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NASA NTRS1989

Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.

Osswald, G. A.↗

NASA NTRS1994

Development of nonintrusive, scatter-independent techniques for measurement of liquid density inside dense sprays

A nonintrusive optical technique for measuring the liquid density in sprays used to simulate LOX injector flows is under development. This manuscript is a report on work toward that development which is currently in progress. The technique is a scatter-independent, absorption-based approach which depends on the numerical inversion of a collection of absorption profiles. For the case in which visible radiation passes through liquid-gas interfaces so numerous in sprays, substantial reductions and alterations in the signal result from scattering even in the absence of absorption. To avoid these problems, X-Rays will be used as the absorbed radiation. The experimental process is simulated by integrating the absorption spectrum for a known distribution, adding instrument noise to this 'measurement', creating a projection from the 'measurement', filtering the projection, inverting the projection, and comparing the results with the original prescribed distribution.

Hartfield, Roy↗

DOE OSTI2021

Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Here, we present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering 130× speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave + local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of ~10 000 electrons. Finally, we observe good parallel scalability of our implementation with 92% efficiency at 22× speedup for a system with 620 electrons

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Temperature of a tungsten spallation target

We discuss the heat load inside a neutron spallation target made of tungsten hit by an 800 MeV proton beam. This problem is important for the Neutron Target project, where a spallation target will be surrounded by an extended graphite or beryllium cube to create a neutron target. The idea of a free-neutron target enables the measurement of neutron-induced reactions in inverse kinematics. This idea is part of the LANSCE strategy to stay a worldwide leader for neutron-induced research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1973

Application of Papkovich-Neuber potentials to a crack problem.

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered in this paper. A closed form solution using four harmonic functions is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically.

Kassir, M. K.↗

NASA NTRS1981

Investigations of medium wavelength magnetic anomalies in the eastern Pacific using MAGSAT data

The suitability of using magnetic field measurements obtained by MAGSAT is discussed with regard to resolving the medium wavelength anomaly problem. A procedure for removing the external field component from the measured field is outlined. Various methods of determining crustal magnetizations are examined in light of satellite orbital parameters resulting in the selection of the equivalent source technique for evaluating scalar measurements. A matrix inversion of the vector components is suggested as a method for arriving at a scalar potential representation of the field.

Harrison, C. G. A.↗

NASA NTRS1994

NCAR CCM2 simulation of the modern Antarctic climate

The National Center for Atmospheric Research (NCAR) community climate model version 2 (CCM2) simulation of the circumpolar trough, surface air temperature, the polar vortex, cloudiness, winds, and atmospheric moisture and energy budgets are examined to validate the model's representation of the present-day Antarctic climate. The results show that the CCM2 can well simulate many important climate features over Antarctica, such as the location and intensity of the circumpolar trough, the coreless winter over the plateau, the intensity and horizontal distribution of the surface inversion, the speed and streamline pattern of the katabatic winds, the double jet stream feature over the southern Indian and Pacific oceans, and the arid climate over the continent. However, there are also some serious errors in the model. Some are due to old problems but some are caused by the new parameterizations in the model. The model errors over high southern latitudes can be summarized as follows: The circumpolar trough, the polar vertex, and the westerlies in midlatitudes are too strong; the semiannual cycle of the circumpolar trough is distorted compared to the observations; the low centers of the circumpolar trough and the troughs in the middle and upper troposphere are shifted eastward by 15 deg - 40 deg longitude; the surface temperatures are too cold over the plateau in summer and over the coastline in winter; the polar tropopause continues to have a cold bias; and the cloudiness is too high over the continent. These biases are induced by two major factors: (1) the cloud optical properties in tropical and middle latitudes, which cause the eastward shift of troughs and surface low centers and the error in the semiannual cycle, and (2) the cold bias of the surface air temperature, which is attributed to the oversimulation of cloudiness over the continent, especially during summer, and the uniform 2-m-thick sea ice. The constant thickness of sea ice suppresses the energy flux from the ocean to the atmosphere and hence reduces the air temperature near the coast during winter. Finally, although the simulated Antarctic climate still suffers these biases, the overall performance of the CCM2 is much better than that of the CCM1-T42. Therefore the CCM2 is good enough to be used for climate change studies, especially over Antarctica.

