Search NASA⌕ Search

SEARCH · Search NASA

Results for “generalized spherical harmonics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was developed using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure–property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of theoretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures involving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for α-uranium (α-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced experimental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of α-U during heating. In conclusion, it is shown that the developed framework can be used to simulate microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quantifying Microstructure Variability in Laser Powder Bed Fusion 316 L Stainless Steel Microstructures with Spatial Statistics

Here, we have explored data-driven methods for material microstructure quantification that improve sensitivity to microstructural changes compared to traditional approaches. The methods integrate multiple microstructural properties, including grain morphology, crystallographic orientation, and material phase information. The simpler method employs maps of the Euclidean distance transformation metric to evaluate the morphology of grain boundary networks. The more intensive approach employs generalized spherical harmonic mapping for crystallographic orientations, per-pixel phase information, and a variational auto-encoder for dimensionality reduction and results in a multidimensional clustering of by microstructure similarity. Applied to an experimental dataset of additively manufactured steel, both methods detected slight variations in samples produced under nominally identical processing conditions. Both methods were able to distinguish between samples from multiple (nominally identical) builds, while the generalized spherical harmonics-based method could additionally cluster data samples rotated at two orientations on the build plate. The improved sensitivity of the methods, demonstrated through comparison with traditional microstructure characterization techniques, offers advantages for microstructure quantification and comparisons in advanced manufacturing applications.

SS316L↗
DOE OSTI2021

Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data

Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this study, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.

42 ENGINEERING↗
DOE OSTI2024

Solidification and crystallographic texture modeling of laser powder bed fusion Ti-6Al-4V using finite difference-monte carlo method

Laser powder bed fusion (LPBF) additive manufacturing makes near-net-shaped parts with reduced material cost and time, rising as a promising technology to fabricate Ti-6Al-4V, a widely used titanium alloy in aerospace and medical industries. However, LPBF Ti-6Al-4V parts produced with 67° rotation between layers, a scan strategy commonly used to reduce microstructure and property inhomogeneity, have varying grain morphologies and weak crystallographic textures that change depending on processing parameters. Here, this study predicts LPBF Ti-6Al-4V solidification at three energy levels using a finite difference-Monte Carlo method and validates the simulations with large-area electron backscatter diffraction (EBSD) scans. The developed model accurately shows that a <001> texture forms at low energy and a <111> texture occurs at higher energies parallel to the build direction but with a lower strength than the textures observed from EBSD. A validated and well-established method of combining spatial correlation and general spherical harmonics representation of texture is developed to calculate a difference score between simulations and experiments. The quantitative comparison enables effective fine-tuning of nucleation density (N 0 ) input, which shows a nonlinear relationship with increasing energy level. Future improvements in texture prediction code and a more comprehensive study of N 0 with different energy levels will further advance the optimization of LPBF Ti-6Al-4V components. These developments contribute a novel understanding of crystallographic texture formation in LPBF Ti-6Al-4V, the development of robust model validation and calibration pipeline methodologies, and provide a platform for mechanical property prediction and process parameter optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Clustering Algorithm for AM Parts using GSH and EDT with Autoencoder

SAND2025-10103O The Clustering Algorithm for AM Parts Using GSH and (EDT With Autoencoder is a software tool. It uses a clustering algorithm for additive manufacturing (AM) parts using generalized spherical harmonics (GSH) and Euclidean distance transform (EDT) with an autoencoder to quantify material microstructure. The tool offers improved sensitivity to microstructural changes compared to traditional approaches. The tool integrates multiple microstructural properties, such as grain morphology, crystallographic orientation, and material phase information, to provide a comprehensive analysis of material microstructures. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Rodgers, Theron [Sandia National Lab. (SNL-CA), Li↗
NASA NTRS1980

Spherical harmonic analysis of a synoptic climatology generated with a global general circulation model

Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.

