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NASA NTRS1993

Testing the pressure-confined Ly alpha cloud model

The Ly-alpha absorption line forest, seen in quasar spectra, is generally interpreted as being due to cosmologically distributed 'clouds' of primordial gas. Analyses of the observations reveal that the number distribution can be described by power laws: dN/dz is proportional to (1 + z)(sup gamma) and dN/dN(sub HI) is proportional to N(sub HI)(sup -beyda), where N(sub HI) is the HI column density. The typical values for power law indices range between 2 is approximately less than gamma is approximately less than 2.6 and 1.7 is approximately less than gamma is approximately less than 1.9. One model postulates that the Ly-alpha clouds are optically thin entities, photoionized by the background UV flux, J(sub nu) is proportional to (1 + z)(sup j), and confined by an adiabatically evolving intercloud medium (ICM): P(z) is proportional to (1 + z)(sup 5). Analytic studies of this model suggest that the ensuing Ly-alpha line statistics can account for the observations (in particular, the dN/dz and the dN/dN(sub HI) distributions) if the cloud mass spectrum is a power law dN/dN is proportional to M(sup -delta), delta is approximately 1.9, and j is approximately 4. One of the simplifying assumptions incorporated into these studies is the existence of a large mass range for the clouds at all epochs, the validity of which is questionable. The pressure-confined model is investigated using a 1-D spherically symmetric hydrodynamical code to simulate cloud evolution over the epoch 1.8 less than z less than 6. This enables us to relax many of the assumptions incorporated in the analytic studies.

Babul, Arif↗

NASA NTRS1999

Ocean Turbulence: Two-Point Closure Model Momentum, Heat and Salt Vertical Diffusivities in the Presence of Shear - Paper 3

In papers 1 and 2 we have presented the results of the most updated 1-point closure model for the turbulent vertical diffusivities of momentum, heat and salt, K(sub m,h,s). In this paper, we derive the analytic expressions for K(sub m,h,s) using a new 2-point closure model that has recently been developed and successfully tested against some approx. 80 turbulence statistics for different flows. The new model has no free parameters. The expressions for K(sub m, h. s) are analytical functions of two stability parameters: the Turner number R(sub rho) (salinity gradient/temperature gradient) and the Richardson number R(sub i) (temperature gradient/shear). The turbulent kinetic energy K and its rate of dissipation may be taken local or non-local (K-epsilon model). Contrary to all previous models that to describe turbulent mixing below the mixed layer (ML) have adopted three adjustable "background diffusivities" for momentum. heat and salt, we propose a model that avoids such adjustable diffusivities. We assume that below the ML, K(sub m,h,s) have the same functional dependence on R(sub i) and R(sub rho) derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking measured by Gargett et al. (1981). The procedure frees the model from adjustable background diffusivities and indeed we use the same model throughout the entire vertical extent of the ocean. Using the new K(sub m,h, s), we run an O-GCM and present a variety of results that we compare with Levitus and the KPP model. Since the traditional 1-point (used in papers 1 and 2) and the new 2-point closure models used here represent different modeling philosophies and procedures, testing them in an O-GCM is indispensable. The basic motivation is to show that the new 2-point closure model gives results that are overall superior to the 1-point closure in spite of the fact that the latter rely on several adjustable parameters while the new 2-point closure has none. After the extensive comparisons presented in papers 1 and 2, we conclude that the new model presented here is overall superior for it not only is parameter free but also 2 because is part of a more general turbulence model that has been previously successfully tested on a wide variety of other types of turbulent flows.

Canuto, V. M.↗

NASA NTRS2012

Broadband Noise Prediction When Turbulence Simulation Is Available - Derivation of Formulation 2B and Its Statistical Analysis

We show that a simple modification of Formulation 1 of Farassat results in a new analytic expression that is highly suitable for broadband noise prediction when extensive turbulence simulation is available. This result satisfies all the stringent requirements, such as permitting the use of the exact geometry and kinematics of the moving body, that we have set as our goal in the derivation of useful acoustic formulas for the prediction of rotating blade and airframe noise. We also derive a simple analytic expression for the autocorrelation of the acoustic pressure that is valid in the near and far fields. Our analysis is based on the time integral of the acoustic pressure that can easily be obtained at any resolution for any observer time interval and digitally analyzed for broadband noise prediction. We have named this result as Formulation 2B of Farassat. One significant consequence of Formulation 2B is the derivation of the acoustic velocity potential for the thickness and loading terms of the Ffowcs Williams-Hawkings (FW-H) equation. This will greatly enhance the usefulness of the Fast Scattering Code (FSC) by providing a high fidelity boundary condition input for scattering predictions.

