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NASA NTRS1985

Statistical methods for astronomical data with upper limits. I - Univariate distributions

The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.

Feigelson, E. D.↗

NASA NTRS1985

Flammability Limits of Gases Under Low Gravity Conditions

The purpose of this combustion science investigation is to determine the effect of zero, fractional, and super gravity on the flammability limits of a premixed methane air flame in a standard 51 mm diameter flammability tube and to determine, if possible, the fluid flow associated with flame passage under zero-g conditions and the density (and hence, temperature) profiles associated with the flame under conditions of incipient extinction. This is accomplished by constructing an appropriate apparatus for placement in NASA's Lewis Research Center Lear Jet facility and flying the prescribed g-trajectories while the experiment is being performed. Data is recorded photographically using the visible light of the flame. The data acquired is: (1) the shape and propagation velocity of the flame under various g-conditions for methane compositions that are inside the flammable limits, and (2) the effect of gravity on the limits. Real time accelerometer readings for the three orthogonal directions are displayed in full view of the cameras and the framing rate of the cameras is used to measure velocities.

Strehlow, R. A.↗

NASA NTRS1986

Limits on coronal material in normal galaxies

Measurements of the X-ray surface brightness of a face on disk galaxy M101, have previously been used to place upper limits on the power radiated by a hot corona. Such analysis contrains the effective density of the disk; either it must be so low that the remnants drive a fast hot wind (low radiated power) or so high that the remnant temperature at overlap is low (low X-ray power). These X-ray measurements are here used to constrain the properties of the population of supernova remnants evolving in the disk. This adds a further constraint since young remnants evolving in higher density radiate more of their energy in X-rays, whether or not they eventually overlap to generate a hot corona. The strength of this second limit depends strongly on the density history of the remnants and on the assumed supernova rate. For evaporative evolution the analysis rules out McKee and Ostriker ISM model in particular and evaporative evolution in general unless the supernova rate is at least several times lower than current expectations. For standard Sedov evolutions, the density limit marginally admits evolution in 0.2 cu m, a popular alternative to the McKee and Ostriker model.

Mccammon, D.↗

NASA NTRS1985

An observed upper limit on stratospheric hydrogen peroxide

Observations collected by a ground-based heterodyne receiver of an emission from the 7(0.7)-6(1.5) rotational torsional transition of H2O2 at 270.610 GHz are studied. An integrated spectrometer output of the data obtained at Mauna Kea, Hawaii in late May and early June of 1983 is presented. The removal of the ozone line background profile from the data is described. With no signal detected in the output of a 256-channel filter spectrometer the calculation of an upper limit on stratospheric H2O2 is possible. The utilization of the mixing ratio profile of Sze and Ko (1984) to compute the limit of H2O2 is examined. An upper limit for H2O2 of approximately 1 x 10 to the 14th/cu cm between 30-50 km is established.

De Zafra, R. L.↗

NASA NTRS1986

Confidence limits for small numbers of events in astrophysical data

The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations. Convenient tables and approximate formulae are here presented for confidence limits which are based on such Poisson and binomial statistics. The limits in the tables are given for all confidence levels commonly used in astrophysics.

Gehrels, N.↗

NASA NTRS1986

Limits on supernova rates and interstellar densities from X-ray observations of M101

Measurements of the X-ray surface brightness of a face-on disk galaxy M101 have previously been used to place upper limits on the power radiated by a hot corona. Such analysis constrains the effective density of the disk; either it must be so low that the remnants drive a fast hot wind (low radiated power), or so high that the remnant temperature at overlap is low (low X-ray power). These X-ray measurements are here used to constrain the properties of the population of supernova remnants evolving in the disk. This adds a further constraint since young remnants evolving in higher density radiate more of their energy in X-rays, whether or not they eventually overlap to generate a hot corona. The strength of this second limit depends strongly on the density history of the remnants (e.g., evaporative vs. nonevaporative evolution) and on the assumed supernova rate. For evaporative evolution the analysis rules out the McKee (1977) and Ostriker (1977) interstellar medium model in particular and evaporative evolution in general unless the supernova rate is at least several times lower than current expectations. For standard Sedov evolutions, the density limit marginally admits 0.2/cu cm, a popular alternative to the McKee and Ostriker model.

