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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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NASA NTRS1978

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Mcclelland, J.↗
NASA NTRS1988

Cluster-cluster correlations and constraints on the correlation hierarchy

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes in hierachical clustering models. The distributions which saturate these constraints are the Rayleigh-Levy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.

Hamilton, A. J. S.↗
NASA NTRS1979

The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.

Mcclelland, J.↗
NASA NTRS1981

Energy normalization of TV viewed optical correlation (automated correlation plane analyzer for an optical processor)

An automatic correlation plane processor that can rapidly acquire, identify, and locate the autocorrelation outputs of a bank of multiple optical matched filters is described. The read-only memory (ROM) stored digital silhouette of each image associated with each matched filter allows TV video to be used to collect image energy to provide accurate normalization of autocorrelations. The resulting normalized autocorrelations are independent of the illumination of the matched input. Deviation from unity of a normalized correlation can be used as a confidence measure of correct image identification. Analog preprocessing circuits permit digital conversion and random access memory (RAM) storage of those video signals with the correct amplitude, pulse width, rising slope, and falling slope. TV synchronized addressing of 3 RAMs permits on-line storage of: (1) the maximum unnormalized amplitude, (2) the image x location, and (3) the image y location of the output of each of up to 99 matched filters. A fourth RAM stores all normalized correlations. A normalization approach, normalization for cross correlations, a system's description with block diagrams, and system's applications are discussed.

Grumet, A.↗
NASA NTRS1949

Heat Transfer from High-Temperature Surfaces to Fluids. III - Correlation of Heat-Transfer Data for Air Flowing in Silicon Carbide Tube with Rounded Entrance, Inside Diameter of 3/4 Inch, and Effective Length of 12 Inches: Correlation of Heat-Transfer Data for Air Flowing in Silicon Carbide Tube with Rounded Entrance, Inside Diameter of 3/4 Inch, and Effective Length of 12 Inches - Part 3

A heat-transfer investigation was conducted with air flowing through an electrically heated silicon carbide tube with a rounded entrance, an inside diameter of 3/4 inch, and an effective heat-transfer length of 12 inches over a range of Reynolds numbers up to 300,000 and a range of average inside-tube-wall temperature up to 2500 R. The highest corresponding local outside-tube-wall temperature was 3010 R. Correlation of the heat-transfer data using the conventional Nueselt relation wherein physical properties of the fluid were evaluated at average bulk temperature resulted in a separation of data with tube-wall-temperature level. A satisfactory correlation of the heat-transfer data was obtained, however, by the use of modified correlation parameters wherein the mass velocity G (or product of average air density and velocity evaluated at bulk temperature P(sub b)V(sub b)) in the Reynolds number was replaced by the product of average air velocity evaluated at the bulk temperature and density evaluated at either the average inside-tube-wall temperature or the average film temperature; in addition, all the physical properties of air were correspondingly evaluated at either the average inside-tube-wall temperature or the average film temperature.

Sams, Eldon W.↗
NASA NTRS1992

Measuring Omega and the real correlation function from the redshift correlation function

Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form. The amplitude of the distortion depends on the cosmological density parameter Omega. Practical formulas are derived here which can be applied to redshift galaxy catalogs to measure Omega in the linear regime. The formulas also yield the real underlying correlation function in the linear regime, corrected for peculiar velocities.

Hamilton, A. J. S.↗
NASA NTRS1992

Scalar rate correlation at a turbulent liquid free surface - A two-regime correlation for high Schmidt numbers

An experimental correlation is derived for gas absorption at a turbulent, shear-free liquid interface. The correlation is expressed in terms of the liquid-side turbulence intensity, liquid-side macroscale, and the properties of the diffusing gas and solvent. The transfer coefficient increases linearly with rms velocity up to a point where the eddy Reynolds number reaches a critical (Schmidt number dependent) value. At higher velocities, there is a more rapid linear rise. The slope of the lower Reynolds number region is proportional to the square root of the diffusivity; at Reynolds numbers much higher than that of the break point, the slope becomes independent of diffusivity.

Khoo, Boo-Cheong↗
NASA NTRS1976

Measures and models for angular correlation and angular-linear correlation

Population models for dependence between two angular measurements and for dependence between an angular and a linear observation are proposed. The method of canonical correlations first leads to new population and sample measures of dependence in this latter situation. An example relating wind direction to the level of a pollutant is given. Next, applied to pairs of angular measurements, the method yields previously proposed sample measures in some special cases and a new sample measure in general.

