Results for “Matrix elements” — Page 62

NASA NTRS2010

Probabilistic Structural Analysis Program

NASA/NESSUS 6.2c is a general-purpose, probabilistic analysis program that computes probability of failure and probabilistic sensitivity measures of engineered systems. Because NASA/NESSUS uses highly computationally efficient and accurate analysis techniques, probabilistic solutions can be obtained even for extremely large and complex models. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety-critical and one-of-a-kind systems, as well as for maintaining a level of quality while reducing manufacturing costs for larger-quantity products. NASA/NESSUS has been successfully applied to a diverse range of problems in aerospace, gas turbine engines, biomechanics, pipelines, defense, weaponry, and infrastructure. This program combines state-of-the-art probabilistic algorithms with general-purpose structural analysis and lifting methods to compute the probabilistic response and reliability of engineered structures. Uncertainties in load, material properties, geometry, boundary conditions, and initial conditions can be simulated. The structural analysis methods include non-linear finite-element methods, heat-transfer analysis, polymer/ceramic matrix composite analysis, monolithic (conventional metallic) materials life-prediction methodologies, boundary element methods, and user-written subroutines. Several probabilistic algorithms are available such as the advanced mean value method and the adaptive importance sampling method. NASA/NESSUS 6.2c is structured in a modular format with 15 elements.

Pai, Shantaram S.↗

NASA NTRS1987

Neural network based feed-forward high density associative memory

A novel thin film approach to neural-network-based high-density associative memory is described. The information is stored locally in a memory matrix of passive, nonvolatile, binary connection elements with a potential to achieve a storage density of 10 to the 9th bits/sq cm. Microswitches based on memory switching in thin film hydrogenated amorphous silicon, and alternatively in manganese oxide, have been used as programmable read-only memory elements. Low-energy switching has been ascertained in both these materials. Fabrication and testing of memory matrix is described. High-speed associative recall approaching 10 to the 7th bits/sec and high storage capacity in such a connection matrix memory system is also described.

Daud, T.↗

NASA NTRS1988

Prediction of high temperature metal matrix composite ply properties

The application of the finite element method (superelement technique) in conjunction with basic concepts from mechanics of materials theory is demonstrated to predict the thermomechanical behavior of high temperature metal matrix composites (HTMMC). The simulated behavior is used as a basis to establish characteristic properties of a unidirectional composite idealized an as equivalent homogeneous material. The ply properties predicted include: thermal properties (thermal conductivities and thermal expansion coefficients) and mechanical properties (moduli and Poisson's ratio). These properties are compared with those predicted by a simplified, analytical composite micromechanics model. The predictive capabilities of the finite element method and the simplified model are illustrated through the simulation of the thermomechanical behavior of a P100-graphite/copper unidirectional composite at room temperature and near matrix melting temperature. The advantage of the finite element analysis approach is its ability to more precisely represent the composite local geometry and hence capture the subtle effects that are dependent on this. The closed form micromechanics model does a good job at representing the average behavior of the constituents to predict composite behavior.

Caruso, J. J.↗

NASA NTRS1980

A solution of the variational equations for elliptic orbits in rotating coordinates

For elliptic reference orbits, formulas are given for the perturbation state transition matrix of the two-body problem. The formulas relate perturbations expressed in a local vertical rotating coordinate system and are valid for motion in the linear neighborhood of reference orbits with e in the range of 0 to 1. The elements of the state transition matrix are expressed in terms of natural parameters (horizontal and radial velocity, radius, eccentricity, true anomaly, etc.) at the initial and final points. In addition to the general form, a simplified version, valid for small eccentricity orbits, is given.

Jones, J. B.↗

NASA NTRS2021

Hypersonic Second Mode Instability Response to Shaped Roughness

An experimental campaign was conducted on a 7-degree half-angle cone in the NASA Langley Research Center 20-Inch Mach 6 Wind Tunnel to examine the influence of arrays of regularly spaced roughness elements on instability growth and transition. The primary element shape was a pair of elliptical planform ramps that were inclined at equal and opposite angles with respect to the local streamwise direction. The element shapes were designed to induce transient growth disturbances that would lead to sustained azimuthal modulation of the boundary layer flow while limiting the nearfield disturbances to avoid an immediate, i.e., effective tripping of the boundary layer. The bulk of the run matrix consisted of testing different element height sat free stream unit Reynolds numbers ranging from 9.8 to 13.1 million per meter. Other element shapes previously designed for tripping hypersonic boundary layers were also implemented. The model was instrumented with surface mounted Kulite ® and PCB ® pressure transducers and thermocouples. Spectra from the PCBs ® indicated clear suppression of the second-mode instability; however, neither the PCB ® spectra nor the heat transfer data presented strong evidence for delayed turbulent flow. Complementary stability computations likewise demonstrated second-mode reduction, particularly just downstream of the roughness, but also revealed a rise in first mode (streak-instability) amplitudes from the baseline that was likely responsible for the earlier transition observed for taller roughness cases.

