Absorbing boundary conditions for the wave equation and parallel computing

Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equation. In turn this application gives the idea of introducing a layer close to the truncation boundary which leads to a new way of optimizing absorbing boundary conditions for truncating domains. We optimize the conditions in the case of straight boundaries and illustrate our analysis with numerical experiments both for truncating domains and the Schwarz waveform relaxation algorithm.

     

Acetate- and thiol-capped monodisperse ruthenium nanoparticles: XPS, XAS, and HRTEM studies

Monodisperse ruthenium nanoparticles were prepared by reduction of RuCl3 in 1,2-propanediol. The mean particle size was controlled by appropriate choice of the reduction temperature and the acetate ion concentration. Colloidal solutions in toluene were obtained by coating the metal particles with dodecanethiol. High-resolution transmission electron microscopy (HRTEM), X-ray photoelectron spectroscopy (XPS), and X-ray absorption spectroscopy (XANES and EXAFS for the Ru K-absorption edge) were performed on particles of two different diameters, 2 and 4 nm, and in different environments, polyol/acetate or thiol. For particles stored in polyol/acetate XPS studies revealed superficial oxidation limited to one monolayer and a surface coating containing mostly acetate ions. Analysis of the EXAFS spectra showed both oxygen and ruthenium atoms around the ruthenium atoms with a Ru-Ru coordination number N smaller than the bulk value, as expected for fine particles. In the case of 2 nm acetate-capped particles N is consistent with particles made up of a metallic core and an oxidized monolayer. For 2 nm thiol-coated particles, a Ru-S bond was evidenced by XPS and XAS. For the 4 nm particles XANES and XPS studies showed that most of the ruthenium atoms are in the zerovalent state. Nevertheless, in both cases, when capped with thiol, the Ru-Ru coordination number inferred from EXAFS is much smaller than for particles of the same size stored in polyol. This is attributed to a structural disorganization of the particles by thiol chemisorption. HRTEM studies confirm the marked dependence of the structural properties of the ruthenium particles on their chemical environment; they show the acetate-coated particles to be single crystals, whereas the thiol-coated particles appear to be polycrystalline.     

One-pot synthesis of oxazoles using isocyanide surrogates

We wish to present herein a simple one-pot synthesis of 2,5-disubstituted oxazoles, starting from benzyl halides and acyl chlorides. The in situ formation of isocyanides, followed by the addition of an acyl chloride in the presence of a base leads to the desired oxazoles in good yields.     

Tris(triphenylphosphine)rhodium cyano and triphenylcyanoborate complexes: Structures and a DFT study

The structures of [Rh(CN)(PPh₃)₃](EtOH) (1), [Rh(NCBPh₃)(PPh₃)₃] (2), and [Rh(CNBPh₃)(PPh₃)₃] (3) are reported together with a density functional theory (DFT) study of the model compounds [Rh(NCBH₃)(PH₃)₃] and [Rh(CNBH₃)(PH₃)₃]. Compound 1 crystallizes in space group Pc with a = 10.4798(15) Å, b = 12.5410(18) Å, c = 19.974(3) Å and = 112.215(6)°; compound 2 crystallizes in space group with a = 12.929(2) Å, b = 14.362(2) Å, c = 17.575(3) Å and = 92.544(3)°, = 90.214(3)°, = 113.831(3)°; compound 3 crystallizes in space group with a = 12.915(2), b = 14.296(2), c = 17.664(3) Å and = 92.469(3)°, = 90.088(3)°, = 113.768(3)°. All three complexes show slight tetrahedral distortion from ideal square planar geometry (largest for 1). Differences in the reactivity and stability of 2 and 3 are interpreted according to the results of a density functional theory study.     

Turbulence Models and Large Eddy Simulations Applied to Ascending Mixed Convection Flows

Coolant flows in the cores of current gas-cooled nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be significantly modified from the forced convection condition by the action of buoyancy, and the thermal-hydraulic regime is no longer one of pure forced convection. These modifications are associated primarily with changes to the turbulence structure. Flow laminarization may occur, and in that event heat transfer rates may be as low as 40% of those in the corresponding forced convection case. The present work is concerned with the modelling of such ??mixed?? convection flows in a vertical heated pipe. All fluid properties are assumed to be constant and buoyancy is accounted for within the Boussinesq approximation. Six different Eddy Viscosity Models (EVMs) are examined against experimental measurements and the direct numerical simulation (DNS) data of You et?al. (Int J Heat Mass Transfer 46:1613?C1627, 2003). The EVMs selected for study embody distinct physical refinements with respect to the parent high-Reynolds-number k-?? model. Large Eddy Simulations employing the classical Smagorinsky sub-grid-scale model are also presented. It is found that the early EVM scheme of Launder and Sharma (1974) is the turbulence model in the closest agreement with direct simulation results for the ratio of mixed-to-forced convection Nusselt number, Nu/Nu ₀; the model in the poorest accord with the DNS data is a k-??-SST formulation. However, in relation to comparisons with both numerical and experimental data for forced convection Nusselt number, Nu ₀, the present work reveals that some of the more recent models perform better than the Launder-Sharma scheme. No single scheme is in consistently close agreement with the numerical simulation flow profiles.     

Effects of several lanthanide trichloride hydrates on the melting behavior and spherulitic superstructure of poly(ethylene oxide)

Binary mixtures of poly(ethylene oxide) (PEO) with the trichloride hydrates of lanthanum, cerium, europium, terbium, and ytterbium have been studied with calorimetry, polarized optical microscopy, and infrared spectroscopy. Melting‐point depression of the PEO‐rich phase occurs in all cases. At sufficiently high concentrations of the low molecular weight lanthanide complex, crystallization of the polymer is absent. The lighter lanthanides with larger ionic radii, such as lanthanum and cerium, are more effective in suppressing PEO crystallization from solution or the molten state because they are more oxophilic. The spherulitic superstructure of PEO disappears at rather low concentrations of the lanthanide salts, between 2 and 8 mol % Ln³⁺. Lanthanum and terbium are most efficient at disrupting the formation of PEO spherulites, and europium is least efficient. Infrared spectroscopy identifies twisting and wagging vibrational absorptions of CH₂ groups in the polymer that are sensitive to the morphologies of these mixtures. Modifications of the PEO infrared absorbances in the presence of these five lanthanide salts correlate more closely with the presence or absence of major PEO melting, not the formation of a spherulitic superstructure. The phase behavior is rather simple, with no evidence of eutectic solidification upon cooling from the molten state. Multiple melting endotherms are observed in the differential scanning calorimetry heating traces of binary mixtures containing 8 mol % Yb³⁺ and between 10 and 20 mol % Eu³⁺, but the concentration dependence of these first‐order endothermic transitions is not characteristic of eutectic phase behavior. The presence of trivalent cations, such as Eu³⁺ or Yb³⁺, in these complexes perturbs the crystallization kinetics of PEO upon cooling from the molten state, as well as the melting behavior upon heating. Ion–dipole or electrostatic interactions between the lanthanide cation and the ether oxygen of PEO might alter the surface free energy at the periphery of the crystalline lamellae and perturb the chain‐folding characteristics of PEO. Consequently, coupling between the amorphous matrix and the PEO crystallites is strengthened, and this provides stability for the existence of multiple‐chain‐folded crystals composed of rather thin lamellae that could be responsible for multiple melting behavior. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2200–2213, 2003