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NASA NTRS1985

Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy

Statistical procedures taken from the field of survival analysis have been adapted to astronomical usage and have been applied to a sample of stars in the B-V color range between 0.1 and 0.5 with measured soft X-ray luminosities and projected equatorial velocities. The two-sample problem and linear regression problem with arbitrarily censored data were studied. A new method for determining the linear regression between two random variables in the presence of arbitrary censoring has been developed which can also be used for a likelihood-ratio test for the independence of two random variables and for principal-component analysis in the presence of arbitrary censoring. The required numerical computations can be carried out straightforwardly and rapidly.

Schmitt, J. H. M. M.↗

NASA NTRS1984

The three-dimensional compressible flow in a radial inflow turbine scroll

This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.

Hamed, A.↗

NASA NTRS1985

The propagation of ultraheavy cosmic-ray nuclei revisited

The propagation of ultraheavy (Z = 30 or more) cosmic-ray nuclei is investigated theoretically in the leaky-box model, expanding the analysis of Brewster et al. (1983) to include more individual nuclides and account for recent findings with respect to source compositions, cross sections, and the dependence of escape length and spectral characteristics on rigidity. The results of numerical computations are presented in tables and graphs and compared with observational data (from HEAO-3) and other theoretical predictions. Good agreement is obtained for Z = 32-42 and 50-58 using a solar-system source with a first-ionization-potential correlation factor and the solar-system abundances given by Anders and Ebihara (1982).

Brewster, N. R.↗

NASA NTRS1985

On the electromagnetic scattering from infinite rectangular conducting grids

The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms.

Christodoulou, C.↗

NASA NTRS1986

Transfer function analysis of thermospheric perturbations

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

Mayr, H. G.↗

NASA NTRS1986

Theory of homogeneous nucleation - A chemical kinetic view

A simple function with two undetermined parameters has been used in place of the Thomson-Gibbs relation to relate the activation energy of the vaporization reaction to cluster size. The parameters are iterated to assume optimum values in numerical computation so experimental data may be correlated. Calculations show this approach closely predicts and correlates available data for water, benzene, and ethanol. The nucleation formulism is redeveloped with an emphasis on the chemical kinetic view. Surface tension of the liquid and free energy of droplet formation are not used in its derivation.

Yang, C. H.↗

NASA NTRS1986

Numerical and experimental investigation of nonswirling and swirling confined jets

An investigation of the influence of large scale structures on the flow development for coaxial jets with sudden expansion (with and without swirl) is presented. Both an experimental study and numerical predictions were performed for a configuration corresponding to that considered by Johnson and Bennett and Roback and Johnson. The effects of large scale structures on the swirling and nonswirling flows are documented, in particular their influence on turbulence modeling and the numerical simulation. The ensemble-averaged, time-dependent Navier-Stokes equations are solved by an LBI procedure to predict the turbulent flow field. Effects of artificial dissipation and placement of the upstream boundary in the numerical computation are also discussed.

Brondum, D. C.↗

NASA NTRS1985

Modelling of three-dimensional shock wave turbulent boundary layer interactions

The accuracy of numerical computations of the three-dimensional sharp fin flow field using the Reynolds-averaged Navier-Stokes equations is examined. Computed flows are compared with a set of benchmark experiments at Mach 3 for two different Reynolds numbers. A detailed comparison is performed between experimental data and separate computational results for the three-dimensional sharp fin for a 10 deg fin angle in order to examine the accuracy of two different turbulence models. The computed surface pressure for the fin at a 20 deg angle is compared with recent experimental data. The computed yaw angle profiles are shown to be sensitive to the turbulence model. In the immediate vicinity of the surface, the calculated results using the Baldwin-Lomax (1978) model are in better agreement with the data than the Jones-Launder (1972) model. Within the inner portion of the boundary layer, both models tend to underpredict the yaw angle.

Knight, D. D.↗

NASA NTRS1985

Theoretical and experimental studies in support of the geophysical fluid flow experiment

Meteorologists and astrophysicists interested in large scale planetary and solar circulations have come to recognize the importance of rotation and stratification in determining the character of these flows. In particular, the effect of latitude-dependent Coriolis force on nonlinear convection is thought to play a crucial role in such phenomena as differential rotation on the Sun, cloud band orientation on Jupiter, and the generation of magnetic fields in thermally driven dynamos. The continuous low-gravity environment of the orbiting space shuttle offers a unique opportunity to make laboratory studies of such large-scale thermally driven flows under the constraint imposed by rotation and sphericity. This is possible because polarization forces in a dielectric liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC) is an implementation of this ideal in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large a-c voltage. The experiment, to be flown on Spacelab III (currently set for launch April 29, 1985), will explore non-linear mode selection and high Rayleigh number turbulence in a rotating convecting spherical shell of liquid. Experiments will be carried out in a low driving parameter range where some limited numerical experimentation is currently feasible, as well as in a parameter range significantly beyond numerical computation for many years.

