Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.

Stability of Transparent Spherically Symmetric Thin Shells and Wormholes

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations.Comment: 12 pages, 7 figures, revtex. Final form to appear in Phys. Rev.

Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism

We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation - joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit.Comment: Minor LaTeX error corrected. GRjunction for GRTensorII is available from http://astro.queensu.ca/~grtensor/GRjunction.htm

Practical applications of biomechanical principles in resistance training: moments and moment arms

Exercise professionals routinely prescribe resistance training to clients with varied goals. Therefore, they need to be able to modify the difficulty of a variety of exercises and to understand how such modifications can alter the relative joint loading on their clients so to maximise the potential for positive adaptation and to minimise injury risk. This paper is the first in a three part series that will examine how a variety of biomechanical principles and concepts have direct relevance to the prescription of resistance training for the general and athletic populations as well as for musculoskeletal injury rehabilitation. In this paper, we start by defining the terms moment (torque), moment arms, compressive, tensile and shear forces as well as joint stress (pressure). We then demonstrate how an understanding of moments and moment arms is integral to the exercise professionals’ ability to develop a systematic progression of variations of common exercises. In particular, we examine how a variety of factors including joint range of motion, body orientation, type of external loading, the lifter’s anthropometric proportions and the position of the external load will influence the difficulty of each exercise variation. We then highlight the primary results of several selected studies which have compared the resistance moment arms and joint moments, forces or stresses that are encountered during selected variations of common lower body resistance training exercises. We hope that exercise professionals will benefit from this knowledge of applied resistance training biomechanics and be better able to systematically progress exercise difficulty and to modify joint loading as a result. The two remaining articles in this series will focus on the neuromechanical properties of the human musculoskeletal system and better understanding the biomechanical implications of a variety of alternative resistance training techniques, respectively

Static Ricci-flat 5-manifolds admitting the 2-sphere

We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions. The 2-fold infinity of cases that result are studied by way of new coordinates (which are in most cases global) and the cases likely to be of interest in any physical approach are distinguished on the basis of the nakedness and geometrical mass of their associated singularities. It is argued that the entire class of solutions has to be considered unstable about the exceptional solutions: the black string and soliton cases. Any physical theory which admits the non-exceptional solutions as the external vacuua of a collapsing object has to accept the possibility of collapse to zero volume leaving behind the weakest possible, albeit naked, geometrical singularities at the origin.Finally, it is pointed out that these types of solutions generalize, in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension

Microscopic non-equilibrium theory of quantum well solar cells

We present a microscopic theory of bipolar quantum well structures in the photovoltaic regime, based on the non-equilibrium Green's function formalism for a multi band tight binding Hamiltonian. The quantum kinetic equations for the single particle Green's functions of electrons and holes are self-consistently coupled to Poisson's equation, including inter-carrier scattering on the Hartree level. Relaxation and broadening mechanisms are considered by the inclusion of acoustic and optical electron-phonon interaction in a self consistent Born approximation of the scattering self energies. Photogeneration of carriers is described on the same level in terms of a self energy derived from the standard dipole approximation of the electron-photon interaction. Results from a simple two band model are shown for the local density of states, spectral response, current spectrum, and current-voltage characteristics for generic single quantum well systems.Comment: 10 pages, 6 figures; corrected typos, changed caption Fig. 1, replaced Fig.

A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

We describe a simple family of analytical coordinate systems for the Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are spatially isotropic. Spatial slices of constant coordinate time $t$ feature a trumpet geometry with an asymptotically cylindrical end inside the horizon at a prescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the free parameter for the family. The slices also have an asymptotically flat end at spatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpet geometry and become flat -- in this limit, our coordinates reduce to Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure

Bilateral vs. unilateral countermovement jumps: comparing the magnitude and direction of asymmetry in elite academy soccer players

The aims of the present study were to compare the magnitude and direction of asymmetry in comparable bilateral and unilateral countermovement jumps (CMJ). Forty-five elite academy soccer players from under-23 (n = 15), under-18 (n = 16) and under-16 (n = 14) age groups performed bilateral and unilateral CMJ as part of their routine pre-season fitness testing. For the magnitude of asymmetry, no significant differences were evident for any metric between tests. However, eccentric impulse asymmetry was significantly greater than mean force and concentric impulse in both bilateral and unilateral tests (p < 0.01). For the direction of asymmetry, Kappa coefficients showed poor levels of agreement between test measures for all metrics (mean force = -0.15; concentric impulse = -0.07; eccentric impulse = -0.13). Mean jump data was also presented relative to body mass for each group. For the bilateral CMJ, significant differences were evident between groups, but showed little consistency in the same group performing better or worse across metrics. For the unilateral CMJ, eccentric impulse was the only metric to show meaningful differences between groups, with the under-18 group performing significantly worse than under-23 and under-16 players. This study highlights that despite the magnitude of asymmetry being similar for each metric between comparable bilateral and unilateral CMJ, consistency in the direction of asymmetry was poor. In essence, if the right limb produced the larger force or impulse during a bilateral CMJ, it was rare for the same limb to perform superior during the unilateral task. Thus, practitioners should be aware that bilateral and unilateral CMJ present different limb dominance characteristics and should not use one test to represent the other when measuring between-limb asymmetries