A Rodrigues' formula for the Laguerre polynomials.
Rodrigues type formula for generalized Laguerre polynomials based upon semigroup property for solutions of heat equation and generating function related to source solution
HEAT EQUATION↗
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Results for “functional properties”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Fluorescence studies of nucleotides and polynucleotides. I.
Fluorescence properties of nucleotides, polynucleotides and phosphorylated derivatives as function of temperature, pH and ionic strength
Reich, E.↗
A noniterative method of obtaining Tchebycheff rational approximations
Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy
Hagar, H., Jr.↗
Transient solutions of the Fokker-Planck equation for a class of first-order phase- locked loops
Eigenfunction expansions of reduced nonGaussian phase error transition probability density function for first order tracking loop, analyzing spectral properties of Fokker-Planck equation
La Frieda, J. R.↗
Parametric fit to electron transport properties
Experimental data acquired over the past few years were gathered, and parametric fits made to these data. The following properties of electron transport were represented by simple functions of atomic number and energy: transmitted electron number, transmitted electron spectra, range, backscatter coefficient, angular distribution, energy deposition, bremsstrahlung intensity and energy spectra, and bremsstrahlung angular distribution and photon attenuation. The formulas cover the energy ranges of interest in space shielding problems (0.1 to 10.0 MeV). Procedures for using these formulas in practical situations are suggested.
Lonergan, J. A.↗
Solar system applications of Mie theory and of radiative transfer of polarized light
A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.
Whitehill, L. P.↗
Technical, analytical and computer support
The development of a rigorous mathematical model for the design and performance analysis of cylindrical silicon-germanium thermoelectric generators is reported that consists of two parts, a steady-state (static) and a transient (dynamic) part. The material study task involves the definition and implementation of a material study that aims to experimentally characterize the long term behavior of the thermoelectric properties of silicon-germanium alloys as a function of temperature. Analytical and experimental efforts are aimed at the determination of the sublimation characteristics of silicon germanium alloys and the study of sublimation effects on RTG performance. Studies are also performed on a variety of specific topics on thermoelectric energy conversion.
Source record↗
Properties of heuristic search strategies
A directed graph is used to model the search space of a state space representation with single input operators, an AND/OR is used for problem reduction representations, and a theorem proving graph is used for state space representations with multiple input operators. These three graph models and heuristic strategies for searching them are surveyed. The completeness, admissibility, and optimality properties of search strategies which use the evaluation function f = (1 - omega)g = omega(h) are presented and interpreted using a representation of the search process in the plane. The use of multiple output operators to imply dependent successors, and thus obtain a formalism which includes all three types of representations, is discussed.
Vanderbrug, G. J.↗
Theory of disordered Heisenberg ferromagnets
A Green's function technique is used to calculate the magnetic properties of Heisenberg ferromagnets in which the exchange interactions deviate randomly in strength from the mean interaction. Systems of sc, bcc, and fcc topologies and of general spin values are treated. Disorder produces marked effects in the density of spin wave states, in the form of enhancement of the low-energy density and extension of the energy band to higher values. The spontaneous magnetization and the Curie temperature decrease with increasing disorder. The effects of disorder are shown to be more pronounced in the ferromagnetic than in the paramagnetic phase.
Stubbs, R. M.↗
Attenuation and phase dispersion in the atmosphere due to the microwave spectrum of oxygen
Radio wave propagation in the 40- to 140-GHz band through the earth's atmosphere is strongly influenced by the behavior of the O2 microwave spectrum. This behavior causes the transfer function to depend critically upon altitude. The spectroscopic properties of O2 are discussed and reduced to engineering formulas expressing attenuation and phase dispersion rates in terms of frequency and meteorological parameters. The theory is supported on several accounts by reliable spectroscopic measurements. Pressure scanning spectroscopy is used to investigate the O2 microwave spectrum under simulated atmospheric conditions. The application of spectroscopic information to analytical treatments of transfer properties for inhomogeneous slant paths is demonstrated. Attenuation and phase dispersion between 49 and 72 GHz are evaluated for zenith and tangential paths.
Liebe, H. J.↗
Impact resistance of fiber composite blades used in aircraft turbine engines
Resistance of advanced fiber reinforced epoxy matrix composite materials to ballistic impact was investigated as a function of impacting projectile characteristics, and composite material properties. Ballistic impact damage due to normal impacts, was classified as transverse (stress wave delamination and splitting), penetrative, or structural (gross failure). Steel projectiles were found to be gelatin ice projectiles in causing penetrative damage leading to reduced tensile strength. Gelatin and ice projectiles caused either transverse or structural damage, depending upon projectile mass and velocity. Improved composite transverse tensile strength, use of dispersed ply lay-ups, and inclusion of PRD-49-1 or S-glass fibers correlated with improved resistance of composite materials to transverse damage. In non-normal impacts against simulated blade shapes, the normal velocity component of the impact was used to correlate damage results with normal impact results. Stiffening the leading edge of simulated blade specimens led to reduced ballistic damage, while addition of a metallic leading edge provided nearly complete protection against 0.64 cm diameter steel, and 1.27 cm diameter ice and gelatin projectiles, and partial protection against 2.54 cm diameter projectiles of ice and gelatin.
