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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗
NASA NTRS1986

Nonlinear filtering for spacecraft attitude estimation

Nonlinear filtering techniques are applied to spacecraft attitude estimation using quaternion parameterization for the attitude kinematics. By replacing the angular velocity vector by the gyro output vector, a state dependent noise vector is introduced in the seven-dimensional system equations. The resulting conditional probability density function from the Ito differential rule is governed by the Fokker Planck partial differential equation which is approximated by the second order mean and covariance differential equations. In order to minimize computer loading, the covariance propagation is carried out in six-dimensional state space using a matrix transformation. The star tracker data is used to update the covariance matrix in the seven-dimensional space. The algorithm is simulated for an earth pointing spacecraft mission, using Monte Carlo samples of gyro and star measurements. The performance of the second order filter is compared with the extended Kalman Filter through several simulation runs and drift rates have been identified.

Vathsal, S.↗
NASA NTRS1988

Integrated structural-aerodynamic design optimization

This paper focuses on the processes of simultaneous aerodynamic and structural wing design as a prototype for design integration, with emphasis on the major difficulty associated with multidisciplinary design optimization processes, their enormous computational costs. Methods are presented for reducing this computational burden through the development of efficient methods for cross-sensitivity calculations and the implementation of approximate optimization procedures. Utilizing a modular sensitivity analysis approach, it is shown that the sensitivities can be computed without the expensive calculation of the derivatives of the aerodynamic influence coefficient matrix, and the derivatives of the structural flexibility matrix. The same process is used to efficiently evaluate the sensitivities of the wing divergence constraint, which should be particularly useful, not only in problems of complete integrated aircraft design, but also in aeroelastic tailoring applications.

Haftka, R. T.↗
NASA NTRS1990

Matrix elements in the coupled-cluster approach - With application to low-lying states in Li

A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.

Martensson-Pendrill, Ann-Marie↗
NASA NTRS1993

SXRF determination of trace elements in chondrule rims in the unequilibrated CO3 chondrite, ALH A77307

The concentrations of Ni, Cu, Zn, Ga, Ge, and Se in five chondrule rims in the CO3 chondrite ALH A77307 (3.0) using the synchrotron x-ray fluorescence (SXRF) microprobe at Brookhaven National Laboratory were determined. The data show that the trace element chemistry of rims on different chondrules is remarkably similar, consistent with data obtained for the major elements by electron microprobe. These results support the idea that rims are not genetically related to individual chondrules, but all sampled the same reservoir of homogeneously mixed dust. Of the trace elements analyzed Zn and Ga show depletions relative to CI chondrite values, but in comparison with bulk CO chondrites all the elements are enriched by approximately 1.5 to 3.5 x CO. The high concentrations of the highly volatile elements Se and Ga and moderately volatile Zn (1.5 to 2 x CO) in rims show that matrix is the major reservoir of volatile elements in ALH A77307.

Brearley, Adrian J.↗
NASA NTRS1993

A noniterative improvement of Guyan reduction

In determining the natural modes and frequencies of a linear elastic structure, Guyan reduction is often used to reduce the size of the mass and stiffness matrices and the solution of the reduced system is obtained first. The reduced system modes are then expanded to the size of the original system by using a static transformation linking the retained degrees of freedom to the omitted degrees of freedom. In the present paper, the transformation matrix of Guyan reduction is modified to include additional terms from a series accounting for the inertial effects. However, the inertial terms are dependent on the unknown frequencies. A practical approximation is employed to compute the inertial terms without any iteration. This new transformation is implemented in NASTRAN using a DMAP sequence alter. Numerical examples using a cantilever beam illustrate the necessary condition for allowing a large number of additional terms in the proposed series correction of Guyan reduction. A practical example of a large model of the Plasma Motor Generator module to be flown on a Delta launch vehicle is also presented.

Ganesan, N.↗
NASA NTRS1998

Atmospheric Probe Model: Construction and Wind Tunnel Tests

The material contained in this document represents a summary of the results of a low speed wind tunnel test program to determine the performance of an atmospheric probe at low speed. The probe configuration tested consists of a 2/3 scale model constructed from a combination of hard maple wood and aluminum stock. The model design includes approximately 130 surface static pressure taps. Additional hardware incorporated in the baseline model provides a mechanism for simulating external and internal trailing edge split flaps for probe flow control. Test matrix parameters include probe side slip angle, external/internal split flap deflection angle, and trip strip applications. Test output database includes surface pressure distributions on both inner and outer annular wings and probe center line velocity distributions from forward probe to aft probe locations.

