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NASA NTRS1973

A unified development of several techniques for the representation of random vectors and data sets

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Bundick, W. T.↗

NASA NTRS1974

Spin projection of single-determinant wavefunctions

The components of the one- and two-particle density matrices resulting from spin projection of a single-determinant wave function are rederived by the method of expansion in terms of the natural orbitals of charge density, and the results are found to diverge from those given by Harriman and Sando for the two-particle case. The theory is generalized to include molecules with unequal numbers of electrons and basis orbitals and is applied to a number of organic molecules and ions. The correctness and internal consistency of the results argue in favor of the modification described.

Phillips, D. H.↗

NASA NTRS1975

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Hubbard, W. B.↗

NASA NTRS1983

The economics of data acquisition computers for ST and MST radars

Some low cost options for data acquisition computers for ST (stratosphere, troposphere) and MST (mesosphere, stratosphere, troposphere) are presented. The particular equipment discussed reflects choices made by the University of Alaska group but of course many other options exist. The low cost microprocessor and array processor approach presented here has several advantages because of its modularity. An inexpensive system may be configured for a minimum performance ST radar, whereas a multiprocessor and/or a multiarray processor system may be used for a higher performance MST radar. This modularity is important for a network of radars because the initial cost is minimized while future upgrades will still be possible at minimal expense. This modularity also aids in lowering the cost of software development because system expansions should rquire little software changes. The functions of the radar computer will be to obtain Doppler spectra in near real time with some minor analysis such as vector wind determination.

Watkins, B. J.↗

NASA NTRS1988

Development of a liquid-fed water resistojet

A concept for a forced-flow once-through water vaporizer for application to resistojet thrusters was evaluated as an element of a laboratory model thruster and tested to investigate its operating characteristics. The vaporizer design concept employs flow swirling to attach the liquid flow to the boiler chamber wall, providing for separation of the two liquid phases. This vaporizer was modified with a nozzle and a centrally-located heater to facilitate vaporization, superheating, and expansion of the propellant, allowing it to function as a resistojet. Performance was measured at thrust levels ranging from 170 to 360 mN and at power levels ranging from 443 to 192 W. Maximum measured specific impulse was 192 sec.

Morren, W. Earl↗

NASA NTRS1988

Development of a liquid-fed water resistojet

A concept for a forced-flow once-through water vaporizer for application to resistojet thrusters was evaluated as an element of a laboratory model thruster and tested to investigate its operating characteristics. The vaporizer design concept employs flow swirling to attach the liquid flow to the boiler chamber wall, providing for separation of the two liquid phases. This vaporizer was modified with a nozzle and a centrally-located heater to facilitatite vaporization, superheating, and expansion of the propellant, allowing it to function as a resistojet. Performance was measured at thrust levels ranging from 170 to 360 mN and at power levels ranging from 443 to 192 W. Maximum measured specific impulse was 192 sec.

Morren, W. Earl↗

NASA NTRS1992

Catalog-to-catalog reductions - Results for the FK, N30, and GC catalogs

It is shown that previous computations of catalog-to-catalog differences, whether by the bin-and-average method or by least-squares adjustment combined with an expansion in an incomplete set of basis functions, have all been performed at inappropriate epoch(s) of place. As a consequence, such results are frequently much more informative regarding the systematic differences between the proper motion systems than they are with respect to the systematic differences between the positional systems. Moreover, and for the same reason, some sets of proper motion differences really do not portray the true state of the evolution of the proper motion systems. Finally, this has practical effects in other astrometrical work, for instance, in the analysis of earth rotation time series. This error is corrected by arguing for a more meaningful epoch of place for catalog-to-catalog comparisons. This method of infinitely overlapping circles is applied at these other epochs to the FK sequence of catalogs, the N30, and the GC, and as a corollary the effectiveness of this new technique is shown.

