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Results for “Radial basis function”

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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64 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Search for Correlations between Turbulence and Star Formation in LITTLE THINGS Dwarf Irregular Galaxies

Turbulence has the potential for creating gas density enhancements that initiate cloud and star formation (SF), and it can be generated locally by SF. To study the connection between turbulence and SF, we looked for relationships between SF traced by FUV images, and gas turbulence traced by kinetic energy density (KED) and velocity dispersion (v {sub disp}) in the LITTLE THINGS sample of nearby dIrr galaxies. We performed 2D cross-correlations between FUV and KED images, measured cross-correlations in annuli to produce correlation coefficients as a function of radius, and determined the cumulative distribution function of the cross-correlation value. We also plotted on a pixel-by-pixel basis the locally excess KED, v {sub disp}, and H i mass surface density, Σ{sub HI}, as determined from the respective values with the radial profiles subtracted, versus the excess SF rate density Σ{sub SFR}, for all regions with positive excess Σ{sub SFR}. We found that Σ{sub SFR} and KED are poorly correlated. The excess KED associated with SF implies a ∼0.5% efficiency for supernova energy to pump local H i turbulence on the scale of the resolution here, which is a factor of ∼2 too small for all of the turbulence on a galactic scale. The excess v {sub disp} in SF regions is also small, only ∼0.37 km s{sup −1}. The local excess in Σ{sub HI} corresponding to an excess in Σ{sub SFR} is consistent with a H i consumption time of ∼1.6 Gyr in the inner parts of the galaxies. The similarity between this timescale and the consumption time for CO implies that CO-dark molecular gas has comparable mass to H i in the inner disks.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. Here, to address the slow convergence of the $κ=±1$ states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10 -8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Comparative analysis of atmospheric parameters from high-resolution spectroscopic sky surveys: APOGEE, GALAH, Gaia -ESO

SDSS-IV APOGEE-2, GALAH, and Gaia-ESO are high-resolution, ground-based, multi-object spectroscopic surveys providing fundamental stellar atmospheric parameters and multiple elemental abundance ratios for hundreds of thousands of stars of the Milky Way. Data from these and other surveys contribute to investigations of the history and evolution of the Galaxy. We undertake a comparison between the most recent data releases of these surveys to investigate the accuracy and precision of derived parameters by placing the abundances on an absolute scale. We also discuss the correlations in parameter and abundance differences as a function of main parameters. Uncovering the variants provides a basis to continue the efforts of future sky surveys. Quality samples from the APOGEE-GALAH (15 537 stars), APOGEE-GES (804 stars), and GALAH-GES (441 stars) overlapping catalogs were collected. We investigated the mean variants between the surveys, and linear trends were also investigated. We compared the slope of correlations and mean differences with the reported uncertainties. The average and scatter of v rad , T eff , log g, [M/H], and v micro , along with numerous species of elemental abundances in the combined catalogs, show that in general there is a good agreement between the surveys. We find large radial velocity scatters ranging from 1.3 km s -1 to 4.4 km s -1 when comparing the three surveys. We observe some weak trends (e.g., in ΔT eff vs. Δlog g for the APOGEE-GES stars) and a clear correlation in the v micro - Δv micro planes in the APOGEE-GALAH common sample. For [α/H], [Ti/H] (APOGEE-GALAH giants), and [Al/H] (APOGEE-GALAH dwarfs) potential strong correlations are discovered as a function of the differences in the main atmospheric parameters, and we also find weak trends for other elements. In general we find good agreement between the three surveys within their respective uncertainties. However, there are certain regimes in which strong variants exist, which we discuss. There are still offsets larger than 0.1 dex in the absolute abundance scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

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↗
DOE OSTI2020

Discriminating Accretion States via Rotational Symmetry in Simulated Polarimetric Images of M87

In 2017 April, the Event Horizon Telescope observed the shadow of the supermassive black hole at the core of the elliptical galaxy Messier 87. While the original image was constructed from measurements of the total intensity, full polarimetric data were also collected, and linear polarimetric images are expected in the near future. We propose a modal image decomposition of the linear polarization field into basis functions with varying azimuthal dependence of the electric vector position angle. We apply this decomposition to images of ray traced general relativistic magnetohydrodynamics simulations of the Messier 87 accretion disk. Furthermore, for simulated images that are physically consistent with previous observations, the magnitude of the coefficient associated with rotational symmetry, β2, is a useful discriminator between accretion states. We find that at 20 μas resolution, $| {\beta }_{2}| $ is greater than 0.2 only for models of disks with horizon-scale magnetic pressures large enough to disrupt steady accretion. We also find that images with a more radially directed electric vector position angle correspond to models with higher black hole spin. Our analysis demonstrates the utility of the proposed decomposition as a diagnostic framework to improve constraints on theoretical models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Spectrum and structure of octet and decuplet baryons and their positive-parity excitations

