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NASA NTRS2004

A Geomagnetic Estimate of Mean Paleointensity

To test a statistical hypothesis about Earth's magnetic field against paleomagnetism, the present field is used to estimate time averaged paleointensity. The estimate uses the modem magnetic multipole spectrum R(n), which gives the mean square induction represented by spherical harmonics of degree n averaged over the sphere of radius a = 6371.2 km. The hypothesis asserts that the low degree multipole powers of the core-source field are distributed as chi-squared with 2n+l degrees of freedom and expectation values {R(n)} = K[(n+l/2)/n(n+l](c/a)(sup 2n+4), where c is the 3480 km radius of Earth's core. (This is compatible with a usually mainly geocentric axial dipolar field). Amplitude K is estimated by fitting theoretical to observational spectra through degree 12. The resulting calibrated expectation spectrum is summed through degree 12 to estimate expected square intensity {F(sup 2)}. The sum also estimates {F(sup 2)} averaged over geologic time, in so far as the present magnetic spectrum is a fair sample of that generated in the past by core geodynamic processes.

Voorhies, Coerte↗
NASA NTRS1979

Linear ruby scale and one megabar

The accuracy and validity of certain techniques used in studying high-pressure transitions have been investigated. Experiments which place upper limits of about 20 GPa and about 50 GPa on pressures practically attainable using uniaxial supported opposed anvil devices with tungsten carbide pistons and uniaxial opposed flat anvil diamond devices, respectively, are reported. Direct static determinations of the transition pressures of GaP by two different methods are described. The values obtained indicate that the linear ruby scale increasingly overestimates the transition pressure as the pressure rises above 10 GPa. It is further shown that the use of shock-based marker materials, such as silver, as the basis of pressure measurement in X-ray diffraction studies leads to bulk moduli of cubic carbides which are in extreme disagreement with expected values.

Ruoff, A. L.↗
NASA NTRS1989

Theoretical study of the dipole moment function of OH(X2Pi)

A theoretical study of the sensitivity of the dipole moment function (DMF) of the X2Pi ground state of OH to basis-set saturation and to refinements in the correlation treatment is presented. Emphasis is placed on determining the slope of the DMF at r(e) and the r value at which the maximum occurs. Consideration is given to the effect of oxygen polarization functions up through h type, expansion of the active orbital space to include the O 3d-delta orbital, the effect of higher excitations using the averaged coupled-pair functional method, and the effect of evaluating the dipole moment as an energy derivative rather than as an expectation value. The theoretical DMFs obtained here, which should be the most accurate to date, differ markedly from an empirical DMF of Turnbull and Lowe that is based on experimentally derived intensity ratios. The theoretical DMFs agree better with a recently published DMF of Nelson et al., but suggest that this empirical DMF is also inaccurate for r greater than 2.3 a0.

Langhoff, Stephen R.↗
NASA NTRS1987

IRAS observations of supernova remnants - A comparison between their infrared and X-ray cooling rates

A comparison is presented between the total IR and X-ray cooling rates of nine selected Galactic supernova remnants. The observed IR-to-X-ray cooling ratio (IRX ratio) values are larger than unity for most remnants, ranging from five for the adiabatic remnant Puppis A, to about 1000 for RCW 86. Most of the observed IR emission from the remnants can be attributed to thermal emission from dust collisionally heated by the shocked plasma. A comparison between the theoretical and observed IRX ratio shows that only two of the nine remnants have IRX ratios within a factor of about three of the expected value. Puppis A, Kepler, Tycho, and SN 1006 have IRX ratios that are significantly smaller than the theoretically predicted value, suggesting that the dust is significantly depleted in the ambient medium into which they are expanding.

Dwek, Eli↗
NASA NTRS1997

Advection in Accretion Disk Boundary Layers

Recent numerical simulations of accretion disk boundary layers have shown qualitatively the importance tance of advected energy in the inner region of the disk. In this short paper we present quantitative results of advective boundary layers in the optically thick regime. Numerical results are obtained for various systems, by means of a one-dimensional time-dependent numerical code. At high accretion mass rates, dot-M approx. = 10(exp -4) solar mass/yr, or low values of the viscosity parameter, alpha approx. = 0.001-0.01 (characteristic of FU Orionis systems and some symbiotic stars), the optical thickness in the inner part of the disk becomes very large (tau much greater than 1). The disk, unable to cool efficiently, becomes geometrically thick (H/r approx. = 0.5). The energy dissipated in the dynamical boundary layer is radiated outward to larger radii and advected into the star. The boundary-layer luminosity is only a fraction of its expected value; the rest of the energy is advected into the star. The fraction of the advected energy is zeta = L(sub adv)/L(sub acc) approx. = 0.1 in symbiotic stars (accretion onto a low-mass main-sequence star) and zeta approx. = 0.2 in FU Ori systems (accretion onto a pre-main sequence star).