Farassat, Fereidoun↗

NASA NTRS1963

Orbit determination and prediction, and computer programs

Orbit determination and prediction programs are needed to generate ephemerides for the satellite. Orbit determination is from tracking data consisting of angles only, and is based on a modified version of a method by R. E. Briggs and J. W. Slowey of the Smithsonian Institution. Trends in the data due to perturbations from a Keplerian orbit are removed before this process, and estimates of the orbital elements from individual passes are combined statistically to produce refined estimates. Ephemeris calculation is by a semi-analytic method in which deviations from a Keplerian orbit are obtained by integrating the perturbing forces. The programs to implement these procedures have been written for both the IBM 7090 and the IBM 1620 computers.

EPHEMERIS↗

NASA NTRS1983

An update on the life analysis of spur gears

An analytical method for predicting surface fatigue life of gears was presented. General statistical methods were outlined, showing the application of the general methods to a simple gear mesh. Experimentally determined values for constants in the life equation were given. Comparison of the life theory with test results and AGMA standards was made. Gear geometry pertinent to life calculations was reviewed.

Coy, J. J.↗

NASA NTRS1996

Determination of 2,3,7,8-chlorine-substituted dibenzo-p-dioxins and -furans at the part per trillion level in United States beef fat using high-resolution gas chromatography/high-resolution mass spectrometry

As part of the U.S. EPA Dioxin Reassessment Program, the 2,3,7,8-chlorine-substituted dibenzo-p-dioxins and furans were measured at part per trillion (ppt) levels in beef fat collected from slaughter facilities in the United States. This is the first statistically designed national survey of these compounds in the U.S. beef supply. Analyte concentrations were determined by high-resolution gas chromatography/high-resolution mass spectrometry, using isotope dilution methodology. Method limits of detection on a whole weight basis were 0.05 ppt for TCDD and 0.10 ppt for TCDF, 0.50 ppt for the pentas (PeCDDs/PeCDFs)/hexas (HxCDDs/HxCDFs)/heptas (HpCDDs/HpCDFs), and 3.00 ppt for the octas (OCDD/OCDF). Method detection and quantitation limits were established on the basis of demonstrated performance criteria utilizing fortified samples rather than by conventional signal-to-noise or variability of response methods. The background subtraction procedures developed for this study minimized the likelihood of false positives and increased the confidence associated with reported values near the detection limits. Mean and median values for each of the 2,3,7,8-Cl-substituted dioxins and furans are reported, along with the supporting information required for their interpretation. The mean toxic equivalence values for the samples are 0.35 ppt (nondetects = 0) and 0.89 ppt (nondetects = 1/2 LOD).

Benzofurans/analysis↗

NASA NTRS2013

Cohesive Modeling of Transverse Cracking in Laminates with a Single Layer of Elements per Ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks

VanDerMeer, Frans P.↗

NASA NTRS2017

Temperature Increase Reduces Global Yields of Major Crops in Four Independent Estimates

Wheat, rice, maize, and soybean provide two-thirds of human caloric intake. Assessing the impact of global temperature increase on production of these crops is therefore critical to maintaining global food supply, but different studies have yielded different results. Here, we investigated the impacts of temperature on yields of the four crops by compiling extensive published results from four analytical methods: global grid-based and local point-based models, statistical regressions, and field-warming experiments. Results from the different methods consistently showed negative temperature impacts on crop yield at the global scale, generally underpinned by similar impacts at country and site scales. Without CO2 fertilization, effective adaptation, and genetic improvement, each degree-Celsius increase in global mean temperature would, on average, reduce global yields of wheat by 6.0%, rice by 3.2%, maize by 7.4%, and soybean by 3.1%. Results are highly heterogeneous across crops and geographical areas, with some positive impact estimates. Multi-method analyses improved the confidence in assessments of future climate impacts on global major crops and suggest crop- and region-specific adaptation strategies to ensure food security for an increasing world population.

Zhao, Chuang↗

NASA NTRS2020

Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens

Modeling the effects of atmospheric turbulence on optical beam propagation is a key element in the design and analysis of free-space optical communication systems. Numerical wave optics simulations provide a particularly useful technique for understanding the degradation of the optical field in the receiver plane when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such an application, we use a split-step method modeling the turbulence along the propagation path as a series of thin random phase screens with modified von Karman refractive index statistics using the Hufnagel-Valley turbulence profile to determine the effective structure constant for each screen. In this work, we employ a space-to-ground case study to examine the irradiance and phase statistics for both uniformly and non-uniformly spaced screens along the propagation path and compare to analytical results. We find that better agreement with the analytical theory is obtained using a non-uniform spacing with the effective structure constant for each screen chosen to minimize its contribution to the scintillation in the receiver plane. We evaluate this method as a flexible alternative to other standard layered models used in astronomical imaging applications.

