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NASA NTRS1977

High-energy heavy-ion scattering and the optical phase shift function

Within the framework of the Glauber approximation, an exact expression for the optical phase shift function is derived which takes into account the center-of-mass correlation function. We calculate total and differential cross sections using the first-order term for the shift function and compare them with the usual (first-order) optical limit results and, for the lighter nuclei, with the exact Glauber results. The nucleus-nucleus elastic scattering amplitude does not exhibit the large-q divergence which characterizes the usual optical limit. The obtained results improve the calculated total and differential cross sections dramatically for light nuclei, and significantly for medium and heavy nuclei.

Franco, V.↗

NASA NTRS1973

On Lidar Sounding of the Atmosphere to Estimate Static and Dynamic Characteristics of Aerosol Inhomogeneities

1. A possible application of intensity fluctuations of a pulse light signal reflected by atmospheric aerosols is analyzed by the correlation method to evaluate static (medium sizes, shape) and dynamic (speed and direction of movement, lifetime) characteristics of aerosol inhomogeneities. The aerosol inhomogeneities are assumed to be expanded, pressed, disintegrated and originated constantly in accordance with random laws, the set of inhomogeneities as a whole traveling together with air masses and having predominant movement in wind direction. It is shown that the characteristics of aerosol inhomogeneities considered can be expressed by the coefficients of the correlation function expansion of the reflected signal fluctuation intensity in Tailor series. 2/ Correlation systems for evaluating static and dynamic characteristics of driving objects can be divided into two types according to the kind and quantity of used information: the systems with coordinates of the information removal "points" to be fixed in space, and the systems with a parallel simultaneous information removal at discrete moments of time. The systems for determination of wind direction considered in are the examples of the first type system. However, the operating information removal for two points is insufficient to estimate completely static and dynamic characteristics of inhomogenities, their quantity ought to be increased up to three of them for two-dimensional problem and up to four of them for three-dimensional problem as it is usually done in the ionospheric studies. The second type systems are used for the investigation of a medium shape and speed of the clouds according to photographs made from satellites. These systems are also used for solution of navigation problems. The use of optical quantum generators with a scanning beam is seen to increase greatly the working information removal in comparison with the first type systems. Nevertheless, scanning rate is not sufficient sometimes in order· to consider a general picture of aerosol inhomogeneities to be stationary. In this connection the use of the systems of second type treatment becomes a matter of essential difficulty. 3. Aerosol inhomogeneities simulation has been carried out on the basis of the digital computer experiments with the aim of estimating static and dynamic characteristics of inhomogeneities by an optical beam in the atmosphere at different scanning procedures. The dependence of determination accuracy of these characteristics on the type of chosen laws of aerosol particle distribution in the atmosphere, the parameters of inhomogeneities geometry, their speed and the law of scanning have been obtained.

Zuev, V. E.↗

NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗

NASA NTRS1981

Mean dyadic Green's function for a two layer random medium

The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.

Zuniga, M. A.↗

NASA NTRS1994

Multipath noise reduction spread spectrum signals

The concepts of early-prompt delay tracking, multipath correction of early-prompt delay tracking from correlation shape, and carrier phase multipath correction are addressed. In early-prompt delay tracking, since multipath is always delayed with respect to the direct signals, the system derives phase and pseudorange observables from earlier correlation lags. In multipath correction of early-prompt delay tracking from correlation shape, the system looks for relative variations of amplitude across the code correlation function that do not match the predicted multipath-free code cross-correlation shape. The system then uses deviations from the multipath-free shape to infer the magnitude of multipath, and to generate corrections pseudorange observables. In carrier phase multipath correction, the system looks for variations of phase among plural early and prompt lags. The system uses the measured phase variations, along with the general principle that the multipath errors are larger for later lags, to infer the presence of multipath, and to generate corrections for carrier-phase observables.

Meehan, Thomas K.↗

NASA NTRS1974

Use of cross-correlation measurements to investigate noise generating regions of a real jet engine and a model jet

Cross-correlations are reported of the jet static pressure fluctuations (as measured with a B and K microphone fitted with a nose cone), with the far-field radiated sound pressure. These measurements were made for various probe positions and a large number of far-field positions (at various angles). In addition, the tests were run for a number of different jet exit velocities. The measured, normalized cross-correlation functions vary between 0.004 and 0.155. These values depend upon the angular position of the far-field microphone, the jet exit Mach number, and the position of the probe. In addition, the cross-correlation technique was employed to study the symmetry of the far-field radiated sound about the jet axis. Third-octave analyses of both the probe signal and the far-field radiated sound were made. This is the first time correlation measurements have been made on a jet engine. In addition, a report is given on an extensive noise survey of a model jet. The correlations are related to sound source functions and jet source regions are discussed.