Godon, Patrick↗
NASA NTRS2003

Interleaved Observation Execution and Rescheduling on Earth Observing Systems

Observation scheduling for Earth orbiting satellites solves the following problem: given a set of requests for images of the Earth, a set of instruments for acquiring those images distributed on a collecting of orbiting satellites, and a set of temporal and resource constraints, generate a set of assignments of instruments and viewing times to those requests that satisfy those constraints. Observation scheduling is often construed as a constrained optimization problem with the objective of maximizing the overall utility of the science data acquired. The utility of an image is typically based on the intrinsic importance of acquiring it (for example, its importance in meeting a mission or science campaign objective) as well as the expected value of the data given current viewing conditions (for example, if the image is occluded by clouds, its value is usually diminished). Currently, science observation scheduling for Earth Observing Systems is done on the ground, for periods covering a day or more. Schedules are uplinked to the satellites and are executed rigorously. An alternative to this scenario is to do some of the decision-making about what images are to be acquired on-board. The principal argument for this capability is that the desirability of making an observation can change dynamically, because of changes in meteorological conditions (e.g. cloud cover), unforeseen events such as fires, floods, or volcanic eruptions, or un-expected changes in satellite or ground station capability. Furthermore, since satellites can only communicate with the ground between 5% to 10% of the time, it may be infeasible to make the desired changes to the schedule on the ground, and uplink the revisions in time for the on-board system to execute them. Examples of scenarios that motivate an on-board capability for revising schedules include the following. First, if a desired visual scene is completely obscured by clouds, then there is little point in taking it. In this case, satellite resources, such as power and storage space can be better utilized taking another image that is higher quality. Second, if an unexpected but important event occurs (such as a fire, flood, or volcanic eruption), there may be good reason to take images of it, instead of expending satellite resources on some of the lower priority scheduled observations. Finally, if there is unexpected loss of capability, it may be impossible to carry out the schedule of planned observations. For example, if a ground station goes down temporarily, a satellite may not be able to free up enough storage space to continue with the remaining schedule of observations. This paper describes an approach for interleaving execution of observation schedules with dynamic schedule revision based on changes to the expected utility of the acquired images. We describe the problem in detail, formulate an algorithm for interleaving schedule revision and execution, and discuss refinements to the algorithm based on the need for search efficiency. We summarize with a brief discussion of the tests performed on the system.

Khatib, Lina↗
NASA NTRS1987

Heat transfer with very high free-stream turbulence and heat transfer with streamwise vortices

Two experimental programs related to augmentation of heat transfer by complex flow characteristics are reviewed. The first program deals with very high turbulence (up to 63 percent) which was shown to result in Stanton numbers as much as five times the expected values. Results from a number of trials show that fixing the free stream velocity, x-Reynolds number, turbulence intensity and integral length scale does not fix the Stanton number. Two such cases were found in which the Stanton number of one was 40 percent larger than the other. Mean velocity and mean temperature profiles are presented, as well as profiles of turbulence intensity within the boundary layer. The second program deals with vortices originating at bluff bodies and traveling downstream embedded in the wall boundary layer. Velocity vector maps from the boundary layers and distributions of Stanton number on the wall are presented for three types of bodies: square, cylindrical and teardrop. The heat transfer and velocity maps do not show evidence of the expected horseshoe vortices but, instead, show a strong common flow up vortex pair. The fluid mechanic mechanism responsible for this secondary flow field has not yet been identified.

Moffat, Robert J.↗
NASA NTRS1999

ISCCP Cloud Properties Associated with Standard Cloud Types Identified in Individual Surface Observations

