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Results for “spherical harmonic transform”

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
DOE OSTI2023

Scalable self attraction and loading calculations for unstructured ocean tide models

Self attraction and earth-loading effects are important for accurately modeling global tides. A common approach of handling this forcing is to expand mass anomalies into spherical harmonics, which are scaled by load Love numbers to account for elastic earth deformation. We investigate two different approaches to perform these calculations for ocean models that employ unstructured meshes and distributed memory parallelization. The first approach leverages a highly efficient spherical harmonics library, but requires all-to-one and one-to-all communications and interpolation operations between the unstructured and a structured mesh. This approach is compared to a parallel algorithm that computes the spherical harmonic transformations directly on the unstructured mesh with an all-reduce communication. Here, our results show that although the unstructured mesh calculations are more expensive, the scalability of the unstructured mesh approach allows for more efficient spherical harmonics transforms for high-resolution meshes and large processor counts. This methodology enables the efficient inclusion of tidal dynamics large-scale Earth system model simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

GPU-accelerated multitiered iterative phasing algorithm for fluctuation X-ray scattering

The multitiered iterative phasing (MTIP) algorithm is used to determine the biological structures of macromolecules from fluctuation scattering data. It is an iterative algorithm that reconstructs the electron density of the sample by matching the computed fluctuation X-ray scattering data to the external observations, and by simultaneously enforcing constraints in real and Fourier space. This paper presents the first ever MTIP algorithm acceleration efforts on contemporary graphics processing units (GPUs). The Compute Unified Device Architecture (CUDA) programming model is used to accelerate the MTIP algorithm on NVIDIA GPUs. The computational performance of the CUDA-based MTIP algorithm implementation outperforms the CPU-based version by an order of magnitude. Furthermore, the Heterogeneous-Compute Interface for Portability (HIP) runtime APIs are used to demonstrate portability by accelerating the MTIP algorithm across NVIDIA and AMD GPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Effects of Strain and Strain Rate on Dynamic Grain Growth and Subgrain Evolution During Plastic Deformation of an Interstitial-Free Steel at 850 ° C

Here, the effects of strain and strain rate on dynamic grain growth (DGG) and subgrain evolution are reported for an interstitial-free steel deformed at 850 ° C. Microstructures produced during tension tests at true-strain rates of 10 -4 and to 10 -3 s -1 true strains ranging from 0.02 to 0.2 were preserved following deformation. These were characterized using electron backscatter diffraction (EBSD), including the application of spherical harmonic transform indexing to produce high-angular-resolution EBSD (HR-EBSD) data. HR-EBSD data resolved the small misorientation angles of subgrain boundaries while imaging much larger data fields than possible with previously available techniques. The resulting data confirmed that steady-state flow stress is inversely proportional to the average subgrain size and that subgrain boundary misorientation angle increases with strain. The following new observations are reported. The rate of DGG increased with respect to time but decreased with respect to strain as strain rate increased. This behavior is rationalized through a simple model using separate rate parameters for the effects of time and strain. Subgrain size was not constant during steady-state deformation, but decreased slowly with increasing strain. Subgrain size distributions and subgrain boundary misorientation angle distributions were measured, and both remained approximately log-normal during steady-state deformation. Subgrain evolution demonstrated no dependence on parent grain size, crystallographic orientation, or Taylor factor. These new data suggest that steady-state flow stress is more likely controlled by the dislocation density internal to subgrains than by the spacing between subgrain boundaries.

dynamic grain growth↗
DOE OSTI2022

Global Barotropic Tide Modeling Using Inline Self‐Attraction and Loading in MPAS‐Ocean

Abstract We examine ocean tides in the barotropic version of the Model for Prediction Across Scales (MPAS‐Ocean), the ocean component of the Department of Energy Earth system model. We focus on four factors that affect tidal accuracy: self‐attraction and loading (SAL), model resolution, details of the underlying bathymetry, and parameterized topographic wave drag. The SAL term accounts for the tidal loading of Earth's crust and the self‐gravitation of the ocean and the load‐deformed Earth. A common method for calculating SAL is to decompose mass anomalies into their spherical harmonic constituents. Here, we compare a scalar SAL approximation versus an inline SAL using a fast spherical harmonic transform package. Wave drag accounts for energy lost by breaking internal tides that are produced by barotropic tidal flow over topographic features. We compare a series of successively finer quasi‐uniform resolution meshes (62.9, 31.5, 15.7, and 7.87 km) to a variable resolution (45 to 5 km) configuration. We ran MPAS‐Ocean in a single‐layer barotropic mode forced by five tidal constituents. The 45 to 5 km variable resolution mesh obtained the best total root‐mean‐square error (5.4 cm) for the deep ocean ( 1,000 m) tide compared to TPXO8 and ran twice as fast as the quasi‐uniform 8 km mesh, which had an error of 5.8 cm. This error is comparable to those found in other forward (non‐assimilative) ocean tide models. In future work, we plan to use MPAS‐Ocean to study tidal interactions with other Earth system components, and the tidal response to climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