A continuum approach to the three-valence-quark bound-state problem in quantum field theory, employing parametrizations of the necessary kernel elements, is used to compute the spectrum and Poincare-covariant wave functions for all flavor- SU (3) octet and decuplet baryons and their first positive-parity excitations. Such analyses predict the existence of nonpointlike, dynamical quark-quark (diquark) correlations within all baryons; and a uniformly sound description of the systems studied is obtained by retaining flavor-antitriplet-scalar and flavor-sextet-pseudovector diquarks. Thus constituted, the rest-frame wave function of every system studied is primarily S wave in character; and the fast positive-parity excitation of each octet or decuplet baryon exhibits the characteristics of a radial excitation. Importantly, every ground-state octet and decuplet baryon possesses a radial excitation. Hence, the analysis predicts the existence and masses of positive-parity excitations of the Ξ, Ξ*, and Ω baryons, states which have not yet been empirically identified. This body of analysis suggests that the expression of emergent mass generation is the same in all u , d , and s baryons and, notably, that dynamical quark-quark correlations play an essential role in the structure of each one. Furthermore, it also provides the basis for developing an array of predictions that can be tested in new generation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Mechanical Properties of Functionally Graded Concrete Lining for Deep Underground Structures

With the mining depth of coal resources increasing, the thickness of traditional lining for deep mines becomes large. The bearing capacity of the outer lining cannot be fully utilized, so a new type of functionally graded lining structure (FGL) with radial Young’s modulus varying in gradient is proposed. In this study, through theoretical analysis and numerical simulation, the mechanical properties of the functionally graded lining were studied, including the characteristics of the elastic working state and the ultimate bearing state. The influences of the structural parameters of the functionally graded lining, including the inner radius, the thickness, Young’s modulus, the compressive strength of the concrete, Poisson’s ratio, and the number of layers on the mechanical properties were analyzed. The calculation formula of the ultimate bearing capacity of the lining and the calculation formula of the maximum tangential strain at the time of lining failure were put forward. The accuracy of the formula was verified by comparing with the numerical simulation results. The research results provide the basis for the construction of the design theory of a functionally graded lining structure and have great engineering significance for the construction of the kilometer-deep mines in the future.

Li, De-Chun↗
DOE OSTI2023

Blockchain for Fault-Tolerant Grid Operations

Radial topology and vast geographic coverage make distribution systems prone to widespread power outages upon the failure of a single (or multiple) upstream component. Fault-handling algorithms depend heavily on correct estimations of the system’s state to effectively isolate the affected area and reduce the number of affected customers while maintaining operational safety. The work described here leverages the core features of distributed, consensus-based decision-making processes and the immutability of blockchain, and demonstrates their value in improving fault-tolerant grid operations. In this work, blockchain was used to create a trusted data-sharing platform that enables independent actors to reconstruct the system state; this enables distributed resources to make intelligent decisions with limited knowledge. Although the process requires data sharing, its algorithms have been designed to limit the amount of private information that is exchanged, which helps preserve business-sensitive data and maintain customer privacy. In addition, by reducing the information that must be shared, the communication requirements are also reduced; (however, an in-depth analysis of the communication requirements is beyond the scope of this project). The proposed use cases are intended to represent a foundational basis for third parties to develop functional solutions that can eventually be deployed in the field. To further provide guidance, the envisioned use cases have incorporated design requirements that consider the blockchain characteristics and a need to limit information from surrounding resources, which preserve the assumption and the possibility that such resources could belong to different entities. This report presents a detailed design of the three use cases with the tools needed to enable the analysis being tested. The implemented gross error detection method can detect mismatches when the error exceeds 3.8 times the sensor’s rated accuracy. Detection of the circuit breaker state successfully identified the correct states across all simulation tests. A distribution-system power-flow solution in the simulator OpenDSS generally possesses a convergency tolerance of 0.01% on the voltage magnitude. The evaluation of possible reconnection using voltage magnitude—preserving the data ownership—has a voltage magnitude difference smaller than 0.001% from the OpenDSS result. The results preserving data ownership have a difference within the expected power flow tolerance with full knowledge of the system, which surpasses expectations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Machine Learning Driven Contouring of High-Frequency Four-Dimensional Cardiac Ultrasound Data

Automatic boundary detection of 4D ultrasound (4DUS) cardiac data is a promising yet challenging application at the intersection of machine learning and medicine. Using recently developed murine 4DUS cardiac imaging data, we demonstrate here a set of three machine learning models that predict left ventricular wall kinematics along both the endo- and epi-cardial boundaries. Each model is fundamentally built on three key features: (1) the projection of raw US data to a lower dimensional subspace, (2) a smoothing spline basis across time, and (3) a strategic parameterization of the left ventricular boundaries. Model 1 is constructed such that boundary predictions are based on individual short-axis images, regardless of their relative position in the ventricle. Model 2 simultaneously incorporates parallel short-axis image data into their predictions. Model 3 builds on the multi-slice approach of model 2, but assists predictions with a single ground-truth position at end-diastole. To assess the performance of each model, Monte Carlo cross validation was used to assess the performance of each model on unseen data. For predicting the radial distance of the endocardium, models 1, 2, and 3 yielded average R2 values of 0.41, 0.49, and 0.71, respectively. Monte Carlo simulations of the endocardial wall showed significantly closer predictions when using model 2 versus model 1 at a rate of 48.67%, and using model 3 versus model 2 at a rate of 83.50%. These finding suggest that a machine learning approach where multi-slice data are simultaneously used as input and predictions are aided by a single user input yields the most robust performance. Subsequently, we explore the how metrics of cardiac kinematics compare between ground-truth contours and predicted boundaries. We observed negligible deviations from ground-truth when using predicted boundaries alone, except in the case of early diastolic strain rate, providing confidence for the use of such machine learning models for rapid and reliable assessments of murine cardiac function. To our knowledge, this is the first application of machine learning to murine left ventricular 4DUS data. Future work will be needed to strengthen both model performance and applicability to different cardiac disease models.

4D ultrasound↗