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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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At least 19 records
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↗
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↗
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.↗
NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). 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. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗
NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves in Multi Ion Magnetosphere - 1

The further development of a self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves [Khazanov et al., 2003] is presented. In order to adequately take into account the wave propagation and refraction in a multi-ion plasmasphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation. This is a major new feature of the present model and, to the best of our knowledge, the ray tracing equations for the first time are explicitly employed on a global magnetospheric scale in order to self-consistently simulate spatial, temporal, and spectral evolutions of the ring current and electromagnetic ion cyclotron waves. To demonstrate the effects of EMIC wave propagation and refraction on the EMIC wave energy distributions and evolution we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. First, due to the density gradient at the plasmapause, the net wave refraction is suppressed, and He(+)-mode grows preferably at plasmapause. This result is in a total agreement with the previous ray tracing studies, and very clear observed in presented B-field spectrograms. Second, comparison the global wave distributions with the results from other ring current model [Kozyra et al., 1997] reveals that our model provides more intense and higher plasmapause organized distributions during the May, 1998 storm period. Finally, the found He(+)-mode energy distributions are not Gaussian distributions, and most important that wave energy can occupy not only the region of generation, i. e. the region of small wave normal angles, but the entire wave normal angle region and even only the region near 90 degrees. The latter is extremely crucial for energy transfer to thermal plasmaspheric electrons by resonant Landau damping, and subsequent downward heat transport and excitation of stable auroral red arcs.

Khazanov, G. V.↗
NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves in Multi-Ion Magnetosphere

The further development of a self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves (Khazanov et al., 2003) is presented In order to adequately take into account wave propagation and refraction in a multi-ion magnetosphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation. This is a major new feature of the present model and, to the best of our knowledge, the ray tracing equations for the first time are explicitly employed on a global magnetospheric scale in order to self-consistently simulate the spatial, temporal, and spectral evolution of the ring current and of electromagnetic ion cyclotron waves To demonstrate the effects of EMIC wave propagation and refraction on the wave energy distribution and evolution, we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. First, owing to the density gradient at the plasmapause, the net wave refraction is suppressed, and He+-mode grows preferably at the plasmapause. This result is in total agreement with previous ray tracing studies and is very clearly found in presented B field spectrograms. Second, comparison of global wave distributions with the results from another ring current model (Kozyra et al., 1997) reveals that this new model provides more intense and more highly plasmapause-organized wave distributions during the May 1998 storm period Finally, it is found that He(+)-mode energy distributions are not Gaussian distributions and most important that wave energy can occupy not only the region of generation, i.e., the region of small wave normal angles, but all wave normal angles, including those to near 90 . The latter is extremely crucial for energy transfer to thermal plasmaspheric electrons by resonant Landau damping and subsequent downward heat transport and excitation of stable auroral red arcs.

Khazanov, G. V.↗