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.

Socialist Realism instead of Formalism : the Formation and Development of the Soviet Music Control System 1932-1950

Whereas it has been widely assumed in the public that the Soviet music policy system had a “top-down” structure of control and command that directly affected musical creativity, in fact my research shows that the relations between the different levels of the music policy system were vague, and the viewpoints of its representatives differed from each other. Because the representatives of the party and government organs controlling operas could not define which kind of music represented Socialist Realism, the system as it developed during the 1930s and 1940s did not function effectively enough in order to create such a centralised control of Soviet music, still less could Soviet operas fulfil the highly ambiguous aesthetics of Socialist Realism. I show that musical discussions developed as bureaucratic ritualistic arenas, where it became more important to reveal the heretical composers, making scapegoats of them, and requiring them to perform self-criticism, than to give directions on how to reach the artistic goals of Socialist Realism. When one opera was found to be unacceptable, this lead to a strengthening of control by the party leadership, which lead to more operas, one after the other, to be revealed as failures. I have studied the control of the composition, staging and reception of the opera case-studies, which remain obscure in the West despite a growing scholarly interest in them, and have created a detailed picture of the foundation and development of the Soviet music control system in 1932-1950. My detailed discussion of such case-studies as Ivan Dzerzhinskii’s The Quiet Don, Dmitrii Shostakovich’s Lady Macbeth of Mtsensk District, Vano Muradeli’s The Great Friendship, Sergei Prokofiev’s Story of a Real Man, Tikhon Khrennikov’s Frol Skobeev and Evgenii Zhukovskii’s From All One’s Heart backs with documentary precision the historically revisionist model of the development of Soviet music. In February 1948, composers belonging to the elite of the Union of Soviet Composers, e.g. Dmitri Shostakovich and Sergei Prokofiev, were accused in a Central Committee Resolution of formalism, as been under the influence of western modernism. Accusations of formalism were connected to the criticism of the conciderable financial, material and social privileges these composers enjoyed in the leadership of the Union. With my new archival findings I give a more detailed picture of the financial background for the 1948 campaign. The independent position of the music funding organization of the Union of Soviet Composers (Muzfond) to decide on its finances was an exceptional phenomenon in the Soviet Union and contradicted the strivings to strengthen the control of Soviet music. The financial audits of the Union of Soviet Composers did not, however, change the elite status of some of its composers, except for maybe a short duration in some cases. At the same time the independence of the significal financial authorities of Soviet theatres was restricted. The cuts in the governmental funding allocated to Soviet theatres contradicted the intensified ideological demands for Soviet operas.

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'.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

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.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

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.