On the controversy concerning the definition of quark and gluon angular momentum

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on Field Theory.Comment: 41 pages; Some incorrect statements have been rectified and a detailed discussion has been added concerning the momentum carried by quarks and the Ji sum rule for the angular momentu

Buoyancy waves in Pluto's high atmosphere: Implications for stellar occultations

We apply scintillation theory to stellar signal fluctuations in the high-resolution, high signal/noise, dual-wavelength data from the MMT observation of the 2007 March 18 occultation of P445.3 by Pluto. A well-defined high wavenumber cutoff in the fluctuations is consistent with viscous-thermal dissipation of buoyancy waves (internal gravity waves) in Pluto's high atmosphere, and provides strong evidence that the underlying density fluctuations are governed by the gravity-wave dispersion relation.Comment: Accepted 18 June 2009 for publication in Icaru

Double Charge Exchange And Configuration Mixing

The energy dependence of forward pion double charge exchange reactions on light nuclei is studied for both the Ground State transition and the Double-Isobaric-Analog-State transitions. A common characteristic of these double reactions is a resonance-like peak around 50 MeV pion lab energy. This peak arises naturally in a two-step process in the conventional pion-nucleon system with proper handling of nuclear structure and pion distortion. A comparison among the results of different nuclear structure models demonstrates the effects of configuration mixing. The angular distribution is used to fix the single particle wave function.Comment: Added 1 figure (now 8) corrected references and various other change

Design of a Low Speed Fan Stage for Noise Suppression

This report describes the design of a low tip speed, moderate pressure rise fan stage for demonstration of noise reduction concepts. The fan rotor is a fixed-pitch configuration delivering a design pressure ratio of 1.378 at a specific flow of 43.1 lbm/sec/sq ft. Four exit stator configurations were provided to demonstrate the effectiveness of circumferential and axial sweep in reducing rotor-stator interaction tone noise. The fan stage design was combined with an axisymmetric inlet, conical convergent nozzle, and nacelle to form a powered fan-nacelle subscale model. This model has a 22-inch cylindrical flow path and employs a rotor with a 0.30 hub-to-tip radius ratio. The design is fully compatible with an existing NASA force balance and rig drive system. The stage aerodynamic and structural design is described in detail. Three-dimensional (3-D) computational fluid dynamics (CFD) tools were used to define optimum airfoil sections for both the rotor and stators. A fan noise predictive system developed by Pratt & Whitney under contract to NASA was used to determine the acoustic characteristics of the various stator configurations. Parameters varied included rotor-to-stator spacing and vane leading edge sweep. The structural analysis of the rotor and stator are described herein. An integral blade and disk configuration was selected for the rotor. Analysis confirmed adequate low cycle fatigue life, vibratory endurance strength, and aeroelastic suitability. A unique load carrying stator arrangement was selected to minimize generation of tonal noise due to sources other than rotor-stator interaction. Analysis of all static structural components demonstrated adequate strength, fatigue life, and vibratory characteristics

Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N-dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.Comment: 15 page

Testing a model of antecedents and consequences of defensive pessimism and self-handicapping in school physical education

There has been very limited research on the use of self-worth protection strategies in the achievement context of school physical education (PE). Thus, this study aimed to examine some antecedents and consequences of defensive pessimism and self-handicapping. The sample comprised 534 (females n = 275; males n = 259) British pupils recruited from two schools who responded to established questionnaires. Results of structural equation modelling analysis indicated that self-handicapping and defensive pessimism were positively predicted by fear of failure and negatively predicted by competence valuation. In addition, defensive pessimism was negatively predicted by physical self-concept. In turn, defensive pessimism negatively predicted enjoyment in PE and intentions to participate in future optional PE programs. Self-handicapping did not predict enjoyment or intentions. Results from multi-sample structural equation modelling showed the specified model to be largely invariant across males and females. The findings indicate that although both strategies aim to protect one’s self-worth, some of their antecedents and consequences in PE may differ

Investigation of the nonlocal coherent-potential approximation

Recently the nonlocal coherent-potential approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally disordered systems. The NLCPA provides systematic corrections to the widely used coherent-potential approximation (CPA) whilst preserving the full symmetry of the underlying lattice. Here an analytical and systematic numerical study of the NLCPA is presented for a one-dimensional tight-binding model Hamiltonian, and comparisons with the embedded cluster method (ECM) and molecular coherent potential approximation (MCPA) are made.Comment: 18 pages, 5 figure

Systematic and Causal Corrections to the Coherent Potential Approximation

The Dynamical Cluster Approximation (DCA) is modified to include disorder. The DCA incorporates non-local corrections to local approximations such as the Coherent Potential Approximation (CPA) by mapping the lattice problem with disorder, and in the thermodynamic limit, to a self-consistently embedded finite-sized cluster problem. It satisfies all of the characteristics of a successful cluster approximation. It is causal, preserves the point-group and translational symmetry of the original lattice, recovers the CPA when the cluster size equals one, and becomes exact as $N_c\to\infty$. We use the DCA to study the Anderson model with binary diagonal disorder. It restores sharp features and band tailing in the density of states which reflect correlations in the local environment of each site. While the DCA does not describe the localization transition, it does describe precursor effects of localization.Comment: 11 pages, LaTeX, and 11 PS figures, to appear in Phys. Rev. B. Revised version with typos corrected and references adde