Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

A user oriented computer program for the analysis of microwave mixers, and a study of the effects of the series inductance and diode capacitance on the performance of some simple mixers

A user oriented computer program for analyzing microwave and millimeter wave mixers with a single Schottky barrier diode of known I-V and C-V characteristics is described. The program first performs a nonlinear analysis to determine the diode conductance and capacitance waveforms produced by the local oscillator. A small signal linear analysis is then used to find the conversion loss, port impedances, and input noise temperature of the mixer. Thermal noise from the series resistance of the diode and shot noise from the periodically pumped current in the diode conductance are considered. The effects of the series inductance and diode capacitance on the performance of some simple mixer circuits using a conventional Schottky diode, a Schottky diode in which there is no capacitance variation, and a Mott diode are studied. It is shown that the parametric effects of the voltage dependent capacitance of a conventional Schottky diode may be either detrimental or beneficial depending on the diode and circuit parameters

Users guide: Steady-state aerodynamic-loads program for shuttle TPS tiles

A user's guide for the computer program that calculates the steady-state aerodynamic loads on the Shuttle thermal-protection tiles is presented. The main element in the program is the MITAS-II, Martin Marietta Interactive Thermal Analysis System. The MITAS-II is used to calculate the mass flow in a nine-tile model designed to simulate conditions duing a Shuttle flight. The procedures used to execute the program using the MITAS-II software are described. A list of the necessry software and data files along with a brief description of their functions is given. The format of the data file containing the surface pressure data is specified. The interpolation techniques used to calculate the pressure profile over the tile matrix are briefly described. In addition, the output from a sample run is explained. The actual output and the procedure file used to execute the program at NASA Langley Research Center on a CDC CYBER-175 are provided in the appendices

Experimental aerodynamic heating to simulated shuttle tiles

The heat transfer to simulated shuttle thermal protection system tiles was investigated experimentally using a highly instrumented metallic thin wall tile arranged with other metal tiles in a staggered tile array. Cold-wall heating rate data for laminar and turbulent flow were obtained in the Langley 8-foot high temperature tunnel at a nominal Mach number of 7, a nominal total temperature of 3300 R, free-stream unit Reynolds number from 3.4 x 10 to the 5th power to 2.2 x 10 to the 6th power per foot, and free-stream dynamic pressure of 1.8 psia to 9.1 psia. Experimental data are presented to illustrate the effects of flow angularity and gap width on both local peak heating and overall heating loads

Passive and active seismic isolation for gravitational radiation detectors and other instruments

Some new passive and active methods for reducing the effects of seismic disturbances on suspended masses are described, with special reference to gravitational radiation detectors in which differential horizontal motions of two or more suspended test masses are monitored. In these methods it is important to be able to determine horizontal seismic accelerations independent of tilts of the ground. Measurement of changes in inclination of the suspension wire of a test mass, relative to a direction defined by a reference arm of long period of oscillation, makes it possible to carry this out over the frequency range of interest for earth-based gravitational radiation detectors. The signal obtained can then be used to compensate for the effects of seismic disturbances on the test mass if necessary. Alternatively the signal corresponding to horizontal acceleration can be used to move the point from which the test mass is suspended in such a way as to reduce the effect of the seismic disturbance and also damp pendulum motions of the suspended test mass. Experimental work with an active anti-seismic system of this type is described

Implications of Spontaneous Glitches in the Mass and Angular Momentum in Kerr Space-Time

The outward-pointing principal null direction of the Schwarzschild Riemann tensor is null hypersurface-forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history of an outgoing light-like shell. The outward-- pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity) null hypersurface-forming. If the Kerr parameters of mass and angular momentum spontaneously jump across one such asymptotic hypersurface then the asymptotic hypersurface is shown to be the history of an outgoing light-like shell and a wire singularity-free spherical impulsive gravitational wave.Comment: 16 pages, TeX, no figures, accepted for publication in Phys. Rev.

Light-curve modelling constraints on the obliquities and aspect angles of the young Fermi pulsars

In more than four years of observation the Large Area Telescope on board the Fermi satellite has identified pulsed $\gamma$-ray emission from more than 80 young pulsars, providing light curves with high statistics. Fitting the observations with geometrical models can provide estimates of the magnetic obliquity $\alpha$ and aspect angle $\zeta$, yielding estimates of the radiation beaming factor and luminosity. Using $\gamma$-ray emission geometries (Polar Cap, Slot Gap, Outer Gap, One Pole Caustic) and radio emission geometry, we fit $\gamma$-ray light curves for 76 young pulsars and we jointly fit their $\gamma$-ray plus radio light curves when possible. We find that a joint radio plus $\gamma$-ray fit strategy is important to obtain ($\alpha$, $\zeta$) estimates that can explain simultaneous radio and $\gamma$-ray emission. The intermediate-to-high altitude magnetosphere models, Slot Gap, Outer Gap, and One pole Caustic, are favoured in explaining the observations. We find no evolution of $\alpha$ on a time scale of a million years. For all emission geometries our derived $\gamma$-ray beaming factors are generally less than one and do not significantly evolve with the spin-down power. A more pronounced beaming factor vs. spin-down power correlation is observed for Slot Gap model and radio-quiet pulsars and for the Outer Gap model and radio-loud pulsars. For all models, the correlation between $\gamma$-ray luminosity and spin-down power is consistent with a square root dependence. The $\gamma$-ray luminosities obtained by using our beaming factors not exceed the spin-down power. This suggests that assuming a beaming factor of one for all objects, as done in other studies, likely overestimates the real values. The data show a relation between the pulsar spectral characteristics and the width of the accelerator gap that is consistent with the theoretical prediction for the Slot Gap model.Comment: 90 pages, 80 figures (63 in Appendices), accepted for publication in Astronomy and Astrophysic

A Dynamical Systems Approach to Schwarzschild Null Geodesics

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum Lc corresponds to the unstable circular orbit at r=3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r=0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the limit as L goes to infinity, as described in Schwarzschild coordinates, these geodesics begin at r=0, flow along t=constant lines, turn around at r=2M, then continue to r=0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.Comment: 14 pages, 3 Figure

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