Individual surface weather observations from land stations and ships are compared with individual cloud retrievals of the International Satellite Cloud Climatology Project (ISCCP), Stage C1, for an 8-year period (1983-1991) to relate cloud optical thicknesses and cloud-top pressures obtained from satellite data to the standard cloud types reported in visual observations from the surface. Each surface report is matched to the corresponding ISCCP-C1 report for the time of observation for the 280x280-km grid-box containing that observation. Classes of the surface reports are identified in which a particular cloud type was reported present, either alone or in combination with other clouds. For each class, cloud amounts from both surface and C1 data, base heights from surface data, and the frequency-distributions of cloud-top pressure (p(sub c) and optical thickness (tau) from C1 data are averaged over 15-degree latitude zones, for land and ocean separately, for 3-month seasons. The frequency distribution of p(sub c) and tau is plotted for each of the surface-defined cloud types occurring both alone and with other clouds. The average cloud-top pressures within a grid-box do not always correspond well with values expected for a reported cloud type, particularly for the higher clouds Ci, Ac, and Cb. In many cases this is because the satellites also detect clouds within the grid-box that are outside the field of view of the surface observer. The highest average cloud tops are found for the most extensive cloud type, Ns, averaging 7 km globally and reaching 9 km in the ITCZ. Ns also has the greatest average retrieved optical thickness, tau approximately equal 20. Cumulonimbus clouds may actually attain far greater heights and depths, but do not fill the grid-box. The tau-p(sub c) distributions show features that distinguish the high, middle, and low clouds reported by the surface observers. However, the distribution patterns for the individual low cloud types (Cu, Sc, St) occurring alone overlap to such an extent that it is not possible to distinguish these cloud types from each other on the basis of tau-p(sub c) values alone. Other cloud types whose tau-p(sub c) distributions are indistinguishable are Cb, Ns, and thick As. However, the tau-p(sub c) distribution patterns for the different low cloud types are nevertheless distinguishable when all occurrences of a low cloud type are included, indicating that the different low types differ in their probabilities of co-occurrence with middle and high clouds.

Hahn, Carole J.↗
NASA NTRS1993

Low redshift Lyman alpha absorption lines and the dark matter halos of disk galaxies

Recent observations using the Hubble Space Telescope of the z = 0.156 QSO 3C 273 have discovered a surprisingly large number of Ly-alpha absorption lines. In particular, Morris et al. found 9 certain and 7 possible Ly-alpha lines with equivalent widths above 25 mA. This is much larger (by a factor of 5-10) than the number expected from extrapolation of the high-redshift behavior of the Ly-alpha forest. Within the context of pressure-confined models for the Ly-alpha clouds, this behavior can be understood if the ionizing background declines sharply between z is approximately 2 and z is approximately 0. However, this requires that the ionizing photon flux drop as rapidly as the QSO volume emissivity; moreover, the absorbers must have a space density n(sub O) is approximately 2.6(N/10)h/((D/100 kpc)(sup 2)) Mpc(sup -3) where D is the present-day diameter of the absorbers. It is somewhat surprising that such necessarily fragile objects could have survived in such numbers to the present day. It is shown that it is plausible that the atomic hydrogen extents of spiral and irregular galaxies are large enough to produce the observed number of Ly-alpha absorption lines toward 3C 273, and that the neutral column densities and doppler b-values expected under these conditions fall in the range found by Morris et al. (1991).

Maloney, Philip↗
NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗
NASA NTRS1994

Is a data set distributed as a power law? A test, with application to gamma-ray burst brightnesses

We present a method to determine whether an observed sample of data is drawn from a parent distribution that is pure power law. The method starts from a class of statistics which have zero expectation value under the null hypothesis, H(sub 0), that the distribution is a pure power law: F(x) varies as x(exp -alpha). We study one simple member of the class, named the `bending statistic' B, in detail. It is most effective for detection a type of deviation from a power law where the power-law slope varies slowly and monotonically as a function of x. Our estimator of B has a distribution under H(sub 0) that depends only on the size of the sample, not on the parameters of the parent population, and is approximated well by a normal distribution even for modest sample sizes. The bending statistic can therefore be used to test a set of numbers is drawn from any power-law parent population. Since many measurable quantities in astrophysics have distriibutions that are approximately power laws, and since deviations from the ideal power law often provide interesting information about the object of study (e.g., a `bend' or `break' in a luminosity function, a line in an X- or gamma-ray spectrum), we believe that a test of this type will be useful in many different contexts. In the present paper, we apply our test to various subsamples of gamma-ray burst brightness from the first-year Burst and Transient Source Experiment (BATSE) catalog and show that we can only marginally detect the expected steepening of the log (N (greater than C(sub max))) - log (C(sub max)) distribution.

Wijers, Ralph A. M. J.↗
NASA NTRS1965

On stochastic extremum problems - calculus.

Lagrange multiplier technique for determining stationary points /of functions/ or stationary functions /of integrals/ of expected value of random functions with certain random constraints

LAGRANGE MULTIPLIER↗
NASA NTRS1968

Predicted vibration responses of Apollo structure and effects of pressure correlation lengths on response

Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.

R W White↗