Applications of convex analysis and comparison functionals to extremum principles

In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.     

Water in polymer membranes. Part II : Raman scattering from guided laser beams

Simultaneous application of integrated optics and Raman spectroscopy is used to investigate the hydrogen bonding of water in thin dense symmetric membranes of cellulose acetate (CA). A modified X-ray quarter circle goniometer is used to measure refractive index, film thickness, and Raman spectra using guided laser beams and the prism coupler technique. The film remains in a fixed position during all measurements thereby ensuring identical light collection geometries for Raman scattering observed from different wave-guiding modes. To illustrate the technique, Raman scattering of a 3.5 μm film of CA398-10 in the OH stretching region is shown as a function of relative humidity (RH). These spectra show that water sorbed at less than 50% RH is weakly hydrogen-bonded but above 50% RH, sorbed water has the strongly hydrogen-bonded properties of bulk water.     

Orientational ordering in nematic liquid crystals 1CB-d11 dissolved in 5CB-d6

The ²H-N.M.R. spectra of mixtures of the non-mesogenic compound 4-cyano-4'-methylbiphenyl (1CB) and the nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl (5CB) are measured as a function of concentration and temperature. Concentrations of up to 25 mol% 1CB have no effect on the N.M.R. spectrum and therefore on the orientational order of 5CB at a given reduced temperature. The order matrix of the 1CB is calculated from the measured quadrupole couplings. The results are analysed in terms of a model for orientational order that includes two anisotropic terms: (a) interaction between the molecular quadrupole moment and the mean electric field gradient of the medium, and (b) short range repulsive interactions. An estimate of the molecular quadrupole moment tensor of 1CB is obtained from the analysis.     

Fabrication and optimization of uniform output couplers for far-infrared lasers

An improved technique for the fabrication of uniform output couplers for far-infrared lasers has been developed. The technique includes a process for uniformly removing material from the back side of the coupler's substrate to tune the coupler's reflectivity precisely to the specified value for a particular laser line. Depending on the condition of the coupler after use, it can be retuned to another laser line, which lies within the coupler's reflectance envelope. Furthermore, when there is the possibility of lasing at two different laser wavelengths (as happens with some far-infrared lasers), it is possible to optimize the coupler for one wavelength while at the same time detuning the other wavelength. The fabrication and optimization of these devices are discussed.     

Resonant formation of d&mgr;t molecules in deuterium: An atomic beam measurement of muon catalyzed dt fusion

Resonant formation of d&mgr;t molecules in collisions of muonic tritium ( &mgr;t) on D2 was investigated using a beam of &mgr;t atoms, demonstrating a new direct approach in muon catalyzed fusion studies. Strong epithermal resonances in d&mgr;t formation were directly revealed for the first time. From the time-of-flight analysis of 2036+/-116 dt fusion events, a formation rate consistent with 0.73+/-(0.16)(meas)+/-(0.09)(model) times the theoretical prediction was obtained. For the largest peak at a resonance energy of 0.423+/-0.037 eV, this corresponds to a rate of (7.1+/-1.8)x10(9) s(-1), more than an order of magnitude larger than those at low energies.     

Syntheses and structures of two acridine orange polyiodide salts

Polyiodide salts of acridine orange were isolated from solutions of an acridine and I₂ in methylene chloride, ethanol, and acetone. The products from all solutions were found to contain both amorphous and crystalline material. The isolated crystalline product from methylene chloride and ethanol were identical (1), but the product isolated from acetone was different (2). Complex 1 was formulated as [C₁₇H₁₉ N ₃(H)]₂(I)₂ 3I₂. It crystallizes in the monoclinic space group P2₁/n, with a = 9.082(2) Å, b = 24.027(4) Å, c = 10.683(1) Å, = 107.20(1), and D _(calc) = 2.31 Mg/m³. Complex 2 was formulated as [C₁₇H₁₉ N ₃(H)]I₃. It crystallizes in the triclinic space group P – 1, with a = 10.498(2) Å, b = 11.265(2) Å, c = 9.287(1) Å, g 100.88(1), = 94.57(1), = 102.10(1), and D _(calc) = 2.05 Mg/m³.     

Determination of f(s)/f(d) for 7 TeV pp collisions and measurement of the B0→D-K+ branching fraction

The relative abundance of the three decay modes B(0)→D(-)K(+), B(0)→D(-)π(+), and B(s)(0)→D(s)(-)π(+) produced in 7 TeV pp collisions at the LHC is determined from data corresponding to an integrated luminosity of 35 pb(-1). The branching fraction of B(0)→D(-)K(+) is found to be B(B(0)→D(-)K(+)) = (2.01 ± 0.18(stat) ± 0.14(syst)) × 10(-4). The ratio of fragmentation fractions f(s)/f(d) is determined through the relative abundance of B(s)(0)→D(s)(-)π(+) to B(0)→D(-)K(+) and B(0)→D(-)π(+), leading to f(s)/f(d) = 0.253 ± 0.017 ± 0.017 ± 0.020, where the uncertainties are statistical, systematic, and theoretical, respectively.     

Influence of preparation conditions on the depth-dependent composition of AuPd nanoparticles grown on planar oxide surfaces

The high resolution depth profiling capabilities of medium energy ion scattering are employed to determine the depth dependent composition of Au/Pd nanoparticles grown on thin silica films on Si(100) as functions of Au/Pd composition, total metal loading and annealing temperature. We show that, despite the fact that Au is deposited prior to Pd, the surface of the particles is generally enriched in Au compared to the bulk composition. The extent of this Au enrichment decreases with annealing temperature. In addition, we examine the influence of the adsorption of acetic acid on the surface composition of Au/Pd particles grown on thin alumina films on NiAl(110). We find that acetic acid causes limited segregation of Pd to the bimetallic surface of relatively Au-rich particles.