Implementing and using high-order finite element methods

We present theoretical analyses of and detailed timings for two programs which use high-order finite element methods to solve the Navier- Strokes equations in two and three dimensions. The analyses show that algorithms popular in low-order finite element implementations are not always appropriate for high-order methods. The timings show that with the proper algorithms high-order finite element methods are viable for solving the Navier-Stokes equations. We show that it is more efficient, both in time and storage, not to precompute element matrices as the degree of approximating functions increases. We also study the cost of assembling the stiffness matrix versus directly evaluating bilinear forms in two and three dimensions. We show that it is more efficient not to assemble the full stiffness matrix for high-order methods in some cases. We consider the computational issues with regard to both Euclidean and isoparametric elements. We show that isoparametric elements may be used with higher-order elements without increasing the order of computational complexity.     

A Note on Veraverbeke's Theorem

We give an elementary probabilistic proof of Veraverbeke's theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general attained through a single large jump.     

Zero-shift values of automatic and inexpensive strain-gage instrumentation systems

Computer-controlled data-acquisition systems are being used extensively for gathering strain-gage data. This paper explores the relative merits of using modern solidstate digital multi-meters (DDM) to measure the strain-gage resistance directly rather than using a conventional Wheatstone bridge. Both a direct-resistance measurement scheme and a reversed current scheme are compared over long measurements terms of 6 and 12 days using a 6 1/2-digit multimeter. The results show that the reversed current method is superior in maintaining the zero-gage resistance reading at the cost of using several meters. Possibly the direct-resistance method can be improved so that the operation and equipment can be simplified.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 4–6.     

Covalently Binding Atomically Designed Au9 Clusters to Chemically Modified Graphene

Atomic‐resolution transmission electron microscopy was used to identify individual Au₉ clusters on a sulfur‐functionalized graphene surface. The clusters were preformed in solution and covalently attached to the surface without any dispersion or aggregation. Comparison of the experimental images with simulations allowed the rotational motion, without lateral displacement, of individual clusters to be discerned, thereby demonstrating a robust covalent attachment of intact clusters to the graphene surface.     

Regiodivergent and Stereoselective Hydrosilylation of 1,3‐Disubstituted Allenes

Methods for the highly stereoselective and regiodivergent hydrosilylation of 1,3‐disubstituted allenes have been developed. The synthesis of E allylsilanes is accomplished with palladium NHC catalysts, and trisubstituted Z alkenylsilanes are accessed with nickel NHC catalysts. Unsymmetrically substituted allenes are well tolerated with nickel catalysis and afford Z alkenylsilanes. Evidence for a plausible mechanism was obtained through an isotopic double‐labeling crossover study.     

Aerobic Palladium‐Catalyzed Dioxygenation of Alkenes Enabled by Catalytic Nitrite

Catalytic nitrite was found to enable carbon–oxygen bond‐forming reductive elimination from unstable alkyl palladium intermediates, providing dioxygenated products from alkenes. A variety of functional groups were tolerated, and high yields (up to 94 %) were observed with many substrates, also for a multigram‐scale reaction. Nitrogen dioxide, which could form from nitrite under the reaction conditions, was demonstrated to be a potential intermediate in the catalytic cycle. Furthermore, the reductive elimination event was probed with ¹⁸O‐labeling experiments, which demonstrated that both oxygen atoms in the difunctionalized products were derived from one molecule of acetic acid.     