Meecham, W. C.↗

NASA NTRS1989

Superclustering in the explosion scenario

A simple toy model is used to study the spatial distribution of rich clusters in a generic type of explosion scenario. The model, parameterized by the distribution of shell radii and the filling factor, places spherical shells at random and identifies each 'knot' as a cluster. The resulting cluster correlation function is close to a power law extending to the diameter of the largest spheres. Richer clusters form at the intersections of bigger shells and so have stronger correlations. Typical shell radii and filling factors are required to produce the observed number density of clusters. Models with a power-law radius distribution also reproduce the richness distribution of clusters in the Abell catalog. Supercluster multiplicity functions, void probabilities, number counts, topology statistics, and velocity correlations confirm the presence of strong superclustering and quantify the non-Gaussian nature of the model.

Weinberg, David H.↗

NASA NTRS1981

Statistical estimation of correlation for nonstationary aircraft noise

Based on the acoustic radiation theory for a moving source, the estimation of the correlation function of a nonstationary acoustic signal is considered. An estimator is obtained for the acoustic correlation, which is shown to be unbiased and consistent. The estimation procedure can be applied to an aircraft noise measurement, where the reflected wave can be eliminated.

Chow, P. L.↗

NASA NTRS1986

The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes

The three-dimensional structure of the dominant modes of wintertime variability are examined, and the mode structures are determined by an EOF analysis of the coupled vertical mean and shear streamfunction fields for a wide range of time-scale classes. The time mean energy conversions are determined from a two-layer quasigeostrophic model. Lag-cross correlations between the dominant low-frequency modes tend to be small and/or symmetric about zero, the high frequency modes are found to show highly asymmetric sinusoidal cross correlation functions similar to traveling waves, and some intermediate and short-time scale modes exhibit correlations indicating an association with the decaying phases of blocking in the Pacific. It is suggested that the mean flow barotropic (baroclinic) instabilities are an important source of variance for some of the lowest (highest) fluctuations considered.

Schubert, S. D.↗

NASA NTRS1994

Correlated noise in the COBE DMR sky maps

The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from three techniques: angular averages of the covariance matrix, Monte Carlo simulations of two-point correlation functions and direct analysis of the DMR maps. The results from the three methods are mutually consistent. The noise covariance matrix of a DMR sky maps is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occure with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance at 60 deg is 0.45%((sup +0.18)(sub -0.14)) of the mean variance. Additionally, the variance in a given pixel is 0.7% greater than would be expected from a single beam experiment with the same noise properties. Autocorrelation functions suffer from a approximately 1.5 sigma positive bias at 60 deg while cross-correlations have no bias. Published COBE DMR results are not significantly affected by correlated noise.

Lineweaver, C. H.↗

NASA NTRS2023

Exploring the Predictability of the High-Energy Tail of MEE Precipitation Based on Solar Wind Properties

Medium Energy Electron (MEE) precipitation (≳30 keV) ionizes the mesosphere and initiates chemical reactions, which ultimately can reduce mesospheric and stratospheric ozone. Currently, there are considerable differences in how existing parameterizations represent flux response, timing, and duration of MEE precipitation, especially considering its high-energy tail (≳300 keV). This study compares the nature of ≳300 to ≳30 keV electron fluxes to better understand differences within MEE precipitation. The MEE fluxes are estimated from measurements by the Medium Energy Proton and Electron Detector (MEPED) onboard the Polar Orbiting Environmental Satellite (POES) from 2004 to 2014. The fluxes are explored in the context of solar wind drivers: corotating high-speed solar wind streams (HSSs) and coronal mass ejections (CMEs) alongside their associated solar wind properties. Three key aspects of ≳300 keV electron fluxes are investigated: maximum response, peak timing, and duration. The results reveal a structure-dependent correlation (0.89) between the peak fluxes of ≳30 and ≳300 keV electrons. The epsilon coupling function correlates well (0.84) with the ≳300 keV peak flux, independent of solar wind structure. The ≳300 keV flux peaks 0–3 days after the ≳30 keV flux peaks. The highest probability (∼42%) occurs for a 1-day delay, while predictive capabilities increase when accounting for solar wind speed. The ≳300 keV flux response has the highest probability of lasting 4 days for both CMEs and HSSs. The results form a base for a stochastic MEE parameterization that goes beyond the average picture, enabling realistic flux variability on both daily and decadal scales.

