The Floating Ball Paradox

In capillary theory there are two kinds of surface tension. There is the surface tension at the interface between two immiscible fluids. Thomas Young [9] also allowed for there to be a surface tension associated with a liquid-solid interface. He proceeded to use a balance of forces argument to derive the well-known contact angle condition along a liquid-liquid-solid intersection. The validity of this argument has recently been called into question by R. Finn [6]. A floating ball experiment discussed in that paper leads to an apparent paradox. We address this issue.      

Renormalised Steepest Descent in Hilbert Space Converges to a Two-Point Attractor

The result that for quadratic functions the classical steepest descent algorithm in R ^d converges locally to a two-point attractor was proved by Akaike. In this paper this result is proved for bounded quadratic operators in Hilbert space. The asymptotic rate of convergence is shown to depend on the starting point while, as expected, confirming the Kantorovich bounds. The introduction of a relaxation coefficient in the steepest-descent algorithm completely changes its behaviour, which may become chaotic. Different attractors are presented. We show that relaxation allows a significantly improved rate of convergence.     

A free-electron laser generated gamma-ray beam for nuclear physics

The High Intensity Gamma Ray Source (HIγS), a collaborative project between TUNL and the Duke Free Electron Laser Laboratory, is described. An initial experiment and plans for a future research program are discussed briefly.     

A Template‐Free Route to Polypyrrole Nanofibers

A template‐free method for the production of polypyrrole nanofibers is presented. By adding a small amount of bipyrrole into the oxidative polymerization of pyrrole, a drastic change in the morphology of the observed material is observed from large, granular particles to nanofibrils with an average diameter of 20 nm. This simple procedure allows for the production of polypyrrole nanofibers without the presence of surfactants or other structural directing agents. The polypyrrole nanofibers can form stable water dispersions which can be cast into films of sufficient quality to function as chemical sensors for analytes such as ammonia.

     

Exotic Capillary Tubes

In contrast to the standard capillary tube, an exotic capillary tube is a rotationally symmetric tube of variable cross-section which if positioned correctly in a vessel of fluid possesses a continuum of equilibrium configurations. The controlling variables are the capillary constant k = ρ g/σ and the contact angle γ. Lowering the tube slightly from its natural position causes the tube to completely fill up while raising the tube slightly forces the tube to drain out. Other surprising consequences follow.     

Silver-Catalysed Enantioselective Addition of O?H and N?H Bonds to Allenes: A New Model for Stereoselectivity Based on Noncovalent Interactions

The ability of silver complexes to catalyse the enantioselective addition of O H and N H bonds to allenes is demonstrated for the first time by using optically active anionic ligands that were derived from oxophosphorus(V) acids as the sources of chirality. The intramolecular addition of acids, alcohols, and amines to allenes can be achieved with up to 73 % ee. The exploitation of a C H anomeric effect allowed the absolute configuration of a sample of 2-substituted tetrahydrofuran of low ee to be unambiguously assigned by comparison of the chiroptical ORD and VCD measurements with calculated spectra. In the second part of the work, the origin of the stereoselectivity was probed by DFT free-energy calculations of the transition states. A new model of enantiomeric differentiation was developed that was based on noncovalent interactions. This model allowed us to identify the source of stereoselectivity as weak attractive interactions; such dispersive forces are often overlooked in asymmetric catalysis. A new computational approach was developed that represents these interactions as colour-coded isosurfaces that are characterised by the reduced density-gradient profile.     

Thermodynamic and stereochemical aspects of the polymerizability of glycolide and lactide

The ring-opening polymerizations of the dilactones glycolide and the S,S- and S,R-stereoisomers of lactide were studied using quantum mechanical methods. The ring strain and the conformational distribution of these cyclic monomers and of the polymers were calculated, and the effect of the medium on the polymerization was predicted, for both bulk and solution. The polymerizability of the three monomers in the gas phase, that is, nonpolar medium, is much greater than that of δ-valerolactone or 1,4-dioxan-2-one. This difference vanishes in the polar medium chloroform, which is attributed to the fact that, while all of these monomers possess polar cis-lactone bonds, the three dilactones possess small dipole moments. The data are combined to give polymerization enthalpy and free energy values. The four stereoregular lactide polymers did not differ significantly in energy. Accordingly, the ability to synthesize any one of these rests on catalyst specificity (“polymer chain-end control”). Although introduction of sterically demanding methyl groups into glycolide is expected to favor coiled conformations and decrease polymerizability, this was not found to be the case. Good agreement of calculated values with experimental data from the literature was achieved.