Taff, L. G.↗

NASA NTRS1993

Solar activity and oscillation frequency splittings

Solar p-mode frequency splittings, parameterized by the coefficients through order N = 12 of a Legendre polynomial expansion of the mode frequencies as a function of m/L, were obtained from an analysis of helioseismology data taken at Big Bear Solar Observatory during the 4 years 1986 and 1988-1990 (approximately solar minimum to maximum). Inversion of the even-index splitting coefficients confirms that there is a significant contribution to the frequency splittings originating near the solar poles. The strength of the polar contribution is anti correlated with the overall level or solar activity in the active latitudes, suggesting a relation to polar faculae. From an analysis of the odd-index splitting coefficients we infer an uppor limit to changes in the solar equatorial near-surface rotatinal velocity of less than 1.9 m/s (3 sigma limit) between solar minimum and maximum.

Woodard, M. F.↗

NASA NTRS1994

Observation model and parameter partials for the JPL VLBI parameter estimation software MODEST, 19 94

This report is a revision of the document Observation Model and Parameter Partials for the JPL VLBI Parameter Estimation Software 'MODEST'---1991, dated August 1, 1991. It supersedes that document and its four previous versions (1983, 1985, 1986, and 1987). A number of aspects of the very long baseline interferometry (VLBI) model were improved from 1991 to 1994. Treatment of tidal effects is extended to model the effects of ocean tides on universal time and polar motion (UTPM), including a default model for nearly diurnal and semidiurnal ocean tidal UTPM variations, and partial derivatives for all (solid and ocean) tidal UTPM amplitudes. The time-honored 'K(sub 1) correction' for solid earth tides has been extended to include analogous frequency-dependent response of five tidal components. Partials of ocean loading amplitudes are now supplied. The Zhu-Mathews-Oceans-Anisotropy (ZMOA) 1990-2 and Kinoshita-Souchay models of nutation are now two of the modeling choices to replace the increasingly inadequate 1980 International Astronomical Union (IAU) nutation series. A rudimentary model of antenna thermal expansion is provided. Two more troposphere mapping functions have been added to the repertoire. Finally, corrections among VLBI observations via the model of Treuhaft and lanyi improve modeling of the dynamic troposphere. A number of minor misprints in Rev. 4 have been corrected.

Sovers, O. J.↗

NASA NTRS1993

Spectral variations in a collection of AVIRIS imagery

The advent of AVIRIS presents to the scientific community the first opportunity to examine high quality hyperspectral data over areas of interest, while recent developments promise even better data in the future. With these data we may address questions such as: (1) Is such high spectral resolution (0.01 micron) necessary?; and (2) How can we take advantage of the AVIRIS experience in specifying an improved future Landsat satellite? In this paper we describe the use of relatively broadband measurements (20-50 nm) to represent spectral variability. The problem of generality is addressed through consideration of 28 AVIRIS scenes, although analysis of additional areas is clearly desirable. Section 2 defines the expansion of spectra in terms of basis functions, section 3 describes the application to AVIRIS data, and the conclusion, section 4, relates these preliminary results to possible future remote sensing instrumentation such as the planned Landsat 8.

Price, John C.↗

NASA NTRS1997

Probabilistic Micromechanics and Macromechanics for Ceramic Matrix Composites

The properties of ceramic matrix composites (CMC's) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase properties, interphase bonding, amount of matrix voids, and many geometry- or fabrication-related parameters, such as ply thickness and ply orientation. This paper summarizes preliminary studies in which formal probabilistic descriptions of the material-behavior- and fabrication-related parameters were incorporated into micromechanics and macromechanics for CMC'S. In this process two existing methodologies, namely CMC micromechanics and macromechanics analysis and a fast probability integration (FPI) technique are synergistically coupled to obtain the probabilistic composite behavior or response. Preliminary results in the form of cumulative probability distributions and information on the probability sensitivities of the response to primitive variables for a unidirectional silicon carbide/reaction-bonded silicon nitride (SiC/RBSN) CMC are presented. The cumulative distribution functions are computed for composite moduli, thermal expansion coefficients, thermal conductivities, and longitudinal tensile strength at room temperature. The variations in the constituent properties that directly affect these composite properties are accounted for via assumed probabilistic distributions. Collectively, the results show that the present technique provides valuable information about the composite properties and sensitivity factors, which is useful to design or test engineers. Furthermore, the present methodology is computationally more efficient than a standard Monte-Carlo simulation technique; and the agreement between the two solutions is excellent, as shown via select examples.

