Representations of Solutions of Laplacian Boundary Value Problems on Exterior Regions

This paper treats the well-posedness and representation of solutions of Poisson’s equation on exterior regions $U\subsetneq{\mathbb{R}}^{N}$ with N≥3. Solutions are sought in a space E ¹(U) of finite energy functions that decay at infinity. This space contains H ¹(U) and existence-uniqueness theorems are proved for the Dirichlet, Robin and Neumann problems using variational methods with natural conditions on the data. A decomposition result is used to reduce the problem to the evaluation of a standard potential and the solution of a harmonic boundary value problem. The exterior Steklov eigenproblems for the Laplacian on U are described. The exterior Steklov eigenfunctions are proved to generate an orthogonal basis for the subspace of harmonic functions and also of certain boundary trace spaces. Representations of solutions of the harmonic boundary value problem in terms of these bases are found, and estimates for the solutions are derived. When U is the region exterior to a 3-d ball, these Steklov representations reduce to the classical multi-pole expansions familiar in physics and engineering analysis.     

Terahertz absorption spectra of nitromethane

Nitromethane, with its heavy frame and internal rotator, readily evaporates into the atmosphere making it an ideal candidate for remote sensing. Here we present the absorption spectra of gas-phase nitromethane between 9 and 50 cm⁻¹. Measurements were taken using a Bruker IFS 66v Fourier transform far-infrared (FTIR) spectrometer at a resolution of 0.12 cm⁻¹ (0.0036 THz) from 9 to 40 cm⁻¹ and a Bruker Vertex 80v FTIR spectrometer with a resolution of 0.0075 cm⁻¹ (0.00226 THz) from 10 to 50 cm⁻¹. The absorption spectra were measured at multiple pathlengths ranging from 2 to 6 m. These measurements were used to calculate the absorption coefficient of nitromethane as a function of wavenumber.     

Synthesis of E-3-Hydroxymethyl-1-methoxy-4-(1′-pentenyl)benzene

The title compound with exclusively the E-geometry has been synthesized by two independent routes. When this compound was reacted with cerium (IV) ammonium nitrate, it was found that oxidative cyclisation to the corresponding 4-hydroxybenzo-pyrans did not occur. This further defines the structural parameters required for such oxidative cyclisations.     

Theoretical prediction and experimental measurement of the field dependence of the apparent transverse relaxation of hyperpolarized noble gases in lungs

In this work, computer modeling based on a finite element method is used to simulate the T2* relaxation of hyperpolarized noble gases (HNG) in the lungs. A physical model of lung airways consisting of a phantom constructed from micro-capillary fibers of diameters similar to the size of lung airways with semi-permeable walls is also presented. The fibers are surrounded by a liquid medium (water) of magnetic susceptibility similar to lung tissue. Theoretical predictions of the field strength dependence of T2* for 129Xe in the phantom and in vivo rat lung are presented. These predictions are in good agreement with experimental T2* values obtained from the phantoms and in vivo rat lungs (160, 19 and 8 ms) at three different field strengths (0.074, 1.89 and 3T, respectively) using hyperpolarized 129Xe. The strong dependence of T2* on field strength is consistent with the theoretical prediction that low fields may be optimal for HNG MR imaging of the lungs as the decreased T2* at high fields necessitates an increase in bandwidth for conventional MR imaging.     

The copolymerisation of methyl and ethyl methacrylate in supercritical carbon dioxide

This paper reports the free radical dispersion copolymerisation of methyl and ethyl methacrylate in supercritical carbon dioxide. The polymerisation uses a poly(dimethyl siloxane) monomethacrylate macromonomer as the stabiliser. A range of different reaction times was investigated in order to probe the amount of each monomer incorporated in the copolymer. Analysis by ¹H NMR spectroscopy reveals that the monomers behave as in conventional solvents to form a random copolymer. The effect of varying the initiator concentration (initiator 2,2′‐azobisisobutyronitrile, AIBN) on the composition and molecular weights of the resultant copolymers has also been studied.     

Microstructure of triblock copolymers in asphalt oligomers

A model asphalt has been separated into two parts, asphaltene and maltene, through solvent extraction by n-heptane. The interactions of asphaltene and maltene with the triblock copolymer poly(styrene-b-(ethylene-co-butylene)-b-styrene) (SEBS) were investigated by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), dynamic mechanical analysis (DMA), and differential scanning calorimetry (DSC). Asphaltene was found to be essentially immiscible with both blocks of SEBS, while maltene was miscible with SEBS. An unusual sequence of morphological transformations of SEBS microstructure with respect to the addition of maltene was observed. The morphology transformed from hexagonal cylinder, to perforated layers, to lamellae and then back to the original hexagonal cylinder. The observed transformation reflects a limited solubility for both S and EB domains: at lower concentration maltene is a preferential additive for S domains, while increasing concentration the swelling of EB-rich microdomains by maltene becomes significant. The basic understanding of the interactions of the components of asphalt with SEBS gives a simple path to characterize and predict the microstructure of triblock copolymers in asphalt oligomers. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2857–2877, 1997