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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 NTRS1991

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Greenzweig, Yuval↗
NASA NTRS1992

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Greenzweig, Yuval↗
NASA NTRS1977

Backscattering from a Gaussian distributed, perfectly conducting, rough surface

The problem of scattering by random surfaces possessing many scales of roughness is analyzed. The approach is applicable to bistatic scattering from dielectric surfaces, however, this specific analysis is restricted to backscattering from a perfectly conducting surface in order to more clearly illustrate the method. The surface is assumed to be Gaussian distributed so that the surface height can be split into large and small scale components, relative to the electromagnetic wavelength. A first order perturbation approach is employed wherein the scattering solution for the large scale structure is perturbed by the small scale diffraction effects. The scattering from the large scale structure is treated via geometrical optics techniques. The effect of the large scale surface structure is shown to be equivalent to a convolution in k-space of the height spectrum with the following: the shadowing function, a polarization and surface slope dependent function, and a Gaussian factor resulting from the unperturbed geometrical optics solution. This solution provides a continuous transition between the near normal incidence geometrical optics and wide angle Bragg scattering results.

Brown, G. S.↗
NASA NTRS1974

Weighted adaptive algorithms for estimation of Gaussian distribution parameters

Two weighted adaptive algorithms are proposed for updating the estimates of the mean vector and the covariance matrix, respectively, in a multispectral pattern recognition system. To achieve computational efficiency, the auxiliary matrices have been utilized in the algorithm for covariance matrix updating. Enhancements in the performance accuracy of a multispectral processing system and extensions of the Gaussian maximum likelihood classification capabilities to larger scale surveys are the motivations in developing the algorithms presented herein.

Chang, C. Y.↗
NASA NTRS1978

Backscattering from a Gaussian-distributed perfectly conducting rough surface

The original intent of the reported investigation was to find a solution to the composite surface scattering problem which provided for a continuous transition between the near-specular physical optics and wide-angle tilted plane Bragg solutions. The employed approach is based on analytical techniques rather than physical considerations. The analysis employs a perturbation technique developed by Burrows (1967, 1968, 1973), which because of its simplicity, is the key to the entire solution. The analysis is restricted to the case of backscattering from a perfectly conducting surface. General expressions are presented for the scattering from a Gaussian perfectly conducting surface characterized by an anisotropic spectrum and possessing many scales of roughness. The accuracy of the result is dependent upon the large-scale structure having large height excursions and small curvature.

Brown, G. S.↗
NASA NTRS2022

Non-Gaussian Distributions of TOA SW Flux as Observed by MISR and CERES

The Top of Atmosphere (TOA) shortwave (SW) flux, converted from Terra Multi angle Imaging‐SpectroRadiometer (MISR) narrow band albedos, is compared with that measured from Clouds and the Earth’s Radiant Energy System (CERES). We describe the probability density function (PDF) of the monthly TOA SW flux and how the statistical third moment, skewness, can impact the quantification of the flux. The PDF of the SW flux is not normally distributed but positively skewed. In both sets of observations, the near-global (80S-80N) median value of the SW flux is ≈3 W/m 2 less than the mean value, due to the positive skewness of the distribution. The near-global mean TOA SW flux converted from MISR is about 7 W/m 2 (≈7%) less than CERES measured flux during the last two decades. Surprisingly, hemispheric asymmetry exists with TOA SW observations from Terra platform. SH reflects 3.92 W/m 2 and 1.15 W/m 2 more mean SW flux than NH, from MISR and CERES Single Scanner Footprint products, respectively. We can infer that the offsetting by morning clouds in the SH is greater than the effect of hemispheric imbalance of SW flux caused by different land masses in two hemispheres. While the characteristics of the two SW fluxes broadly agree with each other, differences in the regional PDF from two different SW fluxes are substantially different over high cloud regions and high altitude regions. Our analysis shows that some parts of the different skewness from two measurements may be attributed to the different calibration of the radiance anisotropy over high cloud scenes.

satellite measurements↗
DOE OSTI2025

Impact of super-Gaussian electron distributions on plasma K-shell emission

Electron distributions in laser-produced plasmas will be driven toward a super-Gaussian distribution due to inverse bremsstrahlung absorption [Langdon, Phys. Rev. Lett. 44, 575 (1980)]. Both theoretical and experimental evidence suggest that fundamental plasma properties are altered by the super-Gaussian distribution. Here, this paper examines how the super-Gaussian distribution affects the ionization balance and K-shell emission of atomic plasmas, utilizing approximate formulas and detailed collisional-radiative simulations. While the impact on plasma ionization is small, K-shell spectra can be significantly modified. Based on these findings, we demonstrate that K-shell spectroscopy can be used to infer super-Gaussian or other similar nonequilibrium electron distributions.

Atomic spectra↗
DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Inverse bremsstrahlung absorption rate for super-Gaussian electron distribution functions including plasma screening

Here we provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)], and we find the absorption rate under these conditions is increased by as much as ≈ 30% compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at Z = 6 and Te = 400 eV the Langdon prediction for the absorption is in error by a factor of ≈ 2. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to ≈ 30%). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order “M” and the screening length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1971

Simulation of flight maneuver-load distributions by utilizing stationary, non-Gaussian random load histories

Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.

Leybold, H. A.↗
NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗
DOE OSTI2026

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗
DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗
DOE OSTI2023

Detecting deviations from Gaussianity in high-redshift CMB lensing maps

ABSTRACT While the probability density function of the cosmic microwave background (CMB) convergence field approximately follows a Gaussian distribution, primordial non-Gaussianities, and small contributions from structures at low redshifts make the overall distribution slightly non-Gaussian. Some of the late-time component can be modelled using the distribution of galaxies and subtracted off from the original CMB lensing map to produce a map of matter distribution at high redshifts. Using this high-redshift mass map, we are able to directly study the early phases of structure formation. In this work, we forecast the detectability of signatures of non-Gaussianity due to non-linear structure formation at z > 1.2. Assuming the optimal case of no systematics, we find that it is challenging to detect such signatures in current surveys, but future experiments such as the deep field of CMB-S4 will be able to make detections of ∼7σ.

Astronomy & Astrophysics↗
NASA NTRS1991

A continuous mixing model for pdf simulations and its applications to combusting shear flows

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Hsu, A. T.↗