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NASA NTRS1980

The structure of correlation tensors in homogeneous anisotropic turbulence

The study of turbulence with spatially homogeneous but anisotropic statistical properties has applications in space physics and laboratory plasma physics. The first step in the systematic study of such fluctuations is the elucidation of the kinematic properties of the relevant statistical objects, which are the correlation tensors. The theory of isotropic tensors, developed by Robertson, Chandrasekhar and others, is reviewed and extended to cover the general case of turbulence with a pseudo-vector preferred direction, without assuming mirror reflection invariance. Attention is focused on two point correlation functions and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. It is also shown that the vector and pseudo-vector preferred direction cases yield different results. An explicit form of the two point correlation tensor is presented which is appropriate for analyzing interplanetary magnetic fluctuations. A procedure for determining the magnetic helicity from experimental data is presented.

Matthaeus, W. H.↗
NASA NTRS1977

A model for microwave intensity propagation in an inhomogeneous medium

A combined analytic and phenomenological approach, utilizing Maxwell's equations in the Born approximation with radiative transfer theory, is used to describe the propagation of microwave intensity in a scattering medium characterized by three-dimensional random fluctuations in refractive index, as well as nonrandom variations in permittivity, temperature, and loss. This approach yields microwave intensities as a function of polarization, direction, and position. Numerical techniques are presented to solve the transport equations, which include cases of spatially varying coefficients, and highly peaked phase functions. Some computed results illustrating the behavior of microwave intensity in various media are presented. Included are the angular and frequency spectra of thermal emission from semi-infinite media, and the diffuse transmission and reflection response of a scattering layer. The effects of scatterer geometry and scale sizes; correlation function; and gradients in temperature, loss, and scattering parameters are also demonstrated. This model should be particularly useful in interpreting active and passive remote sensing data.

Fisher, A. D.↗
NASA NTRS1978

Two-scale-factor universality near the critical point of fluids

Thermodynamic data from interferometric density profile studies and light-scattering experiments near the critical isochore of Xe, CO2 and SF6 provide a basis for examining the hypothesized two-scale-factor universality for the correlation function of fluids near the gas-liquid critical point. For the investigation, three-scale-factor universality is assumed, with Ising-like critical exponent values obtained through the renormalization group technique. The two thermodynamic scale factors are found from the density profiles, while the scale factor for the correlation length is obtained from the light-scattering data.

Sengers, J. V.↗
NASA NTRS1968

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations, Phase 2

A comparison with NASA conducted simulator studies has shown that the approximate digital method for computing rotor blade flapping responses to random inputs, tentatively suggested in Phase I Report, gives with increasing rotor advance ratio the wrong trend. Consequently, three alternative methods of solution have been considered and are described: (1) an approximate method based on the functional relation between input and output double frequency spectra, (2) a numerical method based on the system responses to deterministic inputs and (3) a perturbation approach. Among these the perturbation method requires the least amount of computation and has been developed in two forms - the first form to obtain the response correlation function and the second for the time averaged spectra of flapping oscillations.

Hohenemser, K. H.↗
NASA NTRS1983

Processing techniques for software based SAR processors

Software SAR processing techniques defined to treat Shuttle Imaging Radar-B (SIR-B) data are reviewed. The algorithms are devised for the data processing procedure selection, SAR correlation function implementation, multiple array processors utilization, cornerturning, variable reference length azimuth processing, and range migration handling. The Interim Digital Processor (IDP) originally implemented for handling Seasat SAR data has been adapted for the SIR-B, and offers a resolution of 100 km using a processing procedure based on the Fast Fourier Transformation fast correlation approach. Peculiarities of the Seasat SAR data processing requirements are reviewed, along with modifications introduced for the SIR-B. An Advanced Digital SAR Processor (ADSP) is under development for use with the SIR-B in the 1986 time frame as an upgrade for the IDP, which will be in service in 1984-5.