Christidis, Z. D.↗
DOE OSTI2022

Analysis of core asymmetries in inertial confinement fusion implosions using three-dimensional hot-spot reconstruction

Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ = 1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. Furthermore, this work establishes a platform to analyze 3D low-mode core asymmetries in ICF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Determination of the ocean circulation using Geosat altimetry

A spherical harmonic model of the sea surface topography complete to degree and order 10 and a model of the earth's geopotential field complete to degree and order 50 have been obtained in a simultaneous solution using Geosat altimeter data and tracking data from 14 different satellites. The sea surface topography model compares well with oceanographic models computed using hydrographic data and ship drift data. Currently, errors in the estimated gravity field model limit the determination of the spherical harmonic coefficients of the general ocean circulation to degrees 10 and lower, corresponding to a minimum wavelength of 4000 km. Error analysis indicates that the correlation between the geoid and the sea surface topography model is less than 0.2, indicating good separation of the geoid and the sea surface topography at wavelengths of 4000 km or longer. Estimates of the scale factor for the significant wave height (H1/3), which is used to compute the electromagnetic bias correction and the bias for the Geosat altimeter, are obtained. The estimate of the H1/3 correction is 3.6 + or - 1.5 percent, and the height bias estimate is zero.

Nerem, R. S.↗
NASA NTRS1975

Gravity fields of the solar system

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

Zendell, A.↗
NASA NTRS1990

A spherical harmonics method for asteroid pole determination

A new and general method is presented for determining pole orientations of unresolved solar system bodies that exhibit brightness variation with rotation. The accuracy of the method is limited only by the number of available apparitions, which imposes the degree where the Legendre expansion must be truncated. It is shown that power spectra of lightcurves provide enough information to extract pole coordinates from the data, independent of body shape and albedo variegation. The method has been tested using several computer-generated synthetic light-curves, and the accuracy is found to be about 5 deg in both the longitude and latitude of the pole, which is considerably better than that obtained from the standard triaxial ellipsoid model. Finally, the new spherical harmonics method has been applied to six well-observed asteroids: 16 Psyche, 22 Kalliope, 39 Laetitia, 44 Nysa, 45 Eugenia, and 349 Dembowska.

Lumme, K.↗
NASA NTRS1991

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.

Ritzwoller, Michael H.↗
NASA NTRS1981

Spherical harmonic analysis of a model-generated climatology

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

Christidis, Z. D.↗
DOE OSTI2023

Quantifying molecular deformation in polymer melts by a generalized Zimm plot approach

The Zimm plot has been widely used to characterize the molecular dimensions of polymers from small-angle scattering experiments, where the reciprocal intensity is analyzed as a function of the square of the magnitude of the scattering wavevector Q. Here, this work explores the benefits of analyzing the reciprocal scattering intensity from deformed polymers, extending the original Zimm plot to anisotropic materials. In the small-angle limit, a tensorial extension of the Guinier law is found for the gyration tensor and the reciprocal single-chain structure factor. In the high-Q limit, application of the spherical harmonic expansion technique to the reciprocal structure factor permits direct model-independent analysis of spatially dependent molecular deformation of polymers. Additionally, the contributions from high-order spherical harmonics become insignificant in the reciprocal-intensity representation. The proposed generalized Zimm plot approach is demonstrated computationally with the affine deformation model and the Rouse model, and experimentally with small-angle neutron scattering measurements of deformed polystyrene melts.

36 MATERIALS SCIENCE↗
NASA NTRS2018

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of ~45 deg between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

Connerney, J. E. P.↗
NASA NTRS1989

Plasma pressure in the environment of Jupiter, inferred from Voyager 1 magnetometer observations

A model combining the internal magnetic field with a self-consistent model of the Jovian magnetodisc was fitted to the Voyager 1 Jovian magnetic field data by means of a generalized inverse technique. The model parameters included the internal field spherical harmonic coefficients as well as with parameters describing the plasma distribution in the magnetosphere. Assuming that the pressure in the middle and outer magnetosphere is related to the unit flux tube volume V through PV exp gamma = const, the model fit yielded a value of 0.88 for gamma. If the hot (30 keV) plasma is transported adiabatically inward under the interchange instability triggered by centrifugal force of the heavy torus ions, losses are not sufficient to account for such a low value of gamma beyond L = 10. Closer to the planet, as the outer edge of the Io plasma torus is approached, PV exp gamma is found to decrease inward, as expected from the particle measurements, which identified an inner boundary of the particle fluxes in that region. With the present stage of the development of magnetodisc models, secular variations of the internal field still remain difficult to estimate.