Tzeng, Ren-Yow↗

NASA NTRS1996

Optimum Transonic Airfoils Based on the Euler Equations

We solve the problem of determining airfoils that approximate, in a least square sense, given surface pressure distributions in transonic flight regimes. The flow is modeled by means of the Euler equations and the solution procedure is an adjoint- based minimization algorithm that makes use of the inverse Theodorsen transform in order to parameterize the airfoil. Fast convergence to the optimal solution is obtained by means of the pseudo-time method. Results are obtained using three different pressure distributions for several free stream conditions. The airfoils obtained have given a trailing edge angle.

Iollo, Angelo↗

DOE OSTI2025

Prediction of neutron production and energy spectrum by the inverse kinematic reaction between an incident 7 Li 3+ beam and a proton target in PHITS

A neutron source using the inverse kinematic reaction between lithium and proton, p( 7 Li, n) 7 Be, achieves forward-directed neutrons, potentially enhancing neutron yield in the forward direction. Despite the advantage, no evaluated-cross-section data for this reaction can be used in Monte Carlo simulation codes, such as PHITS. To solve this problem, this study aims to evaluate the applicability of the user-defined cross-section data, Frag data, for p ( 7 Li, n) 7 Be in PHITS. The simulations reproduced collisions between 7 Li 3+ ions and polypropylene targets. The Frag data was edited based on the JENDL-5 by utilizing the two-body collision kinematics. The neutron yield and angular distribution were investigated in the simulation. As a result, the forward neutron convergence with a reasonable neutron yield and energy spectrum was observed. The expected neutron yield in the forward 1-steradian area is 2.46 × 10 10 n/s when lithium-ion energy and current are 16.45 MeV and 0.1 mA.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

AutoPhaseNN: unsupervised physics-aware deep learning of 3D nanoscale Bragg coherent diffraction imaging

Abstract The problem of phase retrieval underlies various imaging methods from astronomy to nanoscale imaging. Traditional phase retrieval methods are iterative and are therefore computationally expensive. Deep learning (DL) models have been developed to either provide learned priors or completely replace phase retrieval. However, such models require vast amounts of labeled data, which can only be obtained through simulation or performing computationally prohibitive phase retrieval on experimental datasets. Using 3D X-ray Bragg coherent diffraction imaging (BCDI) as a representative technique, we demonstrate AutoPhaseNN, a DL-based approach which learns to solve the phase problem without labeled data. By incorporating the imaging physics into the DL model during training, AutoPhaseNN learns to invert 3D BCDI data in a single shot without ever being shown real space images. Once trained, AutoPhaseNN can be effectively used in the 3D BCDI data inversion about 100× faster than iterative phase retrieval methods while providing comparable image quality.

36 MATERIALS SCIENCE↗

NASA NTRS1972

On the equinoctial orbit elements.

This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.

Broucke, R. A.↗

NASA NTRS1977

The atmosphere of Jupiter from earth-based and spacecraft observations in the thermal infrared

The temperature and cloud structure, relative abundances of H2 and He, and the global climatology of Jupiter's atmosphere have been deduced from Pioneer 10 and 11 infrared radiometer data, along with earth-based observations of the spectrum at 8-14 and 12-24 microns. The H2 and He abundances are near those expected from 'solar' composition. The effective planetary temperature is 125 + or - 3 K. Temperatures at 1.0 bar are near 165 K and drop to 100-110 K at 0.1 bar; an overlying thermal inversion reaches 133-145 K near 0.03 bar. Temperature profiles for various regions of the planet may be quite similar, with differences due to the presence or absence of a thick cloud near 0.7 bar, close to the temperature where NH3 saturation is expected. Remaining problems in the remote sounding of Jupiter's atmosphere are accurate calibration of the global energy balance, sounding in the presence of significant heterogeneity, and temperature recovery of the thermally inverted stratosphere.

