Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Superoperator formalism and chemisorption theory

It is pointed out that the superoperator formalism, developed for the calculation of ionization potentials in molecular physics, is a very powerful tool in chemisorption theory. This is demonstrated by applying the formalism to the Anderson-Newns model and by showing how the different approximate solutions can be obtained by elegant and systematic procedures. It is also pointed out that using the formalism, solutions for more complicated hamiltonians can easily be obtained.

Analysis of microstructure and texture evolution in pure magnesium during symmetric and asymmetric rolling

Asymmetric rolling of commercially pure magnesium was carried out at three different temperatures: room temperature, 200 degrees C and 350 degrees C. Systematic analysis of microstructures, grain size distributions, texture and misorientation distributions were performed using electron backscattered diffraction in a field emission gun scanning electron microscope. The results were compared with conventional (symmetric) rolling carried out under the same conditions of temperature and strain rate. Simulations of deformation texture evolution were performed using the viscoplastic self-consistent polycrystal plasticity model. The main trends of texture evolution are faithfully reproduced by the simulations for the tests at room temperature. The deviations that appear for the textures obtained at high temperature can be explained by the occurrence of dynamic recrystallization. Finally, the mechanisms of texture evolution in magnesium during asymmetric and symmetric rolling are explained with the help of ideal orientations, grain velocity fields and divergence maps displayed in orientation space.

Influence of tool rake angle on the quality of pure magnesium chip-consolidated product

Chips were produced by orthogonal Cutting of cast pure magnesium billet with three different tool rake angles viz., -15 degrees, -5 degrees and +15 degrees on a lathe. Chip consolidation by solid state recycling technique involved cold compaction followed by hot extrusion. The extruded products were characterized for microstructure and mechanical properties. Chip-consolidated products from -15 degrees rake angle tools showed 19% increase in tensile strength, 60% reduction ingrain size and 12% increase in hardness compared to +15 degrees rake chip-consolidated product indicating better chip bonding and grain refinement. Microstructure of the fracture specimen Supports the abovefinding. On the overall, the present work high lights the importance of tool take angle in determining the quality of the chip-consolidated products. (C) 2009 Elsevier B.V. All rights reserved.

Influence of roughness parameters and surface texture on friction during sliding of pure lead over 080 M40 steel

In the present investigation, tests were conducted on a tribological couple made of cylindrical lead pin with spherical tip against 080 M40 steel plates of different textures with varying roughness under both dry and lubricated conditions using an inclined pin-on-plate sliding tester. Surface roughness parameters of the steel plates were measured using optical profilometer. The morphologies of the worn surfaces of the pins and the formation of transfer layer on the counter surfaces were observed using a scanning electron microscope. It was observed that the coefficient of friction and the formation of transfer layer depend primarily on the surface texture of hard surfaces. A newly formulated non-dimensional hybrid roughness parameter called 'xi' (a product of number of peaks and maximum profile peak height) of the tool surface plays an important role in determining the frictional behaviour of the surfaces studied. The effect of surfaces texture on coefficient of friction was attributed to the variation of plowing component of friction, which in turn depends on the roughness parameter 'xi'.

Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within MY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical Molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected self-diffusivity profile for Pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in azeolite system With large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity.Further analysis allowed LIS to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture.

Room-temperature equal channel angular extrusion of pure magnesium

In this paper, we demonstrate a way to impart severe plastic deformation to magnesium at room temperature to produce ultrafine grain size of similar to 250 nm through equal channel angular extrusion (ECAE). The strategy to deform magnesium at lower temperature or to achieve such grain sizes has been proposed as: (i) to obtain a suitable initial orientation with high Schmid factor for basal slip and low Schmid factor for pyramidal/prismatic slip; (ii) to take advantage of low stacking fault energy of basal and high stacking fault energies of prismatic/pyramidal planes in order to relatively work-harden the basal plane with respect to the pyramidal/prismatic plane; and (iii) to lower the temperature of deformation in steps, leading to continual refinement of grains, resulting in finer grain size. The experimental as well as simulated texture of ECAE-processed samples indicate that the deformation mechanism leading to ultrafine grain size is slip-dominated. The recrystallization mechanism during ECAE has been found to be orientation-dependent. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states