Leung, K.↗
NASA NTRS2009

Ultra-Broad-Band Optical Parametric Amplifier or Oscillator

A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter

Strekalov, Dmitry↗
NASA NTRS1989

Angular clustering properties of gamma-ray bursts and quantitative constraints on their distances

Upper limits on the angular correlation function, w(theta), of gamma-ray bursts are obtained which constrain the sources to be very nearby or very distant. The angular clustering properties of the sources in two recent gamma-ray burst catalogs (Golenetskii et al., 1986 and Atteia et al., 1987) have been derived by determining their two-point w(theta) values, and the correlations of both data sets are consistent with w(theta) = 0. It is shown that if the spatial correlation of gamma-ray bursts resembles that of galaxies or galactic clusters, present gamma-ray burst catalogs must be complete to distances in excess of 100 Mpc, while if gamma-ray bursts are associated with a Galactic disk population, then the upper limits on w(theta) constrain the sampling depth to less than two disk scale heights.

Hartmann, Dieter↗
NASA NTRS1986

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗
NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗
NASA NTRS1991

Stochastic mixing of protons from chaotic orbits in the nightside geomagnetosphere

The stochastic mixing of protons in the energy range from 1 to 30 keV in the nightside magnetosphere is studied by calculating the local divergence rate of neighboring orbits and the two-time velocity correlation function. The rate of divergence of neighboring bundles of trajectories is shown to have large bursts with average separation times of order 1 minute per e-folding during the crossing of the central plasma sheet in the region beyond -50 Re. For the Tsyganenko magnetosphere the net amount of orbit divergence is 15 to 20 e-foldings in one hour. The velocity correlations are shown to decay as power laws r-m with a distribution of m values. These results indicate that for short time (less than 1 hour) there is reversibility and memory for the protons but for longer times there is no memory for protons in the nightside magnetosphere.

Horton, W.↗
NASA NTRS2000

Method for suppressing noise in measurements

Techniques of combining separate but correlated measurements to form a second-order or higher order correlation function to suppress the effects of noise in the initial condition of a system capable of retaining memory of an initial state of the system with a characteristic relaxation time. At least two separate measurements are obtained from the system. The temporal separation between the two separate measurements is preferably comparable to or less than the characteristic relaxation time and is adjusted to allow for a correlation between two measurements.

Carson, Paul J.↗
NASA NTRS2011

Michigan Orbital DEbris Survey Telescope Observations of the Geosynchronous Orbital Debris Environment. Observing Years: 2007-2009

NASA uses the Michigan Orbital DEbris Survey Telescope (MODEST), the University of Michigan's 0.61-m aperture Curtis-Schmidt telescope at the Cerro Tololo Inter-American Observatory in Chile, to help characterize the debris environment in geosynchronous orbit; this began in February 2001 and continues to the present day. Detected objects that are found to be on the U.S. Space Surveillance Network cataloged objects list are termed correlated targets (CTs), while those not found on the list are called uncorrelated targets (UCTs). This Johnson Space Center report provides details of observational and data-reduction processes for the entire MODEST dataset acquired in calendar years (CYs) 2007, 2008, and 2009. Specifically, this report describes the collection and analysis of 36 nights of data collected in CY 2007, 43 nights of data collected in CY 2008, and 43 nights of data collected in CY 2009. MODEST is equipped with a 2048 x 2048-pixel charged coupled device camera with a 1.3 by 1.3 deg field of view. This system is capable of detecting objects fainter than 18th magnitude (R filter) using a 5-s integration. This corresponds to a 20-cm diameter, 0.175-albedo object at 36,000 km altitude assuming a diffuse Lambertian phase function. The average number of detections each night over all 3 years was 26. The percentage of this number that represented the UCT population ranged from 34% to 18%, depending on the observing strategy and the field center location. Due to the short orbital arc over which observations are made, the eccentricity of the object s orbit is extremely difficult to measure accurately. Therefore, a circular orbit was assumed when calculating the orbital elements. A comparison of the measured inclination (INC), right ascension of ascending node (RAAN), and mean motion to the quantities for CTs from the U.S. Space Surveillance Network shows acceptable errors. This analysis lends credibility to the determination of the UCT orbital distributions. Figure 1 shows the size distribution of 3,143 objects detected in the data processed for CYs 2007, 2008, and 2009. The actual peak of the absolute magnitude distribution for the functional correlated targets is 10th magnitude, whereas the peak was 11th magnitude in 2002 2003 and 10th magnitude for 2004-2006. An absolute magnitude of 10.5 corresponds to objects with average diameters of 6.3 m, assuming an albedo of 0.175 and a diffuse Lambertian phase function. This result generally agrees with the known sizes of intact satellites. The absolute magnitude distribution for the UCTs is broad, but starts to roll off near 25 cm diameter or 17.5 magnitude. This roll off in the distribution reflects the detection capability of MODEST, not the true nature of the population. The true population is believed to continue at the same slope through fainter magnitudes based on comparisons with the LEO break-up law.