Caudal, G.↗
NASA NTRS1992

The magnetic field of Neptune

A model is given of the planetary magnetic field of Neptune based on a spherical harmonic analysis of the observations obtained by the Voyager 2. Generalized inverse techniques are used to partially solve a severely underdetermined inverse problem, and the resulting model is nonunique since the observations are limited in spatial distribution. Dipole, quadrupole, and octupole coefficients are estimated independently of other terms, and the parameters are shown to be well constrained by the measurement data. The large-scale features of the magnetic field including dipole tilt, offset, and harmonic content are found to characterize a magnetic field that is similar to that of Uranus. The traits of Neptune's magnetic field are theorized to relate to the 'ice' interior of the planet, and the dynamo-field generation reflects this poorly conducting planet.

Connerney, J. E. P.↗
NASA NTRS1994

Limits on coronal reflection using high-frequency solar oscillations

Acoustic waves in the Sun with frequencies above about 5.3 mHz can propagate in the chromosphere. We examine imaged solar intensity data for evidence of reflection of these waves in the upper chromosphere, where the temperature increases by a large factor over a short distance. Our method is to compare the observed and theoretically derived frequency spacings between peaks in the power spectrum. We find that our theoretical frequencies provide the best fit to the data when the reflection in the upper atmosphere is eliminated. In particular, the model of Kumar (1993b), which includes the source depth, and radiative damping, in the calculation of power spectra but ignores chromospheric reflection, gives peak frequencies that are in good agreement with the observations. For acoustic waves of frequency greater than 6 mHz we put an upper limit to the reflectivity of chromosphere and corona, using our method, of about 10%. At a given spherical harmonic degree, the frequency spacing between peaks in the data generally decreases with increasing frequency, because the lower turning point of the waves is moving inward. However, between 5 and 5.5 mHz the frequency spacing increases slightly. This feature is probably associated with the acoustic cutoff frequency in the solar atmosphere, i.e., it indicates a transition from trapped waves to propagating waves. We are able to reproduce the observed behavior by a crude modeling of the solar atmosphere. Further study of these peaks should provide an independent way of exploring the mean structure of the solar atmosphere, particularly around the temperature minimum region.

Kumar, P.↗
NASA NTRS2013

NASA Tech Briefs, Februrary 2013

Topics covered include: Measurements of Ultra-Stable Oscillator (USO) Allan Deviations in Space; Gaseous Nitrogen Orifice Mass Flow Calculator; Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards; Rover Low Gain Antenna Qualification for Deep Space Thermal Environments; Automated, Ultra-Sterile Solid Sample Handling and Analysis on a Chip; Measuring and Estimating Normalized Contrast in Infrared Flash Thermography; Spectrally and Radiometrically Stable, Wideband, Onboard Calibration Source; High-Reliability Waveguide Vacuum/Pressure Window; Methods of Fabricating Scintillators With Radioisotopes for Beta Battery Applications; Magnetic Shield for Adiabatic Demagnetization Refrigerators (ADR); CMOS-Compatible SOI MESFETS for Radiation-Hardened DC-to-DC Converters; Silicon Heat Pipe Array; Adaptive Phase Delay Generator; High-Temperature, Lightweight, Self-Healing Ceramic Composites for Aircraft Engine Applications; Treatment to Control Adhesion of Silicone-Based Elastomers; High-Temperature Adhesives for Thermally Stable Aero-Assist Technologies; Rockballer Sample Acquisition Tool; Rock Gripper for Sampling, Mobility, Anchoring, and Manipulation; Advanced Magnetic Materials Methods and Numerical Models for Fluidization in Microgravity and Hypogravity; Data Transfer for Multiple Sensor Networks Over a Broad Temperature Range; Using Combustion Synthesis to Reinforce Berms and Other Regolith Structures; Visible-Infrared Hyperspectral Image Projector; Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor Change_Detection.m; AGATE: Adversarial Game Analysis for Tactical Evaluation; Ionospheric Simulation System for Satellite Observations and Global Assimilative; Modeling Experiments (ISOGAME); An Extensible, User- Modifiable Framework for Planning Activities; Mission Operations Center (MOC) - Precipitation Processing System (PPS) Interface Software System (MPISS); Automated 3D Damaged Cavity Model Builder for Lower Surface Acreage Tile on Orbiter; Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays; RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers; Powered Descent Guidance with General Thrust-Pointing Constraints; X-Ray Detection and Processing Models for Spacecraft Navigation and Timing; and Extreme Ionizing-Radiation-Resistant Bacterium

Source record↗