Hart, J.↗

NASA NTRS1987

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Pifko, A. B.↗

NASA NTRS1987

Research on knowledge representation, machine learning, and knowledge acquisition

Research in knowledge representation, machine learning, and knowledge acquisition performed at Knowledge Systems Lab. is summarized. The major goal of the research was to develop flexible, effective methods for representing the qualitative knowledge necessary for solving large problems that require symbolic reasoning as well as numerical computation. The research focused on integrating different representation methods to describe different kinds of knowledge more effectively than any one method can alone. In particular, emphasis was placed on representing and using spatial information about three dimensional objects and constraints on the arrangement of these objects in space. Another major theme is the development of robust machine learning programs that can be integrated with a variety of intelligent systems. To achieve this goal, learning methods were designed, implemented and experimented within several different problem solving environments.

Buchanan, Bruce G.↗

NASA NTRS1987

Optical communication with semiconductor laser diodes

A 25 megabit/sec direct detection optical communication system that used Q=4 PPM signalling was constructed and its performance measured under laboratory conditions. The system used a single-mode AlGaAs laser diode transmitter and low noise silicon avalanche photodiode (APD) photodetector. Comparison of measured performance with the theoretical revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10 to the -12 power A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain to use and overestimates of system bit error probability. A procedure is given to numerically compute system performance which uses the more accurate Webb's Approximation of the exact Conradi distribution for the APD ouput signal that does not require excessive amounts of computer time (a few minutes of VAX 8600 CPU time per system operating point). Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. This system achieved a bit error probability of 10 to the -6 power at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700.

Davidson, F.↗

NASA NTRS1987

Reconstruction of a three-dimensional, transonic rotor flow field from holographic interferogram data

Holographic interferometry and computerized aided tomography (CAT) are used to determine the transonic velocity field of a model rotor blade in hover. A pulsed ruby laser recorded 40 interferograms with a 2 ft dia view field near the model rotor blade tip operating at a tip Mach number of 0.90. After digitizing the interferograms and extracting the fringe order functions, the data are transferred to a CAT code. The CAT code then calculates the perturbation velocity in several planes above the blade surface. The values from the holography-CAT method compare favorably with previously obtained numerical computations in most locations near the blade tip. The results demonstrate the technique's potential for three dimensional transonic rotor flow studies.

Kittleson, John K.↗

NASA NTRS1985

A Lagrangian method for the shallow water equations based on a Voronoi mesh - Flows on a rotating sphere

A Lagrangian scheme using the Voronoi mesh is applied to study shallow water flow on a sphere. Discrete approximations to the shallow water equations are obtained for the surfaces of a nonrotating and a rotating sphere, and discrete differential operators are defined for the gradient and the divergence on the sphere. Dissipation is put into the model, when needed, by merging fluid points when they get too close to each other. The full numerical scheme is described and results of numerical computations on various test cases are given, including zonal flow and the Riemann problem.

Augenbaum, J. M.↗

NASA NTRS1986

The generation of capillary instabilities on a liquid jet

The coupling between imposed disturbances and capillary instabilities on a liquid jet is examined. It is shown that in most physical situations the forcing produces neutral waves, which can then turn into growing waves as the profile relaxes or may be amplified nonlinearly by a mechanism of the type considered by Akylas and Benney (1980). The effectiveness of the coupling is expressed quantitatively by numerically computed values of the 'coupling coefficient'.

Leib, S. J.↗

NASA NTRS1986

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

Majda, George↗

NASA NTRS1985

The form of Newtonian cooling in atmospheric tidal theory

The analytical results of Zurek (1986) are applied to compare the vertical-structure equations obtained by Dickinson and Geller (1968) and Lindzen and McKenzie (1967) in solving the classical tidal equations for planetary atmospheres when Newtonian cooling (NC) is included as part of diabatic tidal forcing. The two diabatic forcings are found to be different when the basic state temperature varies with height, and it is recommended that a log-pressure NC formulation be used whenever temperature is made a function of pressure in the radiative-damping calculation. Scaling arguments are presented to show that the choice of NC formulation has significant effects only in cases where the radiative time constants are short (such as the thin CO2 atmosphere of Mars). Numerical computations for that case indicate a difference of 20 percent in amplitude and 15 deg in phase for the (probably meteorologically significant) 4.1-d wavenumber-one Rossby tidal mode.

Zurek, Richard W.↗

NASA NTRS1987

Dark matter in the galactic disk

Observational data on the distributions of tracer stars, F dwarfs and K giants were used as input to obtain self-consistent solutions for the Poisson and Vlasov equations to set bounds on the amount of missing matter in the solar neighborhood. The numerical computations were carried out using Galaxy models which feature multiple disk components and an unseen massive halo. The star data included the mass components and velocity dispersions. Consideration of various possible distributions of the unseen matter leads to the conjecture that half of the disk material in the solar neighborhood has yet to be observed. Techniques for determining if brown dwarfs are a significant component of the missing mass are discussed, as are improved models which would use limited numbers of tracer stars to set further constraints on the amount and distribution of the missing mass.

Bahcall, John N.↗