Orton, G. S.↗

NASA NTRS1984

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

David, R. E.↗

NASA NTRS1992

Stability and bifurcation of quasiparallel Alfven solitons

The inverse scattering transformation (IST) is used to study the one-parameter and two-parameter soliton families of the derivative nonlinear Schroedinger (DNLS) equation. The two-parameter soliton family is determined by the discrete complex eigenvalue spectrum of the Kaup-Newell scattering problem and the one-parameter soliton family corresponds to the discrete real eigenvalue spectrum. The structure of the IST is exploited to discuss the existence of discrete real eigenvalues and to prove their structural stability to perturbations of the initial conditions. Also, though the two-parameter soliton is structurally stable in general, it is shown that a perturbation of the initial conditions may change the two-parameter soliton into a degenerate soliton which, in turn, is structurally unstable. This degenerate, or double pole, soliton may bifurcate due to a perturbation of the initial conditions into a pair of one-parameter solitons. If the initial profile is on compact support, then this pair of one-parameter solitons must be compressive and rarefactive respectively. Finally, the Gelfand-Levitan equations appropriate for the double pole soliton are solved.

Hamilton, R. L.↗

DOE OSTI2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Reflectance spectroscopy - Quantitative analysis techniques for remote sensing applications

The empirical methods and scattering theories that are important for solving remote sensing problems are among the methods for remotely sensed reflectance data analysis presently compared. In the case of the photon mean optical path length concept's implications for reflectance spectra modeling, it is shown that the mean optical path length in a particulate surface is in roughly inverse proportion to the square root of the absorption coefficient. Absorption bands, which are Gaussian in shape when plotted as true absorptance vs photon energy, are also Gaussians in apparent absorptance, although they have a smaller intensity. An apparent continuum in a reflectance spectrum is modeled as a mathematical function that is used to isolate a particular absorption feature for analysis, and it is noted that this continuum should be removed by dividing it into the reflectance spectrum.

Clark, R. N.↗

NASA NTRS1990

Unsteady airloading panel method for prop-fans

An unsteady, linear, compressible, three dimensional lifting surface panel method is presented for use with propellers and prop-fans. Both gust and blade vibration problems can be treated. Derivation of the theory is based on the acceleration potential method and can be considered a generalization of the analogous wing theory to include rotation and multiple blades. As with the wing methods, the integral equation is discretized and solved by matrix inversion. Sample calculations are use to explore the difference between 2D and 3D results and the significance of unsteadiness in angular inflow calculations for propellers. It is shown at the once-per-revolution frequency of propellers, that quasi-steady methods should be adequate. At the high frequencies of interest in noise analysis, 2D strip methods give adequate results away from blade tips. For flutter, frequencies lie in an intermediate range where a full 3D unsteady technique seems to be required.

Hanson, D. B.↗

NASA NTRS2003

Mathematical Investigation of Gamma Ray and Neutron Absorption Grid Patterns for Homeland Defense Related Fourier Imaging Systems

Terrorist suitcase nuclear devices typically using converted Soviet tactical nuclear warheads contain several kilograms of plutonium. This quantity of plutonium emits a significant number of gamma rays and neutrons as it undergoes radioactive decay. These gamma rays and neutrons normally penetrate ordinary matter to a significant distance. Unfortunately this penetrating quality of the radiation makes imaging with classical optics impractical. However, this radiation signature emitted by the nuclear source may be sufficient to be imaged from low-flying aerial platforms carrying Fourier imaging systems. The Fourier imaging system uses a pair of co-aligned absorption grids to measure a selected range of spatial frequencies from an object. These grids typically measure the spatial frequency in only one direction at a time. A grid pair that looks in all directions simultaneously would be an improvement over existing technology. A number of grid pairs governed by various parameters were investigated to solve this problem. By examining numerous configurations, it became apparent that an appropriate spiral pattern could be made to work. A set of equations was found to describe a grid pattern that produces straight fringes. Straight fringes represent a Fourier transform of a point source at infinity. An inverse Fourier transform of this fringe pattern would provide an accurate image (location and intensity) of a point source.

Boccio, Dona↗