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

A Numerical Study of Micrometeoroids Entering Titan's Atmosphere

A study using numerical integration techniques has been performed to analyze the temperature profiles of micrometeors entering the atmosphere of Saturn s moon Titan. Due to Titan's low gravity and dense atmosphere, arriving meteoroids experience a significant cushioning effect compared to those entering the Earth's atmosphere. Temperature profiles are presented as a function of time and altitude for a number of different meteoroid sizes and entry velocities, at an entry angle of 45. Titan's micrometeoroids require several minutes to reach peak heating (ranging from 200 to 1200 K), which occurs at an altitude of about 600 km. Gentle heating may allow for gradual evaporation of volatile components over a wide range of altitudes. Computer simulations have been performed using the Cassini/Huygens atmospheric data for Titan. Keywords micrometeoroid Titan atmosphere 1 Introduction On Earth, incoming micrometeoroids (~100 m diameter) are slowed by collisions with air molecules in a relatively compact atmosphere, resulting in extremely rapid deceleration and a short heating pulse, often accompanied by brilliant meteor displays. On Titan, lower gravity leads to an atmospheric scale height that is much larger than on Earth. Thus, deceleration of meteors is less rapid and these particles undergo more gradual heating. This study uses techniques similar to those used for Earth meteoroid studies [1], exchanging Earth s planetary characteristics (e.g., mass and atmospheric profile) for those of Titan. Cassini/Huygens atmospheric data for Titan were obtained from the NASA Planetary Atmospheres Data Node [4]. The objectives of this study were 1) to model atmospheric heating of meteoroids for a range of micrometeor entry velocities for Titan, 2) to determine peak heating temperatures and rates for micrometeoroids entering Titan s atmosphere, and 3) to create a general simulation environment that can be extended to incorporate additional parameters and variables, including different atmospheric, meteoroid and planetary data. The micrometeoroid entry simulations made using Titan atmospheric data assume that, as on Earth, micrometeors are heated by collision with molecules in the atmosphere. Unlike on Earth where heating pulses last a few seconds and reach temperatures sufficient to melt silicates (> 1600 K [1])