BEYONDPLANCK VIII. Efficient sidelobe convolution and corrections through spin harmonics

We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for BEYONDPLANCK, the first end-to-end Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous Planck LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3–10, depending on the frequency bandlimits, l max and m max . The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for Planck LFI are in good agreement with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Imaging and Segmenting Grains and Subgrains Using Backscattered Electron Techniques

We present two new methods of processing data from backscattered electron signals in a scanning electron microscope to image grains and subgrains. The first combines data from multiple backscattered electron images acquired at different specimen geometries to (1) better reveal grain boundaries in recrystallized microstructures and (2) distinguish between recrystallized and unrecrystallized regions in partially recrystallized microstructures. The second utilizes spherical harmonic transform indexing of electron backscatter diffraction patterns to produce high angular resolution orientation data that enable the characterization of subgrains. Subgrains are produced during high-temperature plastic deformation and have boundary misorientation angles ranging from a few degrees down to a few hundredths of a degree. Here, we also present an algorithm to automatically segment grains from combined backscattered electron image data or grains and subgrains from high angular resolution electron backscatter diffraction data. Together, these new techniques enable rapid measurements of individual grains and subgrains from large populations.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Tests of a simple data merging algorithm for the GONG project

The GONG (Global Oscillation Network Group) project proposes to reduce the impact of diurnal variations on helioseismic measurements by making long-term observations of solar images from six sites placed around the globe. The sun will be observed nearly constantly for three years, resulting in the acquisition of l+ terabyte of image data. To use the solar network to maximum advantage, the images from the sites must be combined into a single time series to determine mode frequencies, amplitudes, and line widths. Initial versions of combined, i.e., merged, time series were made using a simple weighted average of data from different sites taken simultaneously. In order to accurately assess the impact of the data merge on the helioseismic measurements, a set of artificial solar disk images was made using a standard solar model and containing a well known set of oscillation modes and frequencies. This undegraded data set and data products computed from it were used to judge the relative merits of various data merging schemes. The artificial solar disk images were subjected to various instrumental and atmospheric degradations, dependent on site and time, in order to create a set of images simulating those likely to be taken at the site. The degraded artificial solar disk images for the six observing sites were combined in various ways to form merged time series of images and mode coefficients. Various forms of a weighted average were used, including an equally-weighted average, an average with weights dependent upon air mass and averages with weights dependent on various quality assurance parameters. Both the undegraded solar disk image time series and several time series made up of various combinations of the degraded solar disk images from the six sites were subjected to standard helioseismic measurement processing. This processing consisted of coordinate remapping, detrending, spherical harmonic transformation, computation of power series for the oscillation mode coefficients, and mode frequency identification. Visual and statistical evaluation of the merged data sets themselves and differences between the merged and undegraded data set shows good agreement between the two data sets. Some slight differences in image scale and registration appear between the undegraded data set and the various merged data sets. In the set of power series made from the mode coefficients of the merged data sets, some power leakage is observed into the background and into slightly lower l-value modes, especially at higher l-value mode frequencies. The results of the comparison of time series and mode oscillation frequencies of the undegraded data with those of the data merged using weighted averages indicate that, at least for p-mode solar oscillations, a weighted average of either the detrended remapped images or the mode coefficients gives good determination of the mode frequencies and adequate-to-good determination of the amplitudes and widths of the mode frequency lines. This conclusion is most advantageous to the analysis of the massive amounts of data to be received by the GONG network.

Williams, W. E.↗
NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗
NASA NTRS2000

Retrieving the Balanced Winds on the Globe as a Generalized Inverse Problem

A generalized inverse technique is applied to retrieve two types of balanced winds that characterize the large-scale dynamics of the atmosphere: rotational winds based upon the linear balance equation, and divergent winds based upon the vorticity budget equation. Both balance equations are singular at or near the equator. The balance equations are transformed in spherical harmonic function space to an under-determined system, for which the scale-weighed least-squares solution consists of a sum of principal and singular components. The principal components represent the response to the source function for the regular eigenmodes, while the singular components are determined by the projection of an independent measurement on the singular eigenmodes. The method was tested with the NCEP/NCAR reanalysis data in which a quasi-balance condition exists. A realistic balanced wind field is retrievable when the singular components are computed based upon the reanalyzed wind data.