Murthy, Pappu L. N.↗

NASA NTRS2003

Instrument for Measuring Cryo CTE

Coefficient of thermal expansion is an integral part of the performance of optical systems, especially for those, which operate at cryogenic temperatures. The measurement of the coefficient of relevant materials has been of continuous interest. Besides commercial measurement sources, development of one-of-a-kind tools have always been of interest due to local needs. This paper describes one such development at the University of Alabama in Huntsville (UAH). The approach involves two vertical rods (one sample and one reference) on a flat platform. A probe bar is held horizontally atop the two samples. A temperature change will generally cause rotation of the probe bar. A mirrored surface on one end of the probe bar is used to measure the rotation using the reflection of an incident laser beam upon it. A position-sensing detector measures the change of the reflected beam spot position. Using other known quantities, the change determines the coefficient of thermal expansion of the sample material as a function of temperature. A parallel measurement of the rotation of the sample support platform is also performed to account for any unwanted background effects. This system has been demonstrated in a cryogenic chamber at the NASA Marshall Space Flight Center X-ray Calibration Facility (XRCF). We present the system details, achievable sensitivity, and up-to-date experimental performance.

Vikram, Chandra S.↗

NASA NTRS2004

Thermophysical ESEM and TEM Characterization of Carbon Fibers CTE, Spectroscopy and Roughness Studies at High Temperatures

Accurate determination of the transverse properties of carbon fibers is important for assessment and prediction of local material as well as global structural response of composite components. However the measurements are extremely difficult due to the very small diameters of the fibers (few microns only) and must be conducted within a microscope. In this work, environmental scanning electron microscope (ESEM) and transmission electron microscope (TEM) are used to determine the transverse coefficient of thermal expansion of different carbon fibers as a function of temperature.

Ochoa, Ozden O.↗

NASA NTRS2004

Plasma Dispersion Function for the Kappa Distribution

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

Podesta, John J.↗

NASA NTRS1977

The geopotential in nonsingular orbital elements

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

Nacozy, P. E.↗

NASA NTRS1989

Semiclassical approximations in the coherent-state representation

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

Kurchan, J.↗

NASA NTRS1978

A theory of local and global processes which affect solar wind electrons. 1: The origin of typical 1 AU velocity distribution functions: Steady state theory

A detailed first principle kinetic theory for electrons which is neither a classical fluid treatment nor an exospheric calculation is presented. This theory illustrates the global and local properties of the solar wind expansion that shape the observed features of the electron distribution function, such as its bifurcation, its skewness and the differential temperatures of the thermal and suprathermal subpopulations. Coulomb collisions are substantial mediators of the interplanetary electron velocity distribution function and they place a zone for a bifurcation of the electron distribution function deep in the corona. The local cause and effect precept which permeates the physics of denser media is modified for electrons in the solar wind. The local form of transport laws and equations of state which apply to collision dominated plasmas are replaced with global relations that explicitly depend on the relative position of the observer to the boundaries of the system.

Scudder, J. D.↗

NASA NTRS1990

Microwave conductivity of laser ablated YBaCuO superconducting films and its relation to microstrip transmission line

The discovery of high temperature superconductor oxides has raised the possibility of a new class of millimeter and microwave devices operating at temperatures considerably higher than liquid helium temperatures. Therefore, materials properties such as conductivity, current density, and sheet resistance as a function of temperature and frequency, possible anisotropies, moisture absorption, thermal expansion, and others, have to be well characterized and understood. The millimeter wave response was studied of laser ablated YBa2Cu3O(7-x)/LaAlO3 thin films as a function of temperature and frequency. In particular, the evaluation of their microwave conductivity was emphasized, since knowledge of this parameter provides a basis for the derivation of other relevant properties of these superconducting oxides, and for using them in the fabrication of actual passive circuits. The microwave conductivity for these films was measured at frequencies from 26.5 to 40.0 GHz, in the temperature range from 20 to 300 K. The values of the conductivity are obtained from the millimeter wave power transmitted through the films, using a two fluid model.

Bhasin, K. B.↗