Search NASA⌕ Search

SEARCH · Search NASA

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.

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

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

encore : an O ( N g2) estimator for galaxy N -point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

An exact inversion method for extracting orientation ordering by small-angle scattering

Here, we outline a nonparametric inversion strategy for determining the orientation distribution function (ODF) of sheared interacting rods using small-angle scattering techniques. With the presence of direct inter-rod interaction and fluid mechanical forces, the scattering spectra are no longer characterized by the azimuthal symmetry in the coordinates defined by the principal directions of simple shear conditions, which severely compounds the reconstruction of ODFs based on currently available methods developed for dilute systems. Using a real spherical harmonic expansion scheme, the real-space ODFs are uniquely determined from the anisotropic scattering spectra and their numerical accuracy is verified computationally. Our method can be generalized to extract ODFs of uniaxially anisotropic objects under different flow conditions in a properly transformed reference frame with suitable basis vectors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from the NRHybSur3dq8 surrogate, which provides spherical-harmonic modes up to $\ell$ ≤ 4 (excluding (4, 0) and (4,±1), and including (5, 5)) for mass ratios q ≤ 8, dimensionless spin components s$^{z}_{1,2}$ ϵ[–0.8, 0.8], and inclination angles θ ϵ [0, π]. Waveforms are supplied on the interval t ϵ [–5000M, –100 M) and the model autoregressively generates the plus and cross polarizations (h + , h x ) on t ϵ [–100 M, 130M]. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required ~15 h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of 840,000 samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth.

black-hole merger↗

Charged particle motion in spherically symmetric distributions of magnetic monopoles

The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single monopole, the solution was given long ago by Poincaré. In the case of a uniform distribution of monopoles, the solution can be expressed in terms of parabolic cylinder functions (essentially the eigenfunctions of an inverted harmonic oscillator). Further, this solution is relevant to recent studies of nonassociative star products, symplectic lifts of twisted Poisson structures, and fluids and plasmas of electric and magnetic charges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