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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 NTRS1992

Bose-Einstein correlations in Si + Al and Si + Au collisions at 14.6A GeV/c

The E802 Spectrometer at the Brookhaven Alternating Gradient Synchrotron has been used to measure the correlation in relative momentum between like-sign pions emitted in central Si + Al and Si + Au collisions at 14.6A GeV/c. Data are presented in terms of the correlation function for both identified pi(-) and pi(+) pairs near the nucleon-nucleon center-of-mass rapidity. All parametrizations of the correlation function are consistent with a spherically symmetric source of rms radius 3.5 +/- 0.4 fm and lifetime fm/c.

Abbott, T.↗

NASA NTRS1979

Application of abstract harmonic analysis to the high-speed recognition of images

Methods are constructed for rapidly computing correlation functions using the theory of abstract harmonic analysis. The theory developed includes as a particular case the familiar Fourier transform method for a correlation function which makes it possible to find images which are independent of their translation in the plane. Two examples of the application of the general theory described are the search for images, independent of their rotation and scale, and the search for images which are independent of their translations and rotations in the plane.

Usikov, D. A.↗

NASA NTRS1996

Report on 3- and 4-Point Correlation Statistics in COBE DMR Anisotropy Maps

As part of the work performed under this contract, we have computed the 3- and 4-point correlation functions of the COBE-DMR 2-year and 4-year anisotropy maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data.

Hinshaw, Gary↗

NASA NTRS1986

N-point correlations for biased galaxy formation

A general series expansion of arbitrary accuracy is given for the correlation function of the 'biased' regions of galaxy formation in terms of the mass autocorrelations. It is shown how to calculate the N-point correlations to arbitrary accuracy, and the validity of the various approximations is discussed. The asymptotic values of the N-point correlation functions at their highest point at zero spatial separation are given, and the scaling of these values is discussed.

Jensen, L. G.↗

NASA NTRS1987

Numerical simulations of turbulent trapping in the weak beam-plasma instability

Numerical simulations of the weak beam-plasma instability were done in the turbulent regime where small-scale trapping is a dominant feature of the instability, a regime with behavior not predicted by quasi-linear theory. The results of the simulations were compared with those of a specific model of the turbulence, the so-called 'turbulent trapping' model, which gives precise formulas for the particle correlation functions, and predicts a growth rate well enhanced over the quasi-linear value. It was found that the model gives accurate predictions for the correlation functions. On the other hand, while growth rates were enhanced over the quasi-linear values, the enhancements observed are smaller than expected from the quantitative predictions of the model.

Theilhaber, K.↗

NASA NTRS1993

Cross-correlation between the 170 GHz survey map and the COBE differential microwave radiometer first-year maps

This letter describes results of a cross-correlation between the 170 GHz partial-sky survey, made with a 3.8 deg beam balloon-borne instrument, and the COBE DMR 'Fit Technique' reduced galaxy all-sky map with a beam of 7 deg. The strong correlation between the data sets implies that the observed structure is consistent with thermal variations in a 2.7 K emitter. A chi-square analysis applied to the correlation function rules out the assumption that there is no structure in either of the two maps. A second test shows that if the DMR map has structure but the 170 GHz map does not, the probability of obtaining the observed correlation is small. Further analyses support the assumption that both maps have structure and that the 170 GHz-DMR cross-correlation is consistent with the analogous DMR correlation function. Maps containing various combinations of noise and Harrison-Zel'dovich power spectra are simulated and correlated to reinforce the result. The correlation provides compelling evidence that both instruments have observed fluctuations consistent with anisotropies in the cosmic microwave background.

Ganga, Ken↗

NASA NTRS1981

A stochastic-dynamic model for global atmospheric mass-field statistics

Global atmospheric mass field error correlations based on satellite observations and on numerical forecasts show strong and systematic latitude dependence. A model for the latitude dependent spatial correlation structure of mass field forecast errors is derived from dynamical considerations. Three methods of solution were tested. In the first method, the equation was solved by expansion in spherical harmonics, and the correlation function was computed analytically using the expansion coefficients. In the second method, the finite difference equivalent of the equation was solved using a fast poisson solver. The correlation function was computed using stratified sampling of the individual realizations. In the third method, a higher order equation was derived, and solved directly in finite differences by two successive applications of the fast poisson solver. The three methods were compared for accuracy and efficiency, and the third method was chosen as clearly superior.

Ghil, M.↗

NASA NTRS1988

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗

NASA NTRS1984

Superclustering and the large-scale structure of the Universe

A complete redshift survey of nearby rich galactic clusters is analyzed in terms of a spatial correlation function, the growth of supercluster, the presence of superclusters around the Bootes void and the discovery of a 300 Mpc void. Abell's (1958) statistical sampling of rich clusters is used for the study. Attention is given to the dependence of the correlation function on the richness of the system, with finding that chances are greater of finding rich neighbors closer together than poor neighbors. Samples of redshifts of 4 or less correlate well with clusters of redshift 5 or more. The size of intergalactic voids is proportional to the surrounding galactic excesses. Finally, the superclusters exist on scales of about 100 Mpc/h, which is larger than expected.

