Calculating binary and ternary multiphase equilibria: extensions of the integral area method

The area method was proposed in 1992 to calculate binary and ternary 2-phase equilibria. In its integral form, the method provides both the necessary and sufficient conditions required for the determination of the global minimum reduced Gibbs energy of mixing (Φ). The method has since been applied to the calculation of both pure component and ternary multiphase equilibria in a differential form. However, the extension of the original (2 point) integral area method to the direct calculation of both binary and ternary multiphase equilibria has not been completed. Direct 3 point and modified 2 point search methods have therefore been developed here and used to estimate the phase compositions of a representative binary vapour-liquid-liquid system. The 2 point area method principle has been extended and applied to the calculation of ternary multiphase equilibria using a net volume approach. However, this volume method was found to fail due to an underlying inconsistency in the bounding of the integrated Φ surface by the trial 3-phase region. A new method is proposed that overcomes this problem by minimising the area of intersection between a tangent plane and the Φ surface. This new method has successfully calculated the 3-phase compositions of two simple test systems from a variety of initial mixture starting points.     

Selective Homogeneous Palladium(0)-Catalyzed Hydrogenation of Alkynes to (Z)-Alkenes

Zero-valent palladium precatalysts containing rigid bidentate bis(arylimino)acenaphthene ligands (shown schematically) facilitate the highly stereoselective homogeneous catalytic hydrogenation of alkynes to (Z)-alkenes. Internal, terminal, aryl-substituted, and cyclic alkynes are suitable substrates, as are some enynes, which are chemoselectively hydrogenated to dienes. E=CO(2)Me; R(1), R(2)=4-OCH(3), 4-CH(3), 2,6-(CH(3))(2).     

Hyperfine interactions on151Eu and57Fe in amorphous EuFe2Si2

The magnetic and quadrupole hyperfine interactions in amorphous EuFe₂Si₂ have been measured using⁵⁷Fe and¹⁵¹Eu Mössbauer spectroscopy. The distributions in the various parameters have been found using the Fourier coefficient method. Novel features of the results are that the Eu charge state (4f occupation number) changes between the crystalline and amorphous phases and that whereas in the crystalline phase neither Eu nor Fe is magnetic, both become so in the amorphous phase.     

Dependence of variables construed as an atomic formula

We define a logic D capable of expressing dependence of a variable on designated variables only. Thus D has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic D achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our D avoids some difficulties arising in the original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth of D is definable inside D. We give such a definition for D in the spirit of [11] and [2] and [1].     

Asymptotic analysis of the non-linear behavior of long anisotropic tubes

An asymptotically correct beam model is obtained for a long, thin-walled, circular tube with circumferentially uniform stiffness (CUS) and made of generally anisotropic materials. By virtue of its special geometry certain small parameters cause unusual non-linear phenomena, such as the Brazier effect, to be exhibited. The model is constructed without ad hoc approximations from 3D elasticity by deriving its strain energy functional in terms of generalized 1D strains corresponding to extension, bending, and torsion. Large displacement and rotation are allowed but strain is assumed to be small. Closed-form expressions are provided for the 3D non-linear warping and stress fields, the 1D non-linear stiffness matrix and the bending moment–curvature relationship. In bending, failure could be caused by limit-moment instability, local buckling or material failure of a ply. A procedure to determine the failure load is provided based on the non-linear response, neglecting micro-mechanical failure modes, post-failure behavior, and hygrothermal effects. Asymptotic considerations lead to the neglect of local shell interlaminar and transverse shear stresses for the thin-walled configuration. Results of the theory are illustrated for a few symmetric, antisymmetric angle-ply and unsymmetric layups and show that some previously published theories are not asymptotically correct.     

Nonlinear aeroelasticity of high-aspect-ratio wings excited by time-dependent thrust

Effects of engine placement on flutter characteristics of a very flexible high-aspect-ratio wing are investigated using the code NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft). Gravity for this class of wings plays an important role in flutter characteristics. In the absence of aerodynamic and gravitational forces and without an engine, the kinetic energy of the first two modes are calculated. Maximum and minimum flutter speed locations coincide with the area of minimum and maximum kinetic energy of the second bending and torsion modes. Time-dependent dynamic behavior of a turboshaft engine (JetCat SP5) is simulated with a transient engine model and the nonlinear aeroelastic response of the wing to the engine’s time-dependent thrust and dynamic excitation is presented. Below the flutter speed, at the wing tip and behind the elastic axis, the impulse engine excitation leads to a stable limit cycle oscillation; and for the ramp kind of excitation, beyond the flutter speed, at 75 % span, behind the elastic axis, it produces chaotic oscillation in the wing. Both the excitations above the flutter speed are stabilized, inboard of the wing.     

Positrons in metals with voids,vacancies and surfaces

The behaviour of positrons near monovacancies and voids in a metal is discussed in terms of three contributions to the positron work function for the metal, namely the positron zero-point energy, the positron-electron correlation energy and the surface dipole barrier. The image potential when a positron comes near to a metal surface leads to a deep potential ‘trough’ just outside an exterior metal surface or just inside a void surface. Calculations indicate positron bound states localized at metal surfaces for most metals which should be manifested in a long lived positron lifetime component. The behaviour of positronium near metal surfaces is also discussed.     

Behavior of thin films of poly(oxyethylene)-poly(oxybutylene) copolymers studied by brewster angle microscopy and atomic force microscopy

Surface films of two copolymers of ethylene oxide (E) and butylene oxide (B), namely E23B8 and E87B18, have been examined by Brewster angle microscopy (BAM) and atomic force microscopy (AFM). Isotherms taken on unsupported films of these copolymers at the air-water interface showed a clear gas to liquid phase transition for E57B18 and a barely discernible phase transition for E23B8. The BAM studies showed a gradual brightening of the films as the surface pressure was increased, which was associated with a film thickening and/or a film densification. Several bright spots were also observed within the films, with the number of spots increasing gradually as the film surface pressure was increased. AFM studies of these films did not show any localized ordering, which fits in with the results from our previous X-ray study of these copolymers [Hodges, C. S.; Neville, F.; Konovalov, O.; Gidalevitz, D.; Hamley, I. W.; Langmuir 2006, 22 (21), 8821-8825], where no long-range ordering was observed. AFM imaging showed two sizes of particulates that were irregularly spaced across the film. The larger particulates were associated with silica contaminants from the copolymer synthesis, whereas the smaller particulates were assumed to be aggregated copolymer. An analysis of the semidilute region of the isotherm showed that while both copolymers had intermixed ethylene oxide and butylene oxide units, the lower molecular weight E23B8 copolymer manifested significantly more intermixing than E87B18.     

Mechanical properties of anodized coatings over molten aluminum alloy

A method to measure interfacial mechanical properties at high temperatures and in a controlled atmosphere has been developed to study anodized aluminum surface coatings at temperatures where the interior aluminum alloy is molten. This is the first time that the coating strength has been studied under these conditions. We have investigated the effects of ambient atmosphere, temperature, and surface finish on coating strength for samples of aluminum alloy 7075. Surprisingly, the effective Young's modulus or strength of the coating when tested in air was twice as high as when samples were tested in an inert nitrogen or argon atmosphere. Additionally, the effective Young's modulus of the anodized coating increased with temperature in an air atmosphere but was independent of temperature in an inert atmosphere. The effect of surface finish was also examined. Sandblasting the surface prior to anodization was found to increase the strength of the anodized coating with the greatest enhancement noted for a nitrogen atmosphere. Machining marks were not found to significantly affect the strength.