An efficient palladium-catalyzed cyanation of aryl chlorides is established. In the presence of a highly effective Pd/CM-phos catalyst, cyanation of aryl chlorides proceeds at 70 °C in general, which is the mildest reaction temperature achieved so far for this process. Common functional groups such as keto, aldehyde, ester, nitrile and -NH(2), and heterocyclic coupling partners including N-H indoles are well tolerated. Moreover, a sterically hindered nonactivated ortho,ortho-disubstituted electrophile is shown to be a feasible coupling partner in cyanation.     

On the roles of solid-bound ligand scavengers in the removal of palladium residues and in the distinction between homogeneous and heterogeneous catalysis

We have studied the roles and behavior of typical resin- and silica-bound thiol scavengers in the removal of palladium (Pd) residues and in the determination of the true catalytic species in the Heck coupling of bromobenzene and styrene. The results of Pd scavenging and catalyst poisoning by elemental analysis (EA) and transmission electron microscopy (TEM) indicate that silica-bound thiols have an advantage over resin-bound thiols in residual Pd removal from a Heck reaction solution and that all of these scavengers poison effectively the catalytic species but hardly scavenge Pd clusters, even as small as 1 nm from solution presumably because of the steric barrier. Because of a smaller proportion of soluble Pd clusters, using a molecular Pd precatalyst results in a much higher Pd scavenging efficiency than using a supported Pd particle precatalyst. With the aid of catalyst poisoning by the scavengers, filtration testing and TEM studies further illustrate that Pd clusters are inactive for the Heck reaction over Pd(0)/SiO(2), with molecular Pd(0) being solely active. Studies through EA and thermogravimetric analysis suggest that the bound thiols are leached from the scavengers to a different extent at reaction temperatures of 90-135 °C, probably owing to base-catalyzed decomposition or based-promoted dissociation of functional groups from the surfaces, leading to interaction between leached thiols and a solid Pd precatalyst. Meanwhile, the effect of solid-bound thiol binding to soluble Pd on the efficiency of Pd scavenging and the impact of a scavenger on the Pd leaching from supported Pd particles are discussed.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.     

TG–FTIR analysis applied to the study of thermal behaviour of some edible mushrooms

The article is devoted to the study on the thermal behaviour of three species of edible mushrooms: Boletus edulis (foot and cap), Pleurotus ostreatus (foot and cap), Lactarius deterrimus (cap) by the TG–FTIR-coupled technique, in air, over the 30–900 °C temperature range. The analysis of the TG–DTG–DTA curves reveals the thermal degradation mechanism to be complex and specific to every species under the recording conditions applied. A similar degradation mechanism is noticed for the foot and cap of Pleurotus ostreatus in comparison with the Boletus edulis and Lactarius deterrimus species where the mechanisms are different. The TG–FTIR analysis, combustion heats and IR spectra of the starting samples also support these results. The initial degradation temperatures from TG–DTG indicate the temperature range where these species are thermally stable and their nutrient features maintained making them proper for food. The TG–FTIR analysis gives information on the gaseous species evolved by the thermal degradation bringing thus a contribution to the elucidation of the changes developing by processing the edible mushrooms (industrialization, conservation, culinary preparations, etc.) at temperatures above the initial degradation temperature. At the same time, the environmental impact, when the mushroom failed cultures are burned, is also important.     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.     

Emerging Issues in Nanoparticle Aerosol Science and Technology

Journal of Nanoparticle Research -