Vogel, Jerald M.↗
NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗
NASA NTRSDate not supplied

Computing the effective elasticity of anisotropic porous media from X-ray computed micro-tomography images

Development and optimization of composite materials designed for thermal protection of NASA’s spacecraft requires the understanding of their physical response to high-enthalpy environments. To predict their macro-scale properties and behavior, high-fidelity 3D simulations are performed at the micro-scale on realistic representations of these composites. The digital micro-structures are generated either synthetically or through X-ray micro-tomography reconstructions. One of the main challenges in the prediction of heatshield material structural response is the computation of the effective elasticity of the fibrous composite, as well as the understanding of the deformation and stresses generated at the micro-scale. These are driven by the fiber layout within the micro-structure and the distribution of the infused matrix. In this effort, the micro-mechanical linear elastic behavior of fibrous ablators is modeled through the use of a numerical method based on the Multi-Point Stress Approximation (MPSA) finite volume scheme. The MPSA, a generalization of the more commonly used Multi-Point Flux Approximation (MPFA), was discussed in a previous presentation at the 15th USCCN and in reference. To predict the behavior of fibrous and woven architectures, algorithms that compute the local fiber orientation are used. The implementation of the MPSA was verified using analytical solutions, engineering test cases and compared against legacy Finite Element Analysis (FEA) software. The stress analysis models were then applied to real geometries used by NASA in thermal protection systems such as fibrous preforms and woven materials and the results were compared to experimental data.

Federico Semeraro↗
DOE OSTI2020

Quantum dynamics in strongly driven random dipolar magnets

The random dipolar magnet LiHo x Y 1– x F 4 enters a strongly frustrated regime for small Ho 3+ concentrations with x < 0.05. In this regime, the magnetic moments of the Ho 3+ ions experience small quantum corrections to the common Ising approximation of LiHo x Y 1– x F 4 , which lead to a $\mathbb{Z}_2$-symmetry breaking and small, degeneracy breaking energy shifts between different eigenstates. Here we show that destructive interference between two almost degenerate excitation pathways burns spectral holes in the magnetic susceptibility of strongly driven magnetic moments in LiHo x Y 1– x F 4 . Such spectral holes in the susceptibility, microscopically described in terms of Fano resonances, can already occur in setups of only two or three frustrated moments, for which the driven level scheme has the paradigmatic Λ shape. For larger clusters of magnetic moments, the corresponding level schemes separate into almost isolated many-body Λ schemes, in the sense that either the transition matrix elements between them are negligibly small or the energy difference of the transitions is strongly off-resonant to the drive. This enables the observation of Fano resonances, caused by many-body quantum corrections to the common Ising approximation also in the thermodynamic limit. Finally, we discuss its dependence on the driving strength and frequency as well as the crucial role that is played by lattice dissipation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2018

Dynamics of Gaps Created By Burning in Florida Oak-Saw Palmetto (Quercus, Fagaceae-Serenoa repens, Arecaceae) Scrub

Sandy gaps in the shrub matrix of oak (Quercus L.)-saw palmetto (Serenoa repens (W. Bartram) Small) scrub are created by fire but typically close quickly because of rapid regrowth. Such gaps are important habitat features for rare scrub flora and fauna and appear to have been more common in the historical landscape. We followed, from 1993 to 2016, the dynamics of 12 gaps (32.2-98.1 sq m) created by burning slash piles as part of restoration of long-unburned scrub. Gaps closed slowly, primarily by canopy spread of oaks around the gaps. In the absence of subsequent fire, gaps closed within approximately 12 yr. When burned a second or third time, gap area increased to near the initial after-burn size but then declined in area more rapidly than after the initial fire. Vegetation that reestablished in gaps differed from that of the scrub matrix in having less cover of scrub oaks, less cover of S. repens. > 0.5 m, greater cover of native shrubs and forbs. > 0.5 m, and more bare ground. Soil heating from slash-pile burning killed the roots and rhizomes from which scrub oaks, Serenoa, and ericaceous shrubs sprout; this altered and slowed the after-fire recovery.