J A Salice↗

NASA NTRS1998

Cross Correlation of the 2-10 keV X-Ray Background with Radio Sources: Constraining the Large Scale Structure of the X-Ray Background

We present cross-correlation analyses of the HEAO 2-10 keV diffuse X-ray map with both the combined GB6/Parkes-MIT-NRAO (GB6-PMN) 5 GHz and the FIRST 1.4 GHz radio surveys. The cross-correlation functions (CCFs) of both radio surveys with the unresolved X-ray background were detected at the 5 u level. While the large angular resolution (3 deg) of the X-ray map makes it difficult to separate the contributions of clustering from those of Poisson fluctuations, the amplitude of the CCF provides important constraints on the X-ray emissivity of the radio sources, as well as on the clustering properties of radio and X-ray sources. These constraints are subject to a number of modeling parameters, e.g., X-ray luminosity evolution, clustering evolution, the radio luminosity function, cosmological model, etc. For reasonable choices of parameters the X-ray/FIRST CCF is consistent with a correlation scale length of 6/h Mpc. This is somewhat smaller than the scale length inferred from the autocorrelation function of the FIRST survey and implies that X-ray sources are less strongly clustered than strong radio sources, a result that is consistent with previous constraints on X-ray clustering. The X-ray/GB6-PMN CCF is several times larger and is likely to be dominated by Poisson fluctuations. This implies that approx. 2% of the diffuse X-ray background arises from the GB6-PMN sources.

Boughn, Stephen P.↗

NASA NTRS1991

Exact hierarchical clustering in one dimension

The present adhesion model-based one-dimensional simulations of gravitational clustering have yielded bound-object catalogs applicable in tests of analytical approaches to cosmological structure formation. Attention is given to Press-Schechter (1974) type functions, as well as to their density peak-theory modifications and the two-point correlation function estimated from peak theory. The extent to which individual collapsed-object locations can be predicted by linear theory is significant only for objects of near-characteristic nonlinear mass.

Williams, B. G.↗

NASA NTRS1997

The Richness Dependence of Galaxy Cluster Correlations: Results From A Redshift Survey Of Rich APM Clusters

We analyze the spatial clustering properties of a new catalog of very rich galaxy clusters selected from the APM Galaxy Survey. These clusters are of comparable richness and space density to Abell Richness Class greater than or equal to 1 clusters, but selected using an objective algorithm from a catalog demonstrably free of artificial inhomogeneities. Evaluation of the two-point correlation function xi(sub cc)(r) for the full sample and for richer subsamples reveals that the correlation amplitude is consistent with that measured for lower richness APM clusters and X-ray selected clusters. We apply a maximum likelihood estimator to find the best fitting slope and amplitude of a power law fit to x(sub cc)(r), and to estimate the correlation length r(sub 0) (the value of r at which xi(sub cc)(r) is equal to unity). For clusters with a mean space density of 1.6 x 10(exp -6) h(exp 3) MpC(exp -3) (equivalent to the space density of Abell Richness greater than or equal to 2 clusters), we find r(sub 0) = 21.3(+11.1/-9.3) h(exp -1) Mpc (95% confidence limits). This is consistent with the weak richness dependence of xi(sub cc)(r) expected in Gaussian models of structure formation. In particular, the amplitude of xi(sub cc)(r) at all richnesses matches that of xi(sub cc)(r) for clusters selected in N-Body simulations of a low density Cold Dark Matter model.

Croft, R. A. C.↗

NASA NTRS1974

Direct measurement of sound sources in air jets using the crossed beam correlation technique

Properties of density fluctuations were measured in the turbulent regions of a 2.54 cm air jet, at M = 0.7, 1.0 and 1.94. After calibration tests, it was found that the absorption of infrared radiation at 4.3 microns by the naturally present quantities of carbon-dioxide in air was directly proportional to the air density if a sufficiently wide bandpass (0.08 microns) was used. Moreover, regions of the band could be selected that adequately discriminated against temperature variations. The cross-correlation of two such beams intersecting in the jet gave a measure of the local properties at the intersection point. A derivation is presented relating the local density correlation function to the self and shear generated noise in the far field of the jet. The measured correlations are used to predict the axial distribution of source strengths and the spectrum of noise due to a unit volume of turbulence.

Damkevala, R. J.↗

NASA NTRS1974

Wave propagation in a random medium - A complete set of the moment equations with different wavenumbers

The propagation of waves in a random medium is studied in the 'quasi-optics' and the 'Markov random process' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of moment equations with different transverse coordinates and different wave numbers is then obtained from the Fokker-Planck equation of the characteristic functional. The application of those results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation is briefly discussed.

Lee, L. C.↗

NASA NTRS1991

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, Abbas↗

NASA NTRS1992

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

Khavaran, A.↗