Hypersonics↗

NASA NTRS2021

Hypersonic Second-Mode Instability Response to Shaped Roughness

An experimental campaign was conducted on a 7-degree half-angle cone in the NASA Langley Research Center 20-Inch Mach 6 Wind Tunnel to examine the influence of arrays of regularly spaced roughness elements on instability growth and transition. The primary element shape was a pair of elliptical planform ramps that were inclined at equal and opposite angles with respect to the local streamwise direction. The element shapes were designed to induce transient growth disturbances that would lead to sustained azimuthal modulation of the boundary layer flow while limiting the nearfield disturbances to avoid an immediate, i.e., effective tripping of the boundary layer. The bulk of the run matrix consisted of testing different element height sat free stream unit Reynolds numbers ranging from 9.8 to 13.1 million per meter. Other element shapes previously designed for tripping hypersonic boundary layers were also implemented. The model was instrumented with surface mounted Kulite ® and PCB ® pressure transducers and thermocouples. Spectra from the PCBs ® indicated clear suppression of the second-mode instability; however, neither the PCB ® spectra nor the heat transfer data presented strong evidence for delayed turbulent flow. Complementary stability computations likewise demonstrated second-mode reduction, particularly just downstream of the roughness, but also revealed a rise in first mode (streak-instability) amplitudes from the baseline that was likely responsible for the earlier transition observed for taller roughness cases.

Hypersonics↗

NASA NTRS2021

Hypersonic Second-Mode Instability Response to Shaped Roughness

An experimental campaign was conducted on a 7-degree half-angle cone in the NASA Langley Research Center 20-Inch Mach 6 Wind Tunnel to examine the influence of arrays of regularly spaced roughness elements on instability growth and transition. The primary element shape was a pair of elliptical planform ramps that were inclined at equal and opposite angles with respect to the local streamwise direction. The element shapes were designed to induce transient growth disturbances that would lead to sustained azimuthal modulation of the boundary layer flow while limiting the nearfield disturbances to avoid an immediate, i.e., effective tripping of the boundary layer. The bulk of the run matrix consisted of testing different element height sat free stream unit Reynolds numbers ranging from 9.8 to 13.1 million per meter. Other element shapes previously designed for tripping hypersonic boundary layers were also implemented. The model was instrumented with surface mounted Kulite ® and PCB ® pressure transducers and thermocouples. Spectra from the PCBs ® indicated clear suppression of the second-mode instability; however, neither the PCB ® spectra nor the heat transfer data presented strong evidence for delayed turbulent flow. Complementary stability computations likewise demonstrated second-mode reduction, particularly just downstream of the roughness, but also revealed a rise in first mode (streak-instability) amplitudes from the baseline that was likely responsible for the earlier transition observed for taller roughness cases.

Hypersonics↗

DOE OSTI2021

Prompt Gamma Analysis of ARIES Materials and Updates to the 2015 Calibration Equations

Prompt gamma (PG) analysis is a nondestructive, nuclear, elemental analysis technique that uses charged particle reactions to interrogate a sample, and elements present in the sample matrix are identified through the characteristic gamma-rays emitted from the product nuclei in alpha-p and alpha-n nuclear reactions. This technique has been applied to plutonium oxide packaged in over 4,000 individual 3013 containers, and the concentrations of certain light elements were determined from the integrated peak areas based on a calibration that was published previously. This report provides the results for a new population of 3013 containers packaged with oxide materials produced by the conversion of metal by Advanced Recovery and Integrated Extraction System (ARIES) project using the direct metal oxidation (DMO) process and muffle furnaces. New PG and analytical chemistry data collected since 2015 were added to the existing calibration data sets to refine the calibration parameters. Calibration equations were also developed for determining beryllium and fluorine at low concentrations in high-purity ARIES product oxides. The new fluorine calibration provides an order of magnitude greater sensitivity and results in an additional 1,408 containers in the original population identified as having fluorine as an impurity. Additionally, equations for calculating the lower limits of detection (LLDs) as a function of the actual counting time (live time) were obtained using WLS regression technique for samples in the calibration data set. This resulted in changes to the LLDs published previously.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2006