Lu, Huei-Iin↗
NASA NTRS1972

Sampling functions for geophysics

A set of spherical sampling functions is defined such that they are related to spherical-harmonic functions in the same way that the sampling functions of information theory are related to sine and cosine functions. An orderly distribution of (N + 1) squared sampling points on a sphere is given, for which the (N + 1) squared spherical sampling functions span the same linear manifold as do the spherical-harmonic functions through degree N. The transformations between the spherical sampling functions and the spherical-harmonic functions are given by recurrence relations. The spherical sampling functions of two arguments are extended to three arguments and to nonspherical reference surfaces. Typical applications of this formalism to geophysical topics are sketched.

Giacaglia, G. E. O.↗
DOE OSTI2026

Short and medium range structure in elastic deformation of metallic and covalent glasses

Here, we present a concise methodology to analyze structural response to the applied stress in amorphous solids, including metallic glasses (MG), glassy selenium, silica and polycarbonate, using high energy x-ray diffraction and atomic pair distribution function (PDF) analysis. To assess the structural anisotropy induced by applied axial stress, diffraction data were expanded into spherical harmonics. Using Bessel transformation, components of the structure function were converted into isotropic and anisotropic PDFs. The PDFs were compared to the expected model behavior for ideal elastic deformation to separate homogeneous affine strain from local non-affine strains. In metallic glass the range of non-affine deformation is limited to the nearest neighbor shell, suggesting local strain relaxation under stress that occurs even in the elastic regime. Beyond the second atomic shell strain is uniform. However, in glassy silica, polycarbonate and selenium strong local bonding inhibits local displacements and strain in short range order is accommodated by rotation of local units. Interestingly, beyond a molecular unit, deformation in covalent systems is similar to MG, and response of the medium range order scales with the macroscopic stress.

glassy structure↗
DOE OSTI2024

Filamentary Dust Polarization and the Morphology of Neutral Hydrogen Structures

Filamentary structures in neutral hydrogen (H$\tiny{I}$) emission are well aligned with the interstellar magnetic field, so H$\tiny{I}$ emission morphology can be used to construct templates that strongly correlate with measurements of polarized thermal dust emission. We explore how the quantification of filament morphology affects this correlation. We introduce a new implementation of the Rolling Hough Transform (RHT) using spherical harmonic convolutions, which enables efficient quantification of filamentary structure on the sphere. We use this Spherical RHT algorithm along with a Hessian-based method to construct H$\tiny{I}$-based polarization templates. We discuss improvements to each algorithm relative to similar implementations in the literature and compare their outputs. By exploring the parameter space of filament morphologies with the Spherical RHT, we find that the most informative H$\tiny{I}$ structures for modeling the magnetic field structure are the thinnest resolved filaments. For this reason, we find a ~10% enhancement in the B-mode correlation with polarized dust emission with higher-resolution H$\tiny{I}$ observations. We demonstrate that certain interstellar morphologies can produce parity-violating signatures, i.e., nonzero TB and EB, even under the assumption that filaments are locally aligned with the magnetic field. Finally, we demonstrate that B modes from interstellar dust filaments are mostly affected by the topology of the filaments with respect to one another and their relative polarized intensities, whereas E modes are mostly sensitive to the shapes of individual filaments.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2023

The Impact of Dimensionality Reduction of Ion Counts Distributions on Preserving Moments, With Applications to Data Compression

The field of space physics has a long history of utilizing dimensionality reduction methods to distill data, including but not limited to spherical harmonics, the Fourier Transform, and the wavelet transform. Here, we present a technique for performing dimensionality reduction on ion counts distributions from the Multiscale Mission/Fast Plasma Investigation (MMS/FPI) instrument using a data-adaptive method powered by neural networks. This has applications to both feeding low-dimensional parameterizations of the counts distributions into other machine learning algorithms, and the problem of data compression to reduce transmission volume for space missions. The algorithm presented here is lossy, and in this work, we present the technique of validating the reconstruction performance with calculated plasma moments under the argument that preserving the moments also preserves fluid-level physics, and in turn a degree of scientific validity. The method presented here is an improvement over other lossy compressions in loss-tolerant scenarios like the Multiscale Mission/Fast Plasma Investigation Fast Survey or in non-research space weather applications.

D. da Silva↗
NASA NTRS1987

Equipotential transformation of multipole systems to dipole systems

The vector sum of fields produced by a set of magnetic dipoles with different magnetic moments that are both tilted from the planetary spin axis and offset from the planetary center by different amounts can be used to completely represent a planetary magnetic field in the conventional form of spherical harmonic expansion. The scalar equipotential transformation analytically results in 24 equations that may subsequently be solved for the 24 adjustable parameters in dipole systems with the predetermined main dipole. Attention is given to this method's application to the Jovian magnetic field.

Wang, W. X.↗