Cox, D. P.↗

NASA NTRS1987

Development of confidence limits by pivotal functions for estimating software reliability

The utility of pivotal functions is established for assessing software reliability. Based on the Moranda geometric de-eutrophication model of reliability growth, confidence limits for attained reliability and prediction limits for the time to the next failure are derived using a pivotal function approach. Asymptotic approximations to the confidence and prediction limits are considered and are shown to be inadequate in cases where only a few bugs are found in the software. Departures from the assumed exponentially distributed interfailure times in the model are also investigated. The effect of these departures is discussed relative to restricting the use of the Moranda model.

Dotson, Kelly J.↗

NASA NTRS1987

An upper limit on the sizes of shepherding satellites at Saturn's ring G

An accurate analytical theory of the absorption of energetic magnetospheric particles by an inert satellite is developed for the case in which the radius b of the satellite is much less than the equatorial gyroradius r(g) of the particles and in which r(g) is in turn much less than the radius r of the satellite's orbit. In previous interpretations of Pioneer 11 observations, an estimate of the lifetime against absorption of energetic protons at Saturn's ring G has been made. This lifetime is used in the framework of the absorption theory to establish an upper limit on the sizes of shepherding satellites associated with the ring. The resulting upper limit, ignoring the absorption of the optically observed particulate matter, is given for an assemblage of N satellites of various radii. It is noted that ring G lies outside the Roche limit. No shepherding satellites at ring G were detected optically by Voyagers 1 and 2, and the searches were not comprehensive in longitudinal coverage.

Van Allen, James A.↗

NASA NTRS1987

Cell model and elastic moduli of disordered solids - Low temperature limit

The cell theory has been previously employed to compute the equation of state of a disordered condensed system. It is now generalized to include anisotropic stresses. The condition of affine deformation is adopted, transforming an orginally spherical into an ellipsoidal cell. With a Lennard-Jones n-m potential between nonbonded centers, the formal expression for the deformational free energy is derived. It is to be evaluated in the limit of the linear elastic range. Since the bulk modulus in this limit is already known, it is convenient to consider a uniaxial deformation. To begin with, restrictions are made to the low-temperature limit in the absence of entropy contributions. Young's modulus and Poisson's ratio then follow.

Peng, S. T. J.↗

NASA NTRS1987

Combustion rate limits of hydrogen plus hydrocarbon fuel: Air diffusion flames from an opposed jet burner technique

Combustion of H2/hydrocarbon (HC) fuel mixtures may be considered in certain volume-limited supersonic airbreathing propulsion applications. Effects of HC addition to H2 were evaluated, using a recent argon-bathed, coaxial, tubular opposed jet burner (OJB) technique to measure the extinction limits of counterflow diffusion flames. The OJB flames were formed by a laminar jet of (N2 and/or HC)-diluted H2 mixture opposed by a similar jet of air at ambient conditions. The OJB data, derived from respective binary mixtures of H2 and methane, ethylene, or propane HCs, were used to characterize BLOWOFF and RESTORE. BLOWOFF is a sudden breaking of the dish-shaped OJB flame to a stable torus or ring shape, and RESTORE marks sudden restoration of the central flame by radial inward flame propagation. BLOWOFF is a measure of kinetically-limited flame reactivity/speed under highly stretched, but relatively ideal impingement flow conditions. RESTORE measures inward radial flame propagation rate, which is sensitive to ignition processes in the cool central core. It is concluded that relatively small molar amounts of added HC greatly reduce the reactivity characteristics of counterflow hydrogen-air diffusion flames, for ambient initial conditions.

Pellett, Gerald L.↗

NASA NTRS1987

Imaging performance of annular apertures. VI - Limitations by optical surface deviations

The performance of optical systems is limited by imperfect optical surfaces that degrade the images below the level set by wave theoretical limits. The central irradiance functions are derived for slit and circular apertures with five distributions of wavefront errors and for a range of maximal wavefront deviations. For practical frequency of occurrence distributions of wavefront deviations, the point spread and the image energy integral functions are determined. Practical performances of optical systems are derived and performance limits discussed.

Tschunko, Hubert F. A.↗

NASA NTRS1988

Present imaging limitations to providing a geological assessment of potential sample return sites on Mars

A Mars sample return mission will provide a huge increase in knowledge about the region explored by the roving vehicle. However, presently there are some important limitations on the extent to which the geology of a potential site can be understood prior to landing the sample return vehicle on Mars. These limitations could affect not only the potential science return of the mission but also the safety of the vehicle. These limitations are examined.