History of Metal Veins in Acapulcoite-Lodranite Clan Meteorite GRA 95209

Graves Nunataks (GRA) 95209 has been hailed as the missing link of core formation processes in the acapulcoitelodranite parent asteroid because of the presence of a complex cm-scale metal vein network. Because the apparent liquid temperature of the metal vein (approximately 1500 C) is higher than inferred for the metamorphic grade of the meteorite, questions regarding the vein s original composition, temperature, and mechanism of emplacement have arisen. We have determined trace siderophile element compositions of metals in veins and surrounding matrix in an effort to clarify matters. We analyzed metals in GRA 95209 in a portion of thick metal vein and adjacent metal-rich (30-40 modal%), sulfide poor (less than 1%) matrix by EPMA and LA-ICP-MS for major and trace siderophile elements using methods described by [3]. We also examined metals from a metal-poor (approximately 15 modal%) and relatively sulfide-rich (2-5 modal%) region of the sample. Kamacite is the dominant metal phase in all portions of the sample. In comparison to matrix metal, vein metal contains more schreibersite and less tetrataenite, and is less commonly associated with Fe,Mn,Mg-bearing phosphates and graphite. Vein kamacite contains higher Co, P, and Cr and lower Cu and Ge. These minor variations aside, all metal types in GRA 95209 are fairly homogeneous in terms of their levels of enrichment of compatible siderophile elements (e.g. Pt, Ir, Os) relative to incompatible siderophile elements (e.g. As, Pd, Au), consistent with the loss of metal-sulfide partial melt that characterizes much of the clan. Whatever compositional differences between matrix and vein metal that may have originally existed, they have since largely co-equilibrated to similar restitic trace element compositions. We agree with [2] that metal veins, in their present state, do not represent a liquid composition. The original vein liquid was much more S-rich and emplaced at correspondingly lower liquid temperatures. Much of the Fe,Ni component solidified in cm scale conduits while S-rich melts were expelled and continued to migrate by percolation. The higher troilite content in metal poor regions of the sample results mostly from trapping of a small portion of these melts. The troilite is not remnant primary sulfide. Strong depletions of W, Mo, and especially Ga (greater than 50%, greater than 60%, and greater than 90% depletion, respectively) in metals of the metalpoor GRA 95209 lithology are localized at scales of 10-100 micrometers in the vicinity of graphite spherules. These depletions must have occurred below the temperatures at which cm-scale equilibration occurred, and future work will seek to determine their cause.

Herrin, J. S.↗

NASA NTRS1988

Addressable Inverter Matrix Tests Integrated-Circuit Wafer

Addressing elements indirectly through shift register reduces number of test probes. With aid of new technique, complex test structure on silicon wafer tested with relatively small number of test probes. Conserves silicon area by reduction of area devoted to pads. Allows thorough evaluation of test structure characteristics and of manufacturing process parameters. Test structure consists of shift register and matrix of inverter/transmission-gate cells connected to two-by-ten array of probe pads. Entire pattern contained in square area having only 1.6-millimeter sides. Shift register is conventional static CMOS device using inverters and transmission gates in master/slave D flip-flop configuration.

Buehler, Martin G.↗

NASA NTRS1990

The effect of weak interface on transverse properties of a ceramic matrix composite

Experimental studies conducted at NASA Lewis on SiC reaction-bonded Si3N4 composite system showed that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. It was believed that weakened interfaces were responsible for the decrease in tranverse properties. To support this claim, a two-dimensional FEM analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented using active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, it is found that little or no interfacial bonding exists in the composite, and that an elastic analysis can predict the transverse stiffness and strength.

Shimansky, R. A.↗

NASA NTRS1992

On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure

The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.

Gupta, K. K.↗

DOE OSTI2021

Reduction of the molecular hamiltonian matrix using quantum community detection

Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1998

Microwave Imaging on Metal Objects

This final report for the project discusses the attempts to model, using different methods, microwave image reconstruction. Maximum Entropy Method was not successful. Attempts to use Singular Value Decomposition (SVD) got some good results after initial failure. SVD is based upon a theory of linear algebra, to the effect that any M X N Matrix A whose number of rows M is greater than or equal to its number of columns, N can be written as the product of an M X N column-orthogonal matrix U, an N X N diagonal Matrix, W, with m positive or zero elements (the singular values) and the transposition of an N X N orthogonal matrix V. In microwave imaging, the scattered fields can be expressed by the induced current distribution. The SVD method required more contiguous computer memory than was available. Work was also done on the Conjugate Gradient Method (CGM), which didn't work well when tried earlier. It was found that separation of the imaginary part and the real part during calculation may work. This work was considered incomplete as of the end of the grant period.