Synthesis of Inorganic Structural Isomers By Diffusion‐Constrained Self‐Assembly of Designed Precursors: A Novel Type of Isomerism

The structure of precursors is used to control the formation of six possible structural isomers that contain four structural units of PbSe and four structural units of NbSe₂: [(PbSe)_1.14]₄[NbSe₂]₄, [(PbSe)_1.14]₃[NbSe₂]₃[(PbSe)_1.14]₁[NbSe₂]₁, [(PbSe)_1.14]₃[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₂, [(PbSe)_1.14]₂[NbSe₂]₃[(PbSe)_1.14]₂[NbSe₂]₁, [(PbSe)_1.14]₂[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₁[(PbSe)_1.14]₁[NbSe₂]₁, [(PbSe)_1.14]₂[NbSe₂]₁[(PbSe)_1.14]₁[NbSe₂]₂[(PbSe)_1.14]₁[NbSe₂]₁. The electrical properties of these compounds vary with the nanoarchitecture. For each pair of constituents, over 20 000 new compounds, each with a specific nanoarchitecture, are possible with the number of structural units equal to 10 or less. This provides opportunities to systematically correlate structure with properties and hence optimize performance.     

The effects of substituent grafting on the interaction of pH-responsive polymers with phospholipid monolayers

pH-responsive amphiphilic polymers with suitable graftings have demonstrated highly efficient cell membrane activity and hence are promising applicants for drug-delivery. Grafting the hydrophobic amino acid l-phenylalanine and the hydrophilic methoxy poly(ethylene glycol) amine onto the pendant carboxylic acid moieties of a linear polyamide, poly(l-lysine isophthalamide), can effectively modify the amphiphilicity and conformation of the amphiphilic polymers. Here, the interactions of these polymers with phospholipid monolayers adsorbed on mercury (Hg) electrodes have been studied. AC voltammetry (ACV), rapid cyclic voltammetry (RCV), and electrochemical impedance spectroscopy (EIS) have been applied to monitor phospholipid monolayer associations with different polymer concentrations under different pH values. The polymers interact reversibly with the monolayer shown by altering the monolayer capacitance and inhibiting the phospholipid reorientation in electric field. Polymer grafting enhances the pH-mediated conformational change of the polymers which in turn increases their phospholipid monolayer activity. The most significant monolayer interactions have been observed with the polymer grafted with hydrophobic l-phenylalanine. A low level of PEGylation of the backbone also increases the monolayer activity. The polymer/DOPC interactions have been represented with an impedance model, which takes account of the interaction giving rise to an increase in monolayer capacitance and inhomogeneity and a Debye type dielectric relaxation. The extent of penetration of the polymers into the monolayer is inversely related to the electrical resistance they give rise to during the Debye relaxation. The cell membrane activities of these amphiphilic polymers have been successfully mirrored in this supported DOPC monolayer system, isolating the key parameters for biomembrane activities and giving insight into the mechanism of the interactions. The conclusions from this study provide strategic directions in material design catering to different requirements in biomedical applications.     

Organometallic reactivity: the role of metal-ligand bond energies from a computational perspective

The association and dissociation of ligands plays a vital role in determining the reactivity of organometallic catalysts. Computational studies with density functional theory often fail to reproduce experimental metal-ligand bond energies, but recently functionals which better capture dispersion effects have been developed. Here we explore their application and discuss future challenges for computational studies of organometallic catalysis.     

Metal-containing triarylboron compounds for optoelectronic applications

Triarylboranes have recently emerged as a powerful new class of electron acceptors with great potential as optoelectronic materials. The empty p(z) orbital on the boron centre promotes strong charge-transfer transitions, leading to highly luminescent compounds with colors spanning the entire visible spectrum. Due to intense research efforts over the past decade, many examples now exist of organic molecules based on this structural motif. Only recently, however, have transition metal-containing triarylboranes been closely investigated. These compounds are capable of bright luminescence from a triplet excited state, and have been developed as efficient emissive materials for organic light-emitting diodes (OLEDs) as a result. In addition, their long-lived phosphorescence gives these materials potential as highly selective chemical sensors for small anions using time-gated detection, eliminating interference from background fluorescence. The research of the past several years has now led to a better understanding of the impact of the triarylboron group on the photophysical properties of metal complexes, which we expect will provide many opportunities for research into this class of functional phosphorescent materials.