Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

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.

At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Thermal-vacuum facility with in-situ mechanical loading

The paper describes a thermal-vacuum space simulator used to assess property changes of fiber-reinforced polymer composite systems. The facility can achieve a vacuum of approximately .0000001 torr with temperatures ranging from -200 to +300 F. Some preliminary experimental results are presented for materials subjected to thermal loading up to 200 F. The tests conducted include the evaluation of matrix modulus and strength, coefficients of thermal expansion, and fracture toughness. Though the experimental program is at an early stage, the data appear to indicate that these parameters are influenced by hard vacuum.

Tennyson, R. C.↗
NASA NTRS1981

Determination of magnetic helicity in the solar wind and implications for cosmic ray propagation

Magnetic helicity (Hm) is the mean value of the correlation between a turbulent magnetic field and the magnetic vector potential. A technique is described for determining Hm and its 'reduced' spectrum from the two point magnetic correlation matrix. The application of the derived formalism to solar wind magnetic fluctuations is discussed, taking into account cases for which only single point measurements are available. The application procedure employs the usual 'frozen in approximation' approach. The considered method is applied to an analysis of several periods of Voyager 2 interplanetary magnetometer data near 2.8 AU. During these periods the correlation length, or energy containing length, was found to be approximately 3 x 10 to the 11th cm

Matthaeus, W. M.↗
NASA NTRS1986

Effects of noise on modal parameters identified by the Eigensystem Realization Algorithm

The basic concept of the Eigensystem Realization Algorithm for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators, such as the singular values of the data matrix and modal amplitude coherence, is provided, based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo Simulations are included to support the analytical studies.

Juang, J.-N.↗
NASA NTRS1986

Effects of noise on ERA-identified modal parameters

The basic concept of the Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators such as the singular values of the data matrix and modal amplitude coherence is provided based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo simulations are included to support the analytical studies.

Juang, J.-N.↗
NASA NTRS1989

Numerical solution of large Lyapunov equations

A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.

Saad, Youcef↗
NASA NTRS1993

On the cross-stream spectral method for the Orr-Sommerfeld equation

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Zorumski, William E.↗
NASA NTRS1995

Axtrell, a new CV3 chondrite find from Texas

We describe a previously unreported meteorite found in Axtell, Texas, in 1943. Based on the mineralogical composition and texture of its matrix and the sizes and abundance of chondrules, we classify it as a CV3 carbonaceous chondrite. The dominant opaque phase in the chondrules is magnetite, and that in refractory inclusions is Ni-rich metal (awaruite). Axtell, therefore, belongs to the oxidized subgroup of CV3 chondrites, although unlike Allende it escaped strong sulfidation. The meteorite bears a strong textural resemblance to Allende, and its chondrule population and matrix appear to be quite similar to those of Allende, but its refractory inclusions, thermoluminescence properties, and cosmogenic Co-60 abundances are not. Our data are consistent with a terrestrial age for Axtell of approximately 100 years and a metamorphic grade slightly lower than that of Allende.

Simon, S. B.↗
NASA NTRS2014

Assessment of the Accuracy of the Conventional Ray-Tracing Technique: Implications in Remote Sensing and Radiative Transfer Involving Ice Clouds.

A fundamental problem in remote sensing and radiative transfer simulations involving ice clouds is the ability to compute accurate optical properties for individual ice particles. While relatively simple and intuitively appealing, the conventional geometric-optics method (CGOM) is used frequently for the solution of light scattering by ice crystals. Due to the approximations in the ray-tracing technique, the CGOM accuracy is not well quantified. The result is that the uncertainties are introduced that can impact many applications. Improvements in the Invariant Imbedding T-matrix method (II-TM) and the Improved Geometric-Optics Method (IGOM) provide a mechanism to assess the aforementioned uncertainties. The results computed by the II-TMþIGOM are considered as a benchmark because the IITM solves Maxwell's equations from first principles and is applicable to particle size parameters ranging into the domain at which the IGOM has reasonable accuracy. To assess the uncertainties with the CGOM in remote sensing and radiative transfer simulations, two independent optical property datasets of hexagonal columns are developed for sensitivity studies by using the CGOM and the II-TMþIGOM, respectively. Ice cloud bulk optical properties obtained from the two datasets are compared and subsequently applied to retrieve the optical thickness and effective diameter from Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Additionally, the bulk optical properties are tested in broadband radiative transfer (RT) simulations using the general circulation model (GCM) version of the Rapid Radiative Transfer Model (RRTMG) that is adopted in the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM, version 5.1). For MODIS retrievals, the mean bias of uncertainties of applying the CGOM in shortwave bands (0.86 and 2.13 micrometers) can be up to 5% in the optical thickness and as high as 20% in the effective diameter, depending on cloud optical thickness and effective diameter. In the MODIS infrared window bands centered at 8.5, 11, and 12 micrometers biases in the optical thickness and effective diameter are up to 12% and 10%, respectively. The CGOM-based simulation errors in ice cloud radiative forcing calculations are on the order of 10Wm(exp 2).