Serenoa↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2002

Software for Processing Flight and Simulated Data of the ATIC Experiment

ATIC (Advanced Thin Ionization Calorimeter) is a balloon borne experiment designed to measure the cosmic ray composition for elements from hydrogen to iron and their energy spectra from approx.50 GeV to near 100 TeV. It consists of a Si-matrix detector to determine the charge of a CR particle, a scintillator hodoscope for tracking, carbon interaction targets and a fully active BGO calorimeter. ATIC had its first flight from McMurdo, Antarctica from 28/12/2000 to 13/01/2001. The ATIC flight collected approximately 25 million events. A C++-class library for building different programs for processing flight and simulated data of the ATIC balloon experiment is described. This library is compatible with the ROOT-system and includes classes and methods for solving a number of problems as the following: Reading data files in different formats (raw-data format, ROOT-format, ASCII-format, different formats for simulated data); Transferring all these formats to the only inner format of the library; Reconstruction of trajectories of primary particles with BGO calorimeter only. The Monte-Carlo simulations with GEANT code were used to obtain the basic tables for computing error corridors and chi(sup 2)-values for the trajectories. Obtaining error corridors for searching for signal of primary particle in the Si-matrix; Searching for hit of primary particle in the Si-matrix with using of error corridor and other criteria (chi(sup 2)-values, agreement between signals in Si-matrix and in the upper layer of scintillator and others); Determination of charge of primary particle; Determination of energy deposit in BGO calorimeter.

Panov, A. D.↗
DOE OSTI2024

UN-SiC TRISO Post Irradiation Examination Developmental Work

As part of efforts to strengthen INL?s post irradiation analysis capabilities with non-Advanced Gas Reactor (AGR) tristructural isotropic (TRISO) fuels, two developmental activities were conducted. The first activity was to determine how best to analyze uranium nitride TRISO fuel kernels using electron probe microanalysis, while the second activity focused on developing a method to deconsolidate TRISO fuel particles that have been encased in a silicon carbide matrix. Because these two activities were unrelated, they have been presented separately in this report. Initial EPMA analyses showed nitrogen contents that far exceeded the concentration expected for UN--a line compound. Further examination showed that current literature values for the mass absorption coefficient (MAC) for the N ka X-ray absorbed by U ranged from approximately 1600 to 9500, with most values tending toward 9500. Measuring UN with five different progressively increasing accelerating voltages followed by using the modeling program xMAC suggests the actual MAC is approximately 2115. Additional MAC modifications were required to produce reasonable analytical results. Because of the inaccuracies of necessary MAC coefficients, UN analysis via scanning electron microscopy (SEM) is likely to produce inaccurate results. This is because SEM software does not typically allow the user to alter MACs. Tests have been performed to examine the feasibility of an electrochemical technique to liberate irradiated TRISO fuel from a SiC matrix without damaging the outer pyrolytic carbon layer of the fuel particle. The method is performed by electrochemically exposing the SiC to magnesium metal forming Mg2Si and C. Following exposure, the small SiC samples showed slight mass increases with no evidence of conversion to Mg2Si and C nor obvious degradation of the SiC samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1983

Epoxy hydantoins as matrix resins

Tensile strength and fracture toughness of castings of the hydantoin resins cured with methylenedianiline are significantly higher than MY 720 control castings. Water absorption of an ethyl, amyl hydantoin formulation is 2.1 percent at equilibrium and Tg's are about 160 C, approximately 15 deg below the final cure temperature. Two series of urethane and ester-extended hydantoin epoxy resins were synthesized to determine the effect of crosslink density and functional groups on properties. Castings cured with methylenedianiline or with hexahydrophthalic anhydride were made from these compounds and evaluated. The glass transition temperatures, tensile strengths and moduli, and fracture toughness values were all much lower than that of the simple hydantoin epoxy resins. Using a methylene bishydantoin epoxy with a more rigid structure gave brittle, low-energy fractures, while a more flexible, ethoxy-extended hydantoin epoxy resin gave a very low Tg.

Weiss, J.↗
DOE OSTI2023

Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

Understanding substrate effects on spin dynamics and relaxation is of key importance for spin-based information technologies. However, the key factors that determine such effects, in particular for materials with strong spin-orbit coupling (SOC), have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with SOC and the electron phonon and electron-impurity scattering for spin lifetimes (τ s ) of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on τ s can surprisingly differ by two orders of magnitude. We find that substrate effects on τ s are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle θ ↑↓ , to characterize spin relaxation through intervalley spin-flip scattering. We find that $τ^{-1}_s$ is approximately proportional to the averaged value of sin 2 (θ ↑↓ /2), which serves as a guiding parameter of controlling spin relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Sparse Approximate Multifrontal Factorization with Composite Compression Methods

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