Chahine, Yousef K.↗

NASA NTRS1991

The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow

The effect of an arbitrarily oriented mean passive scalar gradient on one-point passive scalar statistics is studied in homogeneous turbulent shear flow in the limit of rapid shearing. By neglecting the nonlinear inertial transfer to small scales an analytical solution for individual Fourier modes is obtained for the case of unity Prandtl number. This solution is used to compute the development of one-point statistics for the velocity and scalar fields in the inviscid limit. Comparisons to direct numerical simulations of the full nonlinear equations for the same flow show that, in addition to describing the early time response to the imposed shear, the linear solution gives reasonable estimates of several correlation coefficients for the developed shear flow.

Rogers, Michael M.↗

NASA NTRS1975

Instrumental technique in X-ray astronomy

A detailed review of the development of instruments for X-ray astronomy is given with major emphasis on nonfocusing high-sensitivity counter techniques used to detect cosmic photons in the energy range between 0.20 and 300 keV. The present status of X-ray astronomy is summarized together with significant results of the Uhuru observations, and photon interactions of importance for the detection of X-rays in space are noted. The three principal devices used in X-ray astronomy (proportional, scintillation, and solid-state counters) are described in detail, data-processing systems for these devices are briefly discussed, and the statistics of nuclear counting as applied to X-ray astronomy is outlined analytically. Effects of the near-earth X-ray environment and atmospheric gamma-ray production on X-ray detection by low-orbit satellites are considered. Several contemporary instruments are described (proportional-counter systems, scintillation-counter telescopes, modulation collimators), and X-ray astronomical satellite missions are tabulated.

Peterson, L. E.↗

NASA NTRS1980

Microprocessor realizations of range and range-rate filters in radar systems

This paper describes the implementation of digital radar range-rate filters on a microprocessor-based system. A range-rate filter processes a digitized noisy range signal to recover smoothed range data and its derivative, range rate. Two filter designs are implemented. Considerations aiding their efficient operation on an 8-bit microprocessor are discussed. The filters are subjected to a noisy range input signal of known variance, and the associated output signals are statistically analysed to determine noise-rejection characteristics. These results are compared to analytical predictions.

Fleischer, D.↗

NASA NTRS1980

Inventory estimation on the massively parallel processor

This paper describes algorithms for efficiently computing inventory estimates from satellite based images. The algorithms incorporate a one dimensional feature extraction which optimizes the pairwise sum of Fisher distances. Biases are eliminated with a premultiplication by the inverse of the analytically derived error matrix. The technique is demonstrated with a numerical example using statistics obtained from an actual Landsat scene. Attention was given to implementation of the Massively Parallel processor (MPP). A timing analysis demonstrates that the inventory estimation can be performed an order of magnitude faster on the MPP than on a conventional serial machine.

Argentiero, P. D.↗

NASA NTRS1982

Topics in strong Langmuir turbulence

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Nicholson, D. R.↗

NASA NTRS1983

Topics in strong Langmuir turbulence

Nicholson, D. R.↗

NASA NTRS2013

On the Statistical Analysis of X-ray Polarization Measurements

In many polarimetry applications, including observations in the X-ray band, the measurement of a polarization signal can be reduced to the detection and quantification of a deviation from uniformity of a distribution of measured angles of the form alpha plus beta cosine (exp 2)(phi - phi(sub 0) (0 (is) less than phi is less than pi). We explore the statistics of such polarization measurements using both Monte Carlo simulations as well as analytic calculations based on the appropriate probability distributions. We derive relations for the number of counts required to reach a given detection level (parameterized by beta the "number of sigma's" of the measurement) appropriate for measuring the modulation amplitude alpha by itself (single interesting parameter case) or jointly with the position angle phi (two interesting parameters case). We show that for the former case when the intrinsic amplitude is equal to the well known minimum detectable polarization (MDP) it is, on average, detected at the 3sigma level. For the latter case, when one requires a joint measurement at the same confidence level, then more counts are needed, by a factor of approximately equal to 2.2, than that required to achieve the MDP level. We find that the position angle uncertainty at 1sigma confidence is well described by the relation sigma(sub pi) equals 28.5(degrees) divided by beta.

Strohmayer, T. E.↗

NASA NTRS2021

Expected Collision Rates for Tracked Satellites

This analysis estimates collision risks between tracked satellites based on the statistically expected collision rate _Nc and number of collisions Nc, which are closely related to the collision probability Pc. For isolated encounters, Nc equals Pc. For multi-encounter interactions, Nc can exceed Pc and is significantly easier to approximate semi-analytically. Estimating Nc requires integrating the collision rate over time throughout an interaction, with each required _Nc value calculated as a statistical expectation value based on the uncertainty distributions of initial orbital states. The uncertainty distributions are estimated from orbit determination analyses of satellite trajectory measurements. The formulation accounts for the nonlinear orbital motion of the satellites, and derives Nc and _Nc expressions for Monte Carlo simulations as well as semi-analytical approximations for single- and multi-encounter interactions.

Collision Rates↗

NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