Johnson, R. A.↗
NASA NTRS1994

Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

Ray, Terrill W.↗
NASA NTRS1992

Correlation, Cost Risk, and Geometry

The geometric viewpoint identifies the choice of a correlation matrix for the simulation of cost risk with the pairwise choice of data vectors corresponding to the parameters used to obtain cost risk. The correlation coefficient is the cosine of the angle between the data vectors after translation to an origin at the mean and normalization for magnitude. Thus correlation is equivalent to expressing the data in terms of a non orthogonal basis. To understand the many resulting phenomena requires the use of the tensor concept of raising the index to transform the measured and observed covariant components into contravariant components before vector addition can be applied. The geometric viewpoint also demonstrates that correlation and covariance are geometric properties, as opposed to purely statistical properties, of the variates. Thus, variates from different distributions may be correlated, as desired, after selection from independent distributions. By determining the principal components of the correlation matrix, variates with the desired mean, magnitude, and correlation can be generated through linear transforms which include the eigenvalues and the eigenvectors of the correlation matrix. The conversion of the data to a non orthogonal basis uses a compound linear transformation which distorts or stretches the data space. Hence, the correlated data does not have the same properties as the uncorrelated data used to generate it. This phenomena is responsible for seemingly strange observations such as the fact that the marginal distributions of the correlated data can be quite different from the distributions used to generate the data. The joint effect of statistical distributions and correlation remains a fertile area for further research. In terms of application to cost estimating, the geometric approach demonstrates that the estimator must have data and must understand that data in order to properly choose the correlation matrix appropriate for a given estimate. There is a general feeling by employers and managers that the field of cost requires little technical or mathematical background. Contrary to that opinion, this paper demonstrates that a background in mathematics equivalent to that needed for typical engineering and scientific disciplines at the masters or doctorate level is appropriate within the field of cost risk.

Dean, Edwin B.↗
NASA NTRS1980

Mark 3 correlator hardware and software

The Mark 3 correlator system is described in some detail. The correlator system is based on a modular philosophy. Each correlator module independently processes the data from one track pair. Therefore, 28 modules are necessary to complete a full one baseline processor and 84 modules for a full 3 baseline processor. Each correlator module has two interfaces: (1) data and clock from each of the two tracks to be correlated and (2) Computer Automated Measurement and Control (CAMAC) dataway interface to the computer. The processor is organized around the IEEE CAMAC standard architecture, housing 15 correlator modules in each of 6 crates. This allows one pass processing of a full 3 baseline 28 track observation or a 6 baseline (4 station) 14 track observation. The correlator architecture allows easy expansion for up to 8 stations. The computer system is an HP 1000 system utilizing a 16 bit minicomputer with disc and tape peripherals. The processing software is also organized in a modular fashion with many independent but cooperative programs controlling the operation of the Mark 3 processor. Processing time through the correlator is normally real time or faster, with graphics displays providing real time monitor and control of the processing operation.

Whitney, A. R.↗
NASA NTRS1984

Pipelined digital SAR azimuth correlator using hybrid FFT-transversal filter

A synthetic aperture radar system (SAR) having a range correlator is provided with a hybrid azimuth correlator which utilizes a block-pipe-lined fast Fourier transform (FFT). The correlator has a predetermined FFT transform size with delay elements for delaying SAR range correlated data so as to embed in the Fourier transform operation a corner-turning function as the range correlated SAR data is converted from the time domain to a frequency domain. The azimuth correlator is comprised of a transversal filter to receive the SAR data in the frequency domain, a generator for range migration compensation and azimuth reference functions, and an azimuth reference multiplier for correlation of the SAR data. Following the transversal filter is a block-pipelined inverse FFT used to restore azimuth correlated data in the frequency domain to the time domain for imaging.

Wu, C.↗
NASA NTRS1985

Response time correlations for platinum resistance thermometers in flowing fluids

The thermal response of two types of Platinum Resistance Thermometers (PRT's), which are being considered for use in the National Transonic Wind Tunnel Facility, were studied. Response time correlations for each PRT, in flowing water, oil and air, were established separately. A universal correlation, tau WOA = 2.0 + 1264, 9/h, for a Hy-Cal Sensor (with a reference resistance of 100 ohm) within an error of 20% was established while the universal correlation for the Rosemount Sensor (with a reference resistance of 1000 ohm), tau OA = 0.122 + 1105.6/h, was found with a maximum percentage error of 30%. The correlation for the Rosemount Sensor was based on air and oil data only which is certainly not sufficient to make a correlation applicable to every condition. Therefore, the correlation needs more data to be gathered in different fluids. Also, it is necessary to state that the calculation of the parameter, h, was based on the available heat transfer correlations, whose accuracies are already reported in literature uncertain within 20-30%. Therefore, the universal response constant correlations established here for the Hy-Cal and Rosemount sensors are consistent with the uncertainty in the input data and are recommended for future use in flowing liquids and gases.

Pandey, D. K.↗
NASA NTRS1991

A correlational analysis of the effects of changing environmental conditions on the NR atomic hydrogen maser

An extensive statistical analysis has been undertaken to determine if a correlation exists between changes in an NR atomic hydrogen muser's frequency offset and changes in environmental conditions. Data have been acquired over the past 20 months by recording the frequency offset of three NR atomic hydrogen masers along with the relative and absolute humidity, barometric pressure, and ambient temperature of the laboratory in which the masers are maintained. Correlational analyses have been performed comparing barometric pressure, humidity, and temperature with maser frequency offset as functions of time for periods ranging from 5.5 to 17 days. Semi partial correlation coefficients as large as -0.9 have been fond between barometric pressure and maser frequency offset for data covering periods as long as a week. Maser frequency offset and barometric pressure were consistently found to change simultaneously. The correlation between humidity and frequency offset is less predictable, and the resulting semi partial correlation coefficients were usually small when compared with those derived from the relationship between pressure and frequency offset. The time delay between changes in humidity and correlated changes in maser frequency offset was found to vary extensively with no predictable pattern. Analysis of temperature data indicates that, in the most current design, temperature does not significant(y affect maser frequency offset in the laboratory environment. Thus, the results of the analyses disclose a significant statistical correlation between changes in maser frequency offset and changes in barometric pressure. The statistics also reveal some correlation between humidity and frequency offset, bat for reasons to be discussed, the effects of humidity should be considered secondary to the effects of changing barometric pressure.

R. A. Dragonette↗