The violation of the Svetlichny's inequality (SI) [Phys. Rev. D 35, 3066 (1987)] is sufficient but not necessary for genuine tripartite nonlocal correlations. Here we quantify the relationship between tripartite entanglement and the maximum expectation value of the Svetlichny operator (which is bounded from above by the inequality) for the two inequivalent subclasses of pure three-qubit states: the Greenberger-Horne-Zeilinger (GHZ) class and the W class. We show that the maximum for the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838 (1990)] modulo a constant factor, and although it is a function of the three tangle and the residual concurrence, large numbers of states do not violate the inequality. We further show that by design SI is more suitable as a measure of genuine tripartite nonlocality between the three qubits in the W-class states,and the maximum is a certain function of the bipartite entanglement (the concurrence) of the three reduced states, and only when their sum attains a certain threshold value do they violate the inequality.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Extension of Darken's Quadratic Formalism to Dilute Multicomponent Solutions

Darken's quadratic formalism is extended to multicomponent solutions. Equations are developed for the representation of the integral and partial excess free energies, entropies and enthalpies in dilute multicomponent solutions. Quadratic formalism applied to multicomponent solutions is thermodynamically consistent. The formalism is compared with the conventional second order Maclaurin series or interaction parameter representation and the relations between them are derived. Advantages of the quadratic formalism are discussed.

A.C. electrical conductivity of pure and doped potassium perchlorate

A.C. electrical conductivity of potassium perchlorate (KP) has been measured in the temperature range 25�325°C at frequencies ranging from 50�500 Hz using an automated technique. The results are interpreted in terms of a novel mechanism involving Schottky defects in the anion sublattice and Frenkel defects in the cation sublattice. Theconductivity behavior of KP is compared with literature data on similar low-symmetry systems containing polyatomic ions.

Physico-chemical properties of pure and x-ray irradiated single crystals of KAP

Single crystals of potassium hydrogen phthalate (KAP) have been grown by slow evaporation method from aqueous solutions. Thermal analyses indicate that KAP crystals decompose into phthalic anhydride and KOH around 520 K. Electrical properties of single crystals of KAP have been studied along with the effect of X-ray irradiation of the crystals. The electrical transport appears to be associated with tunneling of protons. The irradiated crystal exhibits lower dielectric constant and higher ac conductivity.

Thermodynamic consistency of the interaction parameter formalism

The apparent contradiction between the exact nature of the interaction parameter formalism as presented by Lupis and Elliott and the inconsistencies discussed recently by Pelton and Bale arise from the truncation of the Maclaurin series in the latter treatment. The truncation removes the exactness of the expression for the logarithm of the activity coefficient of a solute in a multi-component system. The integrals are therefore path dependent. Formulae for integration along paths of constant Xi,or X i/Xj are presented. The expression for In γsolvent given by Pelton and Bale is valid only in the limit that the mole fraction of solvent tends to one. The truncation also destroys the general relations between interaction parameters derived by Lupis and Elliott. For each specific choice of parameters special relationships are obtained between interaction parameters.

A numerical survey of relativistic rotating neutron star structures using the Hartle-Thorne formalism

A broad numerical survey of relativistic rotating neutron star structures was compiled using an exhaustive list of presently available equation of state models for neutron star matter. The structure parameters (spherical deformations in mass and radii, the moment of inertia and quadrupole moment, oblateness, and free precession) are calculated using the formalism proposed by Hartle and Thorne (1968). The results are discussed in relation to the relevant observational information. Binary pulsar data and X-ray burst sources provide information on the bulk properties of neutron stars, enabling the derivation of constraints that can be put on the structure of neutron stars and equation of state models.

Grain Growth in ECAE Processed Pure Magnesium

Grain growth kinetics was studied for commercially pure magnesium subjected to equal channel angular extrusion (ECAE). The specimens were ECAE processed upto 4 passes at 523 K following all the three important routes, namely A, 13, and C. Texture and microstructures of the samples were studied using Electron Back Scattered Diffraction (EBSD) technique in a Field Emission Gun Scanning Electron Microscope (FEG-SEM). It was observed that the grain size significantly reduces after ECAE. ECAE process produces a slightly rotated B and C-2 fiber. Static annealing leads to normal grain growth with unimodal distribution of grains through out the temperature range. Average activation energy for grain growth in the temperature range studied is found to be less than the activation energy for lattice diffusion and grain boundary diffusion of magnesium. No significant change in texture during isochronal annealing for 1 hour i.e., the predominant deformation texture remains same.