Solutions of Penrose's Equation

The computational use of Killing potentials which satisfy Penrose's equation is discussed. Penrose's equation is presented as a conformal Killing-Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in spacetimes of Petrov type O, D or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.Comment: To appear in J. Math. Phy

Superintegrable Systems in Darboux spaces

Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Staeckel multiplier transformations). We present tables of the results

Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multiseparability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schrödinger operator, deep connections with special functions, and with quasiexactly solvable systems. Here, we announce a complete classification of nondegenerate (i.e., four-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly ten nondegenerate potentials. ©2007 American Institute of Physic

Fatigue Damage in Notched Composite Laminates Under Tension-Tension Cyclic Loads

The results are given of an investigation to determine the damage states which develop in graphite epoxy laminates with center holes due to tension-tension cyclic loads, to determine the influence of stacking sequence on the initiation and interaction of damage modes and the process of damage development, and to establish the relationships between the damage states and the strength, stiffness, and life of the laminates. Two quasi-isotropic laminates were selected to give different distributions of interlaminar stresses around the hole. The laminates were tested under cyclic loads (R=0.1, 10 Hz) at maximum stresses ranging between 60 and 95 percent of the notched tensile strength

Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems

A Consistent Orbital Stability Analysis for the GJ 581 System

We apply a combination of N-body modeling techniques and automated data fitting with Monte Carlo Markov Chain uncertainty analysis of Keplerian orbital models to radial velocity data to determine long term stability of the planetary system GJ 581. We find that while there are stability concerns with the 4-planet model as published by Forveille et al. (2011), when uncertainties in the system are accounted for, particularly stellar jitter, the hypothesis that the 4-planet model is gravitationally unstable is not statistically significant. Additionally, the system including proposed planet g by Vogt et al. (2012) also shows some stability concerns when eccentricities are allowed to float in the orbital fit, yet when uncertainties are included in the analysis the system including planet g also can not be proven to be unstable. We present revised reduced chi-squared values for Keplerian astrocentric orbital fits assuming 4-planet and 5-planet models for GJ~581 under the condition that best fits must be stable, and find no distinguishable difference by including planet g in the model. Additionally we present revised orbital element estimates for each assuming uncertainties due to stellar jitter under the constraint of the system being gravitationally stable.Comment: 26 pages, 8 figures, 6 tables, accepted for publication in the Astrophysical Journa

Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multi-separability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schroedinger operator, deep connections with special functions and with QES systems. Here we announce a complete classification of nondegenerate (i.e., 4-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in 10 variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly 10 nondegenerate potentials.Comment: 35 page

The New Neurobiology of Severe Psychiatric Disorders and Its Implications for Laws Governing Involuntary Commitment and Treatment

Medical advances have led to statutory changes and common law overrulings. This paper argues that such changes are now needed for laws governing the involuntary commitment and treatment of individuals with severe psychiatric disorders. Recent advances in the understanding of the neurobiology of these disorders have rendered obsolete many assumptions underlying past statutes and legal decisions. This is illustrated by using schizophrenia as an example and examining two influential cases: California’s Lanterman-Petris-Short Act (1969) and Wisconsin’s Lessard decision (1972). It is concluded that laws governing involuntary commitment and treatment need to be updated to incorporate the current neurobiological understanding of severe psychiatric disorders