Abercromby, K. J.↗
NASA NTRS1988

Time evolution of surface chlorophyll patterns from cross-spectrum analysis of satellite color images

The rate of decorrelation of surface chlorophyll patterns as a function of the time separation between pairs of images was determined from two sequences of CZCS images of the Pacific Ocean area adjacent to Vancouver Island, Canada; cloud-free subareas were selected that were common to several images separated in time by 1-17 days. Image pairs were subjected to two-dimensional autospectrum and cross-spectrum analysis in an array processor, and squared coherence estimates found for several wave bands were plotted against time separation, in analogy with a time-lagged cross correlation function. It was found that, for wavelengths of 50-150 km, significant coherence was lost after 7-10 days, while for wavelengths of 25-50 km, significant coherence was lost after only 5-7 days. In both cases, offshore regions maintained coherence longer than coastal regions.

Denman, Kenneth L.↗
NASA NTRS2019

Size and Structure of the Sequence Space of Repeat Proteins

The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family— the total number of sequences in that family—can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occurring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of *30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of frustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family and suggests new strategies for protein design.

Jacopo Marchi↗
NASA NTRS1975

A B-B-G-K-Y framework for fluid turbulence

A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.

Montgomery, D.↗
NASA NTRS1987

Signal averaging technique for noninvasive recording of late potentials in patients with coronary artery disease

An advanced non invasive signal averaging technique was used to detect late potentials in two groups of patients: Group A (24 patients) with coronary artery disease (CAD) and without sustained ventricular tachycardia (VT) and Group B (8 patients) with CAD and sustained VT. Recorded analog data were digitized and aligned using a cross correlation function with fast Fourier transform schema, averaged and band pass filtered between 60 and 200 Hz with a non-recursive digital filter. Averaged filtered waveforms were analyzed by computer program for 3 parameters: (1) filtered QRS (fQRS) duration (2) interval between the peak of the R wave peak and the end of fQRS (R-LP) (3) RMS value of last 40 msec of fQRS (RMS). Significant change was found between Groups A and B in fQRS (101 -/+ 13 msec vs 123 -/+ 15 msec; p < .0005) and in R-LP vs 52 -/+ 11 msec vs 71-/+18 msec, p <.002). We conclude that (1) the use of a cross correlation triggering method and non-recursive digital filter enables a reliable recording of late potentials from the body surface; (2) fQRS and R-LP durations are sensitive indicators of CAD patients susceptible to VT.

NASA Discipline Cardiopulmonary↗
NASA NTRS1992

Comments on the present state and future directions of PDF methods

The one point probability density function (PDF) method is examined in light of its use in actual engineering problems. The PDF method, although relatively complicated, appears to be the only format available to handle the nonlinear stochastic difficulties caused by typical reaction kinetics. Turbulence modeling, if it is to play a central role in combustion modeling, has to be integrated with the chemistry in a way which produces accurate numerical solutions to combustion problems. It is questionable whether the development of turbulent models in isolation from the peculiar statistics of reactant concentrations is a fruitful line of development as far as propulsion is concerned. There are three issues for which additional viewgraphs are prepared: the one point pdf method; the amplitude mapping closure; and a hybrid strategy for replacing a full two point pdf treatment of reacting flows by a single point pdf and correlation functions. An appeal is made for the establishment of an adequate data base for compressible flow with reactions for Mach numbers of unity or higher.

Obrien, E. E.↗