Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.Comment: 19 pages, 5 figures, 7 tables, accepted by the Astronomical Journa

Investigation to advance prediction techniques of the low-speed aerodynamics of V/STOL aircraft

A computer program, VSAERO, has been applied to a number of V/STOL configurations with a view to advancing prediction techniques for the low-speed aerodynamic characteristics. The program couples a low-order panel method with surface streamline calculation and integral boundary layer procedures. The panel method--which uses piecewise constant source and doublet panels-includes an iterative procedure for wake shape and models boundary layer displacement effect using the source transpiration technique. Certain improvements to a basic vortex tube jet model were installed in the code prior to evaluation. Very promising results were obtained for surface pressures near a jet issuing at 90 deg from a flat plate. A solid core model was used in the initial part of the jet with a simple entrainment model. Preliminary representation of the downstream separation zone significantly improve the correlation. The program accurately predicted the pressure distribution inside the inlet on the Grumman 698-411 design at a range of flight conditions. Furthermore, coupled viscous/potential flow calculations gave very close correlation with experimentally determined operational boundaries dictated by the onset of separation inside the inlet. Experimentally observed degradation of these operational boundaries between nacelle-alone tests and tests on the full configuration were also indicated by the calculation. Application of the program to the General Dynamics STOL fighter design were equally encouraging. Very close agreement was observed between experiment and calculation for the effects of power on pressure distribution, lift and lift curve slope

Dynamical Stability and Habitability of Gamma Cephei Binary-Planetary System

It has been suggested that the long-lived residual radial velocity variations observed in the precision radial velocity measurements of the primary of Gamma Cephei (HR8974, HD222404, HIP116727) are likely due to a Jupiter-like planet around this star (Hatzes et al, 2003). In this paper, the orbital dynamics of this plant is studied and also the possibility of the existence of a hypothetical Earth-like planet in the habitable zone of its central star is discussed. Simulations, which have been carried out for different values of the eccentricity and semimajor axis of the binary, as well as the orbital inclination of its Jupiter-like planet, expand on previous studies of this system and indicate that, for the values of the binary eccentricity smaller than 0.5, and for all values of the orbital inclination of the Jupiter-like planet ranging from 0 to 40 degrees, the orbit of this planet is stable. For larger values of the binary eccentricity, the system becomes gradually unstable. Integrations also indicate that, within this range of orbital parameters, a hypothetical Earth-like planet can have a long-term stable orbit only at distances of 0.3 to 0.8 AU from the primary star. The habitable zone of the primary, at a range of approximately 3.1 to 3.8 AU, is, however, unstable.Comment: 25 pages, 7 figures, 3 tables, submitted for publicatio

Wall jet analysis for circulation control aerodynamics. Part 1: Fundamental CFD and turbulence modeling concepts

An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented

Development of a German version of the Oswestry Disability Index. Part 1: cross-cultural adaptation, reliability, and validity

Patient-orientated assessment methods are of paramount importance in the evaluation of treatment outcome. The Oswestry Disability Index (ODI) is one of the condition-specific questionnaires recommended for use with back pain patients. To date, no German version has been published in the peer-reviewed literature. A cross-cultural adaptation of the ODI for the German language was carried out, according to established guidelines. One hundred patients with chronic low-back pain (35 conservative, 65 surgical) completed a questionnaire booklet containing the newly translated ODI, along with a 0-10 pain visual analogue scale (VAS), the Roland Morris Disability Questionnaire, and Likert scales for disability, medication intake and pain frequency [to assess ODI's construct (convergent) validity]. Thirty-nine of these patients completed a second questionnaire within 2weeks (to assess test-retest reliability). The intraclass correlation coefficient for the test-retest reliability of the questionnaire was 0.96. In test-retest, 74% of the individual questions were answered identically, and 21% just one grade higher or lower. The standard error of measurement (SEM) was 3.4, giving a "minimum detectable change” (MDC95%) for the ODI of approximately 9 points, i.e. the minimum change in an individual's score required to be considered "real change” (with 95% confidence) over and above measurement error. The ODI scores correlated with VAS pain intensity (r=0.78, P<0.001) and Roland Morris scores (r=0.80, P<0.001). The mean baseline ODI scores differed significantly between the surgical and conservative patients (P<0.001), and between the different categories of the Likert scales for disability, medication use and pain frequency (in each case P<0.001). Our German version of the Oswestry questionnaire is reliable and valid, and shows psychometric characteristics as good as, if not better than, the original English version. It should represent a valuable tool for use in future patient-orientated outcome studies in German-speaking land

Development of a German version of the Oswestry Disability Index. Part 2: sensitivity to change after spinal surgery

When functional scales are to be used as treatment outcome measures, it is essential to know how responsive they are to clinical change. This information is essential not only for clinical decision-making, but also for the determination of sample size in clinical trials. The present study examined the responsiveness of a German version of the Oswestry Disability Index version 2.1 (ODI) after surgical treatment for low back pain. Before spine surgery 63 patients completed a questionnaire booklet containing the ODI, along with a 0-10 pain visual analogue scale (VAS), the Roland Morris disability questionnaire, and Likert scales for disability, medication intake and pain frequency. Six months after surgery, 57 (90%) patients completed the same questionnaire booklet and also answered Likert-scale questions on the global result of surgery, and on improvements in pain and disability. Both the effect size for the ODI change score 6months after surgery (0.87) and the area under the receiver operating characteristics (ROC) curve for the relative improvement in ODI score in relation to global outcome 6months after surgery (0.90) indicated that the ODI showed good responsiveness. The ROC method revealed that a minimum reduction of the baseline (pre-surgery) ODI score by 18% (equal to a mean 8-point reduction in this patient group) represented the cut-off for indicating a "good” individual outcome 6months after surgery (sensitivity 91.4% and specificity 82.4%). The German version of the ODI is a sensitive instrument for detecting clinical change after spinal surgery. Individual improvements after surgery of at least an 18% reduction on baseline values are associated with a good outcome. This figure can be used as a reliable guide for the determination of sample size in future clinical trials of spinal surger

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 billion years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 < a < 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids' orbit was varied in the range 0 < i < 60 and the semimajor axes were fixed. It turned out that only four 'windows' of stable orbits survive: these are the orbits for the initial inclinations 0 < i < 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.Comment: 15 pages, 12 figures, submitted to CMD

A blast-tolerant sandwich plate design with a polyurea interlayer

AbstractThis paper presents a study of both conventional and modified sandwich plate designs subjected to blast loads. The conventional sandwich Design (1) consists of thin outer (loaded side) and inner facesheets made of fibrous laminates, separated by a layer of structural foam core. In the modified Design (2), a thin polyurea interlayer is inserted between the outer facesheet and the foam core. Comparisons of the two designs are made during a long time period of 5.0ms, initiated by a pressure impulse lasting 0.05ms applied to a single span of a continuous plate. In the initial response period the overall deflections are limited and significant foam core crushing is caused in the conventional design by the incident compression wave. This type of damage is much reduced in the modified design, by stiffening of the polyurea interlayer under shock compression, which provides support to the outer facesheet and alters propagation of stress waves into the foam core. This benefits the long term, bending response and leads to significant reductions in facesheet strains and overall deflection. The total kinetic energy of the modified sandwich plate is much lower than that of a conventionally designed plate, and so is the stored and dissipated strain energy. Similar reductions are found when the conventional and the enhanced sandwich plates have equal overall thickness or equal total mass