remote sensing↗
NASA NTRS2018

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗
NASA NTRS2005

Effects of Control Mode and R-Ratio on the Fatigue Behavior of a Metal Matrix Composite

Composite Because of their high specific stiffness and strength at elevated temperatures, continuously reinforced metal matrix composites (MMC's) are under consideration for a future generation of aeropropulsion systems. Since components in aeropropulsion systems experience substantial cyclic thermal and mechanical loads, the fatigue behavior of MMC's is of great interest. Almost without exception, previous investigations of the fatigue behavior of MMC's have been conducted in a tension-tension, load-controlled mode. This has been due to the fact that available material is typically less than 2.5-mm thick and, therefore, unable to withstand high compressive loads without buckling. Since one possible use of MMC's is in aircraft skins, this type of testing mode may be appropriate. However, unlike aircraft skins, most engine components are thick. In addition, the transient thermal gradients experienced in an aircraft engine will impose tension-compression loading on engine components, requiring designers to understand how the MMC will behave under fully reversed loading conditions. The increased thickness of the MMC may also affect the fatigue life. Traditionally, low-cycle fatigue (LCF) tests on MMC's have been performed in load control. For monolithic alloys, low-cycle fatigue tests are more typically performed in strain control. Two reasons justify this choice: (1) the critical volume from which cracks initiate and grow is generally small and elastically constrained by the larger surrounding volume of material, and (2) load-controlled, low-cycle fatigue tests of monolithics invariably lead to unconstrained ratcheting and localized necking--an undesired material response because the failure mechanism is far more severe than, and unrelated to, the fatigue mechanism being studied. It is unknown if this is the proper approach to composite testing. However, there is a lack of strain-controlled data on which to base any decisions. Consequently, this study addresses the isothermal, LCF behavior of a [0]_32 MMC tested under strain- and load-controlled conditions for both zero-tension and tension-compression loading conditions. These tests were run at 427 C on thick specimens of SiC-reinforced Ti-15-3. For the fully-reversed tests, no difference was observed in the lives between the load- and strain-controlled tests. However, for the zero-tension tests, the strain-controlled tests had longer lives by a factor of 3 in comparison to the load-controlled tests. This was due to the fact that under strain-control the specimens cyclically softened, reducing the cracking potential. In contrast, the load-controlled tests ratcheted toward larger tensile strains leading to an eventual overload of the fibers. Fatigue tests revealed that specimens tested under fully-reversed conditions had lives approximately an order of magnitude longer than for those specimens tested under zero tension. When examined on a strain-range basis, the fully reversed specimens had similar, but still shorter lives than those of the unreinforced matrix material. However, the composite had a strain limitation at short lives because of the limited strain capacity of the brittle ceramic fiber. The composite also suffered at very high lives because of the lack of an apparent fatigue limit in comparison to the unreinforced matrix. The value of adding fibers to the matrix is apparent when the fatigue lives are plotted as a function of stress range. Here, the composite is far superior to the unreinforced matrix because of the additional load-carrying capacity of the fibers.

Source record↗
DOE OSTI2023

Correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field methods

The fully correlated frequency-independent Dirac–Coulomb–Breit Hamiltonian provides the most accurate description of electron–electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac–Coulomb–Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. Here, we also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

A test of the applicability of independent scattering to high albedo planetary regoliths

We show that 'independent scattering' is a useful approximation for high albedo particles whose size and packing density are similar to typical particles in the lunar regolith. Laboratory measurements of the intensity and linear polarization of light scattered from a laboratory sample of glass spheres of know size and composition are compared to radiative transfer calculations of the same observable quantities. Mie scattering is integrated over the size distribution of the particles to determine the mean phase and polarization functions, or phase matrix, of the particle. Assuming that the particles scatter independently, the 'doubling method' is used to rigorously calculate multiple scattering in an optically thick layer of these anisotropically scattering particles. All of the major features 'predicted' in the calculated intensity (double peaks at small phase angles) and polarization (negative branch at small phase angles, large positive peak near 20 degrees phase, and small polarization elsewhere) are observed in the laboratory measurements, with good quantitative agreement indicated at phase angles less than 90 degrees. Even though the particles are supported by physical contact with each other in the sample, as are the particles in planetary regoliths, the independent scattering calculation yields a good approximation to both the intensity and polarization. The physical parameters input to the calculation are only the size distribution of the particles and their complex index of refraction (composition). Significant advantages of this approach are that the phase matrix is calculated from basic physical principles and both the intensity and polarization are determined simultaneously. This model may have broad applications to the interpretation of photometry, spectroscopy, and polarimetry of the icy regoliths of high albedo satellites. The intent of this effort is to perform a controlled experiment that tests the utility of the independent scattering assumption

Goguen, J. D.↗
DOE OSTI2022

Risk matrix for legacy wells within the Area of Review (AoR) of Carbon Capture & Storage (CCS) projects