Friedrich, L. A.↗
Zodiacal light photography
Polarized and red- and blue-filter photographs of zodiacal light obtained by Apollo 17 are analyzed. Attempts were made to identify the cause of subtle change in the observed light and determine the dust composition of the light. A comparison of red and blue images indicates such changes may be caused by particle size distribution and range, number of particles along any given line of sight, particle surface characteristics including dielectric compared to metallic properties, and variations of the parameters as a function of distance from the sun.
Mercer, R. D.↗
The study of electrical conduction mechanisms
The dielectric response of lunar fines 74241,2 is presented in the audio-frequency range and under lunarlike conditions. Results suggest that volatiles are released during storage and transport of the lunar sample. Apparently, subsequent absorption of volatiles on the sample surface alter its dielectric response. The assumed volatile influence disappear after evacuation. A comparison of the dielectric properties of lunar and terrestrial materials as a function of density, temperature, and frequency indicates that if the lunar simulator analyzed were completely devoid of atmospheric moisture it would present dielectric losses smaller than those of the lunar sample. It is concluded that density prevails over temperature as the controlling factor of dielectric permittivity in the lunar regolith and that dielectric losses vary slowly with depth.
Morrison, H. F.↗
Dielectric comparison of lunar and terrestrial fines at lunar conditions
The dielectric properties of lunar fines 74241,2 in the audio-frequency range under lunarlike conditions are presented. Results suggest that volatiles are released during storage and transport of the lunar sample. Apparently, subsequent adsorption of volatiles on the sample surface alters its dielectric response. The assumed volatile influence disappears after evacuation. A comparison of the dielectric properties of lunar and terrestrial materials as a function of density, temperature, and frequency indicates that if the terrestrial sample analyzed were completely devoid of atmospheric moisture, it would present dielectric losses smaller than those of the lunar sample. It is concluded that density prevails over temperature as the controlling factor of dielectric permittivity in the lunar regolith and that dielectric losses vary slowly with depth.
Alvarez, R.↗
Statistical properties of filtered pseudo-random digital sequences
A tutorial presentation of pseudo-random digital sequences, their generation and properties is given. The results of a study of filtered pseudo-random sequences, and their statistical properties are reported. The generator, to be used in a telemetry communications system test unit, must generate its pseudo-random signals by filtering a long digital sequence. Desired signal properties include: (1) approximately Gaussian amplitude probability density function; and (2) signal spectral envelope approximately that of the filter being used in the generator. Filtered maximum-length sequences have been used for this, and similar applications in the past. The results were good for low-pass filtered sequences when the ratio of digital clock frequency to filter cutoff frequency was between fifteen and twenty. However, for higher values of this ratio, a definite skewing of the amplitude density function was observed.
Weathers, G. D.↗
Determination of scattering functions and their effects on remote sensing of turbidity in natural waters
The development of quantitative analytical procedures for relating scattered signals, measured by a remote sensor, was considered. The applications of a Monte Carlo simulation model for radiative transfer in turbid water are discussed. The model is designed to calculate the characteristics of the backscattered signal from an illuminated body of water as a function of the turbidity level, and the spectral properties of the suspended particulates. The optical properties of the environmental waters, necessary for model applications, were derived from available experimental data and/or calculated from Mie formalism. Results of applications of the model are presented.
Ghovanlou, A. H.↗
Externally blown flap impingement parameters
The performance of two externally blown flap (EBF) wind tunnel models was compared with an engine exhaust flap impingement correlation parameter. One model was a four engine EBF triple slotted flap transport. Isolated engine wake surveys were conducted to define the wake properties of five separate engine configurations for which performance data were available. The other model was a two engine EBF transport for which the engine wake properties were estimated. The correlation parameter was a function of engine exhaust dynamic pressure at the flap location, area of engine exhaust flap impingement, total exhaust area at the flap location, and engine thrust. The distribution of dynamic pressure for the first model was measured; however, the distribution for the second model was assumed to be uniform.
Hoad, D. R.↗
Rheology of composite solid propellants during motor casting
Results of casting studies are reviewed so as to define the viscosity criteria insuring the fabrication of defect-free grains. The rheology of uncured propellants is analyzed showing that a realistic assessment of a propellant's flow properties must include measurement of viscosity as a function of shear stress and time after curing agent. Methods for measuring propellant viscosity are discussed, with particular attention given to the Haake-Rotovisko rotational viscometer. The effects of propellant compositional and processing variables on apparent viscosity are examined, as are results relating rheological behavior to grain defect formation during casting.
Klager, K.↗