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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Least Squares Best Fit Method for the Three Parameter Weibull Distribution: Analysis of Tensile and Bend Specimens with Volume or Surface Flaw Failure

Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.

Gross, Bernard↗
NASA NTRS1972

Variations of atmospheric density near 400 km with magnetic activity during the storm period of 28 September to 2 October 1969

Neutral density data were obtained near 400 km (1600 LT) from a microphone density gage on OGO-6 from 0 to 40 deg N geomagnetic latitude for 25 September through 3 October 1969. Several geomagnetic storms occurred during this period. Least squares fits were made to data points on density scatter diagrams. An equation representing the least squares fit was computed for each delay time. The equation of best fit (and the corresponding time delay between the density and the magnetic index which resulted in this best fit) was found by choosing the equation that gave the minimum standard error. The implications of the time differences associated with the best fits at various latitudes and longitudes are discussed with regard to the time delays involved in geomagnetic heating of the neutral upper atmosphere.

Anderson, A. D.↗
NASA NTRS2002

Coronal Heating and the Increase of Coronal Luminosity with Magnetic Flux

We present the observed scaling of coronal luminosity with magnetic flux in a set of quiet regions. Comparison of this with the observed scaling found for active regions suggests an underlying difference between coronal heating in active regions and quiet regions. From SOHO/EIT coronal images and SOHO/MDI magnetograms of four similar large quiet regions, we measure L(sub corona) and Phi(sub total) in random subregions ranging in area from about four supergranules [(70,000 km)(exp 2)] to about 100 supergranules [(0.5 R(sub sun))(exp 2)], where L(sub corona) is the luminosity of the corona in a subregion and Phi(sub total) is the flux content of the magnetic network in the subregion. This sampling of our quiet regions yields a correlation plot of Log L(sub corona) vs Log Phi(sub total) appropriate for comparison with the corresponding plot for active regions. For our quiet regions, the mean values of L(sub corona) and Phi(sub total) both increase linearly with area (simply because each set of subregions of the same area has very nearly the same mean coronal luminosity per unit area and mean magnetic flux per unit area), and in each constant-area set the values of L(sub corona) and Phi(sub total) 'scatter' about their means for that area. This results in the linear least-squares fit to the Log ((L (sub corona)), vs Log ((Phi (sub total)) plot having a slope somewhat less than one. If active regions mimicked our quiet regions in that all large sets of same-area active regions had the same mean coronal luminosity per unit area and same mean magnetic flux per unit area, then the least-squares fit to their Log((L (sub corona)) vs Log((Phi (sub total)) plot would also have a slope of less than one. Instead, the slope for active regions is 1.2. Given the observed factor of three scatter about the least-squares linear fit, this slope is consistent with Phi(sub total) on average increasing linearly with area (A) as in quiet regions, but L(sub corona) on average increasing as the volume (A(exp 1.5)) of the active region instead of as the area. This possibility is reasonable if the heating in active regions is a burning down of previously-stored coronal magnetic energy rather than a steady dissipation of energy flux from below as expected in quiet regions.

Moore, R. L.↗
NASA NTRS1985

Middle Atmosphere Tides at Christchurch (44 Deg S, 17 Deg E) in November 1981 and May 1982

Atmospheric tides at Christchurch were measured at heights of 80 to 100 km, in 2.5 km intervals during the ATMAP campaigns of November 1981 and May 1982. Average components for the 5-day periods, November 19 to 23 and May 3 to 7, were extracted by making an equally weighted least squares fit to the hourly mean values, using the sum of mean, diurnal and semidiurnal terms. Estimates of standard deviation from the least squares fit tend to be less than the variability between successive 5-day samples, but 5 to 8 ms(-1) and 2 to 3 h are typical. At altitudes below 83 km there may be gaps of up to 6 hours during the night which may generate a systematic error in the components. Amplitude and phase characteristics are generally consistent with November 1980 and 1982 and May 1981, although the amplitude of the diurnal EW tide was low in November 1981, with consequent large phase fluctuations.

Fraser, G. J.↗
NASA NTRS1984

A high resolution spectroscopic study of the oxygen molecule

A high resolution spectrometer which incorporates a narrow line width tunable dye laser was used to make absorption profiles of 57 spectral lines in the Oxygen A-Band at pressures up to one atmosphere in pure O2. The observed line profiles are compared to the Voigt, and a collisionally narrowed, profile using a least squares fitting procedure. The collisionally narrowed profile compares more favorable to the observed profiles. Values of the line strengths and self broadening coeffiencients, determined from the least square fitting process, are presented in tabular form. It is found that the experssion by Watson are in closest agreement with the experimentally determined strengths. The self broadening coefficients are compared with the measurements of several other investigators.