The success of CCS depends on the capacity, injectivity, and confinement by the storage medium. Thousands of wells drilled over the past century with the intention to find the trapped oil and gas may penetrate the containment seals. These wells may provide leakage pathways for the CO 2 to escape and contaminate the underground sources of drinking water (USDW) or reach the surface in the worst-case scenario. Identifying the risky wells penetrating the containment seals and predicting their current as well as future well integrity is the most challenging task when limited data is available. Here, this paper proposes a unique methodology for risk assessment of the wells penetrating the containment seals based on the proximity of these wells from the proposed injection location, mechanical integrity, and accessibility of these wells over the lifecycle of the CCS project. This helps in identifying the wells which need immediate attention from the wells that need little to no attention. It also highlights the corrective actions necessary for the success of the CCS project as well as help estimate the approximate cost required to perform the corrective actions. This methodology focuses on all wells (producers, injectors, orphan, abandoned, water, stratigraphic, etc) while the majority of the studies found in literature focused on wells with sustained casing pressure (SCP) reports and cement bond logs (CBL). The proposed risk matrix, if applied to future CCS projects across the globe, will uniformly categorize the wells within the Area of Review (AoR).

58 GEOSCIENCES↗
DOE OSTI2023

Boson star normal modes

Boson stars are gravitationally bound objects that arise in ultralight dark matter models and form in the centers of galactic halos or axion miniclusters. We systematically study the excitations of a boson star, taking into account the mixing between positive and negative frequencies introduced by gravity. We show that the spectrum contains zero-energy modes in the monopole and dipole sectors resulting from spontaneous symmetry breaking by the boson star background. We analyze the general properties of the eigenmodes and derive their orthogonality and completeness conditions which have non-standard form due to the positive-negative frequency mixing. The eigenvalue problem is solved numerically for the first few energy levels in different multipole sectors and the results are compared to the solutions of the Schrödinger equation in fixed boson star gravitational potential. The two solutions differ significantly for the lowest modes, but get close for higher levels. We further confirm the normal mode spectrum in 3D wave simulations where we inject perturbations with different multipoles. As an application of the normal mode solutions, we compute the matrix element entering the evaporation rate of a boson star immersed in a hot axion gas. The computation combines the use of exact wavefunctions for the low-lying bound states and of the Schrödinger approximation for the high-energy excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Harvesting 88 Zr from heavy-ion beam irradiated tungsten at the National Superconducting Cyclotron Laboratory

Tungsten is a commonly used material at many heavy-ion beam facilities, and it often becomes activated due to interactions with a beam. Many of the activation products are useful in basic and applied sciences if they can be recovered efficiently. In order to develop the radiochemistry for harvesting group (IV) elements from irradiated tungsten, a heavy-ion beam containing 88 Zr was embedded into a stack of tungsten foils at the National Superconducting Cyclotron Laboratory and a separation methodology was devised to recover the 88 Zr. The foils were dissolved in 30% hydrogen peroxide, and the 88 Zr was chemically purified from the tungsten matrix and from other co-implanted radionuclides (such as 85 Sr and 88 Y) using strong cation-exchange (AG MP-50) chromatographic resin in sulfuric acid media. The procedure provided 88 Zr in approximately 60 mL 0.5 M sulfuric acid with no detectable radio-impurities. The overall recovery yield for 88 Zr was (92.3 ± 1.2)%. In conclusion, this proof-of-concept experiment has facilitated the development of methodologies to harvest from tungsten and tungsten-alloy parts that are regularly irradiated at heavy-ion beam facilities.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2021

TUMME: Tsinghua University Minnesota Master Equation program

We report that TUMME is a program for assembling and solving master equations for gas-phase chemical kinetics based on chemically significant eigenmodes. TUMME has interfaces to the Gaussian, Polyrate, and/or MSTor output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the coefficient matrix of the master equation. The flux coefficients for reactions with barriers can be calculated by multi-structural variational transition state theory with small-curvature tunneling (MS-VTST/SCT) or by simpler approximations to this such as conventional transition state theory without tunneling (also called RRKM theory). The flux coefficients for barrierless reactions are provided by a hard-sphere model. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and the C++ code can run on a single processor or on multiple processors with OpenMP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Speeding Up Hartree–Fock in JuliaChem with Density Fitting

In this work, the density fitting (DF) approximation is added to the restricted Hartree–Fock (RHF) implementation in the JuliaChem computational chemistry code. Utilizing a DF algorithm that uses symmetry and integral screening, a significant reduction in time to compute the Fock matrix is achieved. The symmetry and screening DF-RHF techniques were adapted to be performed on graphics processing units (GPUs), which are well suited to perform the matrix multiplications that comprise the bulk of the Fock build time in DF-RHF. The JuliaChem DF-RHF GPU algorithm employs a novel approach that automatically switches between two DF-RHF algorithms depending on the number of basis functions in the calculation. The JuliaChem GPU DF-RHF implementation demonstrates up to 2× speedup for Fock build times compared to the existing best-in-class GPU DF-RHF implementation by operating directly on screened intermediate matrices. Due to the high portability of the Julia language code, the JuliaChem CPU and GPU DF-RHF implementations could be benchmarked on a variety of CPU and GPU architectures from multiple hardware vendors.

Hayes, John J. [Ames Laboratory, and Iowa State Un↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