Brownian Motion and Ornstein–Uhlenbeck Processes in Planar Shape Space

We discuss Brownian motion and Ornstein–Uhlenbeck processes specified directly in planar shape space. In particular, we obtain the drift and diffusion coefficients of Brownian motion in terms of Kendall shape variables and Goodall–Mardia polar shape variables. Stochastic differential equations are given and the stationary distributions are obtained. By adding in extra drift to a reference figure, Ornstein–Uhlenbeck processes can be studied, for example with stationary distribution given by the complex Watson distribution. The triangle case is studied in particular detail, and some simulations given. Connections with existing work are made, in particular with the diffusion of Euclidean shape. We explore statistical inference for the parameters in the model with an application to cell shape modelling.      

Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons

Grating coupling of light to surface plasmon-polaritons (SPPs) supported by a thin metal film depends on the detailed geometry of the grating used to couple the incident light to the SPP modes. Here we show experimental and theoretical evidence that, in the case of square gratings having the same pitch and depth, the maximum coupling of light to the SPPs is achieved when the ratio between the groove width and the pitch of the grating is equal to 1/2. A straightforward explanation involving a Fourier analysis of the different grating profiles is given and compared with the experimental results.     

Resin Swelling in Mixed Solvents Analysed using Hansen Solubility Parameter Space

The swelling of resins (Merrifield and HypoGel 200) in mixtures of two solvents was generally found not to vary linearly with the relative amount of each solvent in the mixture. Hansen solubility parameter (HSP) space could be used to define high, medium and low swelling regions for each resin. The variation of resin swelling with binary solvent composition could then be explained based on the HSP parameters of the two solvents and the way in which the line connecting the points corresponding to the two pure solvents bisected the swelling region for the resin. The applicability of the methodology was demonstrated by showing that an appropriate mixture of two green solvents was more effective for solid-phase peptide synthesis on Merrifield resin than use of either individual solvent and could completely replace the use of traditional polar aprotic and chlorinated solvents for this application. It was also shown that the high resin swelling area of Merrifield resin can be used to predict mixtures of green solvents that will dissolve linear, unfunctionalised polystyrene.     

Trialkylaluminum N-Heterocyclic Olefin (NHO) Adducts as Catalysts for the Polymerization of Michael-Type Monomers

The synthesis of new trialkylaluminum adducts with N-heterocyclic olefin (NHO) ligands is described. These well-defined complexes can catalyze the polymerization of various Michael-type monomers, such as 2-vinylpyridine, methylacrylate, and dimethylacrylamide.     

Soft X-ray spectromicroscopy studies of pitting corrosion of reinforcing steel bar

Pitting corrosion of reinforcing steel bar (rebar) imbedded in concrete by chloride ions can cause concrete degradation. It is thus necessary to develop methods to mitigate concrete corrosion which could include using a protective polymer rebar coating. Corrosion studies of polyvinyl butyral-carbon black polymer-coated rebar using soft X-ray fluorescence (XRF) microprobe and micro-X-ray absorption near edge spectroscopy (μ-XANES) are reported in this study. After removal of the polyvinyl butyral-carbon black polymer coating, Fe Lα₁, Mn Lα₁, and O Kα₁ XRF maps were collected as well as Fe and Mn L₃-edge μ-XANES spectra from different regions across the whole rebar surface by collection of total electron yield (TEY) and partial XRF yield (PFY) spectra. The distribution of metallic Fe and Fe corrosion products was determined by analysis of the Fe XRF map. The μ-XANES spectra indicated a higher fraction of Fe (III) phases on the corroded rebar surface, while Fe (II/III) phases were the major corrosion products beneath the surface region. In addition, Mn (II) and Mn (III) were determined as the valence states of the manganese corrosion products.