Ritter, K. J.↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
NASA NTRS1981

Variations in the UV spectrum of a Centauri

Equivalent width and central depth measurements of the ultraviolet absorption lines from the spectrum of the He I variable star a Cen HD 125823 are presented. The measurements are from 53 short wavelength, and 45 long wavelength, high resolution spectrographs taken with the IUE satellite over a 25 day period during July and August of 1978. Central depth measurements were of lines of Cr III, Mn III, V III, C III, Si II, and S II seen in the region between 1245 and 1255 A. Equivalent widths are of the three He I 2(3)s-n(3po) transitions found at 2945, 2829 and 2764 A. The period for cyclic intensity variations in He I is determined using a four parameter, least squares fit to a sinusoid. The IUE observations match both a period of 8.8163 + or - 0.0003 days and a previously unreported period of 9.2532 + or - 0.0003 days with equal minima for the least squares fit. The phase of Cr III maximum relative to He I maximum is found to be 0.53 cycles for the IUE observations.

Fahey, R. P.↗
DOE OSTI2021

The AME 2020 atomic mass evaluation (I). Evaluation of input data, and adjustment procedures*

Abstract This is the first of two articles (Part I and Part II) that presents the results of the new atomic mass evaluation, AME2020. It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II. This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction, decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties. All input data, including both the accepted and rejected ones, are tabulated and compared with the adjusted values obtained from the least-squares fit analysis. Differences with the previous AME2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to AME users.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1974

A simplified package for calculating with splines

This package is designed to solve some of the elementary problems of spline interpretation and least squares fit. The subroutines fall into three basic categories. The first category involves computations with a given spline and/or knot sequence; the second category involves routines which calculate the coefficients of splines which perform a certain task (such as interpolation or least squares fit); and the last category is a banded equation solver for specific linear equations.

Smith, P. W.↗
NASA NTRS1972

An equation of state for oxygen and nitrogen 2

Preliminary equations of state for oxygen and nitrogen are presented which are the result of least squares fitting of the available P-density-T data, heat capacities at constant volume, and data to establish the criteria for phase equilibrium, simultaneously. The equation for nitrogen is applicable to 10,000 atmospheres at temperatures from 70 K to 1300 K, and the equation for oxygen to 350 atmospheres for temperatures from 56 K to 323 K. The development of the functional form of the equation of state, data weighting methods, and the techniques employed for least squares fitting of related data are discussed. Comparisons of the equation of state developed with selected values of experimental P-density-T data, and heat capacity values are included for both fluids.

Stewart, R. B.↗
NASA NTRS2010

FPGA Coprocessor Design for an Onboard Multi-Angle Spectro-Polarimetric Imager

A multi-angle spectro-polarimetric imager (MSPI) is an advanced camera system currently under development at JPL for possible future consideration on a satellite-based Aerosol-Cloud-Environ - ment (ACE) interaction study. The light in the optical system is subjected to a complex modulation designed to make the overall system robust against many instrumental artifacts that have plagued such measurements in the past. This scheme involves two photoelastic modulators that are beating in a carefully selected pattern against each other. In order to properly sample this modulation pattern, each of the proposed nine cameras in the system needs to read out its imager array about 1,000 times per second. The onboard processing required to compress this data involves least-squares fits (LSFs) of Bessel functions to data from every pixel in realtime, thus requiring an onboard computing system with advanced data processing capabilities in excess of those commonly available for space flight. As a potential solution to meet the MSPI onboard processing requirements, an LSF algorithm was developed on the Xilinx Virtex-4FX60 field programmable gate array (FPGA). In addition to configurable hardware capability, this FPGA includes Power -PC405 microprocessors, which together enable a combination hardware/ software processing system. A laboratory demonstration was carried out based on a hardware/ software co-designed processing architecture that includes hardware-based data collection and least-squares fitting (computationally), and softwarebased transcendental function computation (algorithmically complex) on the FPGA. Initial results showed that these calculations can be handled using a combination of the Virtex- 4TM Power-PC core and the hardware fabric.

Pingree, Paula J.↗
DOE OSTI2022

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1997

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

Chamberlain, D. M.↗
DOE OSTI2021

Sound velocities of iron-nickel (Fe90Ni10) alloy up to 8 GPa and 773 K: The effect of nickel on the elastic properties of bcc-iron at high P-T

Sound velocities of iron and iron-based alloys at high pressure and high temperature are crucial for understanding the composition and structure of Earth’s and other telluric planetary cores. In this study, we performed ultrasonic interferometric measurements of both compressional (ν P ) and shear (ν S ) velocities on a polycrystalline body-centered-cubic (bcc)-Fe 90 Ni 10 up to 8 GPa and 773 K. The elastic moduli and their pressure and temperature derivatives are derived from least-square fits to third-order finite strain equations, yielding K S0 = 154.2(8) GPa, G 0 = 73.2(2) GPa, K' S0 = 4.6(2), G' 0 = 1.5(1), ∂K S /∂T = –0.028(1) GPa/K, and ∂G/∂T = –0.023(1) GPa/K. Furthermore, a comparison with literature data on bcc-Fe suggests that nickel not only decreases both P and S wave velocities but also weakens the temperature effects on the elastic moduli of Fe-Ni alloys.

36 MATERIALS SCIENCE↗
NASA NTRS2014

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

strain-gage balance↗