Bahcall, N. A.↗

NASA NTRS1991

Signal processing considerations for low signal to noise ratio laser Doppler and phase Doppler signals

The relative performance of current methods used for estimating the phase and the frequency in LDV and phase Doppler applications in low signal to noise ratio conditions is analyzed. These methods include the Fourier analysis and the correlation techniques. Three methods that use the correlation function for frequency and phase estimations are evaluated in terms of accuracy and speed of processing. These methods include: (1) the frequency estimation using zero crossings counting of the auto-correlation function, (2) the Blackman-Tukey method, and (3) the AutoRegressive method (AR). The relative performance of these methods is evaluated and compared with the Fourier analysis method which provides the optimum performance in terms of the Maximum Likelihood (ML) criteria.

Ibrahim, K. M.↗

NASA NTRS1996

Dynamic Light Scattering From Colloidal Gels

We present a brief, preliminary account of the interpretation of dynamic light scattering from fractal colloidal gels. For small scattering angles, and for high initial colloid particle volume fractions, the correlation functions exhibit arrested decay, reflecting the non-ergodic nature of these systems and allowing us to directly determine the elastic modulus of the gels. For smaller initial volume fractions, the correlation functions decay completely. In all cases, the initial decay is not exponential, but is instead described by a stretched exponential. We summarize the principles of a model that accounts for these data and discuss the scaling behavior of the measured parameters.

Krall, A. H.↗

NASA NTRS1998

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

Hou, Thomas Y.↗

NASA NTRS1973

A method for predicting shock shapes and pressure distributions on two dimensional airfoils at large angles of attack

A method is presented for determining shock envelopes and pressure distributions for two-dimensional airfoils at angles of attack sufficiently large to cause shock detachment and subsonic flow over the windward surface of the airfoil. Correlation functions obtained from exact solutions are used to relate the shock standoff distance at the stagnation and sonic points of the body through a suitable choice for the shock shape. The necessary correlation functions were obtained from perfect gas solutions but may be extended to any gas flow for which the normal shock-density ratio can be specified.

Kaattari, G. E.↗

NASA NTRS1996

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report.

Hinshaw, Gary↗

NASA NTRS1989

Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients

The small-angle scattering approximation of the scalar radiative transfer equation (RTE) is examined for the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic RTE can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. Two transfer equations are obtained describing the average radiant intensity and the spatial correlation function of the intensity fluctuations. The average intensity equation is then solved and applied to a simple propagation scenario. An approximate solution is also derived for the equation giving the correlation function. The developed equations can be applied to problems involving short wavelength electromagnetic wave propagation through media possessing the variable characteristics of turbulence and turbidity, such as plasmas, the atmosphere, and the ocean.

Manning, Robert M.↗

NASA NTRS2001

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.↗

NASA NTRS2015

Results from the Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe (WMAP) mapped the distribution of temperature and polarization over the entire sky in five microwave frequency bands. These full-sky maps were used to obtain measurements of temperature and polarization anisotropy of the cosmic microwave background with the unprecedented accuracy and precision. The analysis of two-point correlation functions of temperature and polarization data gives determinations of the fundamental cosmological parameters such as the age and composition of the universe, as well as the key parameters describing the physics of inflation, which is further constrained by three-point correlation functions. WMAP observations alone reduced the flat Λ cold dark matter (Lambda Cold Dark Matter) cosmological model (six) parameter volume by a factor of > 68, 000 compared with pre-WMAP measurements. The WMAP observations (sometimes in combination with other astrophysical probes) convincingly show the existence of non-baryonic dark matter, the cosmic neutrino background, flatness of spatial geometry of the universe, a deviation from a scale-invariant spectrum of initial scalar fluctuations, and that the current universe is undergoing an accelerated expansion. The WMAP observations provide the strongest ever support for inflation; namely, the structures we see in the universe originate from quantum fluctuations generated during inflation.

The Wilkinson Microwave Anisotropy Probe (WMAP)↗

NASA NTRS1973

Two frequency radar interferometry applied to the measurement of ocean wave height.

Description of a technique for measuring the rms wave height averaged over an area of the sea that is much greater than any horizontal scale of the surface waves. The measurement method involves a nadir looking radar that transmits and receives two continuous monochromatic signals simultaneously. Signal processing at the receiver requires the computation of a correlation function which is shown to depend only on the statistical rms surface elevation of specular points and not on the temporal or spatial frequency spectrum of the wave height or slope. Laboratory measurements have been conducted on wind driven waves, and the measured correlation function compares favorably with the underlying theory.

Weissman, D. E.↗