Zimbelman, James R.↗

NASA NTRS1988

Analysis of limit cycles in control systems for joint dominated structures

An approach to the modeling of limit cycles due to joint nonlinearities in large joint dominated space structures is presented which makes it possible to predict limit cycles and determine their stability. An actively controlled truss structure with nonlinear joints is modeled as a linear system with nonlinear feedback by separating the joint load-displacement characteristics into a linear part, which prevails at large displacements, and a nonlinear part. By replacing the joints by their linear parts, it is possible to perform a standard model decomposition which yields a reduced order linear model. Linear control laws can be easily included into the linear part of the system; nonlinear control laws can be implemented but they must be fed back to the linear model. The modeling approach described here allows straightforward limit cycle analysis.

Mercadal, M.↗

NASA NTRS1989

Limits to the radiative decays of neutrinos and axions from gamma-ray observations of SN 1987A

Gamma-ray observations obtained by the SMM gamma-ray spectrometer in the energy range 4.1-6.4 MeV are used to provide limits on the possible radiative decay of neutrinos and axions emitted by SN 1987A. For branching ratio values for the radiative decay modes of less than about 0.0001, the present limits are more stringent than those based upon the photon flux from decaying relic neutrinos. The data are also used to set an axion mass limit.

Kolb, Edward W.↗

NASA NTRS1989

Orbital migration of protoplanets - The inertial limit

The dynamical evolution of a disk and the orbital migration of an embedded protoplanet are examined. It is shown how the migration of a protoplanet due to density wave torques can suppress the tendency for tidal truncation of the disk. A critical mass is determined as a function of the disk properties that represents the limiting mass that can sustain drift without stalling. This inertial limit is derived analytically, using a quasi-steady state theory, and confirmed by numerical experiment. This result contradicts the claim of Lin and Papaloizou (1986) that such a limit does not exist. Orbital mobility of objects due to density wave torques may have played an important role in the early evolution of the solar system.

Ward, William R.↗

NASA NTRS1990

Limitations of the method of characteristics when applied to axisymmetric hypersonic nozzle design

A design study of axisymmetric hypersonic wind tunnel nozzles was initiated by NASA Langley Research Center with the objective of improving the flow quality of their ground test facilities. Nozzles for Mach 6 air, Mach 13.5 nitrogen, and Mach 17 nitrogen were designed using the Method of Characteristics/Boundary Layer (MOC/BL) approach and were analyzed with a Navier-Stokes solver. Results of the analysis agreed well with design for the Mach 6 case, but revealed oblique shock waves of increasing strength originating from near the inflection point of the Mach 13.5 and Mach 17 nozzles. The findings indicate that the MOC/BL design method has a fundamental limitation that occurs at some Mach number between 6 an 13.5. In order to define the limitation more exactly and attempt to discover the cause, a parametric study of hypersonic ideal air nozzles designed with the current MOC/BL method was done. Results of this study indicate that, while stagnations conditions have a moderate affect on the upper limit of the method, the method fails at Mach numbers above 8.0.

Edwards, Anne C.↗

NASA NTRS1990

Limits on the antiproton/proton ratio in the cosmic radiation from 100 MeV to 1580 MeV

A search for antiprotons (p-bars) in the cosmic radiation with energies below 1580 MeV at the top of the atmosphere was performed using the PBAR balloon-borne magnetic spectrometer. No antiprotons were observed in 124,000 proton events. For the energy interval 100-640 MeV, an upper limit is reported to the p-bar/p ratio of 2.8 x 10 to the -5th at the top of the atmosphere, after correcting for instrumental efficiencies and contributions from secondary particles. No antiproton was observed in the energy interval 640-1580 MeV, which yields an upper limit to the p-bar/p ratio of 6.1 x 10. By combining both data sets, the limits on the p-bar/p ratio can be improved to 2.0 x 10 to the -5th. The detector performance and instrumental efficiencies of the individual detector components are discussed. A detail Monte Carlo calculation was used to evaluate the instrumental efficiency for both antiprotons and protons as a function of momentum.

Salamon, M. H.↗

NASA NTRS1990

Performance limitations of joint variable-feedback controllers due to manipulator structural flexibility

The performance limitations of manipulators under joint variable-feedback control are studied as a function of the mechanical flexibility inherent in the manipulator structure. A finite-dimensional time-domain dynamic model of a two-link two-joint planar manipulator is used in the study. Emphasis is placed on determining the limitations of control algorithms that use only joint variable-feedback information in calculations of control decisions, since most motion control systems in practice are of this kind. Both fine and gross motion cases are studied. Results for fine motion agree well with previously reported results in the literature and are also helpful in explaining the performance limitations in fast gross motions.

Cetinkunt, Sabri↗