Tolliver, C. L.↗

NASA NTRS2016

Hydrogen Isotopic Composition of Apatite in Northwest Africa 7034: A Record of the "Intermediate" H-Isotopic Reservoir in the Martian Crust?

Northwest Africa (NWA) 7034 and its pairings comprise a regolith breccia with a basaltic bulk composition [1] that yields a better match than any other martian meteorite to visible-infrared reflectance spectra of the martian surface measured from orbit [2]. The composition of the fine-grained matrix within NWA 7034 bears a striking resemblance to the major element composition estimated for the martian crust, with several exceptions. The NWA 7034 matrix is depleted in Fe, Ti, and Cr and enriched in Al, Na, and P [3]. The differences in Al and Fe are the most substantial, but the Fe content of NWA 7034 matrix falls within the range reported for the southern highlands crust [6]. It was previously suggested by [4] that NWA 7034 was sourced from the southern highlands based on the ancient 4.4 Ga ages recorded in NWA 7034/7533 zircons [4, 5]. In addition, the NWA 7034 matrix material is enriched in incompatible trace elements by a factor of 1.2-1.5 [7] relative to estimates of the bulk martian crust. The La/Yb ratio of the bulk martian crust is estimated to be approximately 3 [7], and the La/Yb of the NWA 7034 matrix materials ranges from approximately 3.9 to 4.4 [3, 8], indicating a higher degree of LREE enrichment in the NWA 7034 matrix materials. This elevated La/Yb ratio and enrichment in incompatible lithophile trace elements is consistent with NWA 7034 representing a more geochemically enriched crustal terrain than is represented by the bulk martian crust, which would be expected if NWA 7034 represents the bulk crust from the southern highlands. Given the similarities between NWA 7034 and the martian crust, NWA 7034 may represent an important sample for constraining the composition of the martian crust, particularly the ancient highlands. In the present study, we seek to constrain the H isotopic composition of the martian crust using Cl-rich apatite in NWA 7034. Usui et al., [9] recently proposed that a H isotopic reservoir exists within the martian crust that has a H-isotopic composition that is intermediate (δD of 1000-2000per mille) between an isotopically light mantle (Delta D is less than 275per mille [10]) and an isotopically heavy atmosphere (δD of 2500-6100per mille [11, 12]). Apatites in NWA 7034 occur in a number of lithologic domains, however apatites across all lithologic domains have been affected by a Pb-loss event at about 1.5 Ga before present [5], so they are unlikely to have retained a primary composition and are more likely to have equilibrated with fluids within the martian crust that may or may not have exchanged with the martian atmosphere. Equilibration of apatite with crustal fluids is further supported by the chlorine-rich compositions exhibited by apatites in NWA 7034 in comparison to apatites from other martian meteorites (Figure 1; [13]). Cl is more hydrophilic than F, which promotes formation of Cl-rich apatite compositions in fluid-rich systems [e.g., 14, 15-17].

McCubbin, F. M.↗

NASA NTRS1978

Petrology of Apollo 16 breccia 66075

66075 is a coherent, light matrix breccia with a seriate fabric and is composed of large lithic, mineral and glass clasts in a matrix of lithic, mineral and glass fragments. The lithic clasts are ANT-suite rocks and a texturally diverse suite of impact-generated melt-rocks. The mineral fragments in the matrix and the mineral clasts are mostly plagioclase with subordinate amounts of pyroxene and olivine. The mineral compositions and/or bulk compositions of most of the components of the breccia, as well as the U-Pb isotopic systematics, are compatible with an origin involving impact-melting and fragmentation of an ANT-suite protolith. The major element composition of the breccia matrix can be successfully modeled in terms of mixing the observed clast types. Previously suggested components such as 'dunite' and 'KREEP' are absent or occur in very low abundance.

Quick, J. E.↗

NASA NTRS2012

Deducing Wild 2 Components with a Statistical Dataset of Olivine in Chondrite Matrix

Introduction: A preliminary exam of the Wild 2 olivine yielded a major element distribution that is strikingly similar to those for aqueously altered carbonaceous chondrites (CI, CM, and CR) [1], in which FeO-rich olivine is preferentially altered. With evidence lacking for large-scale alteration in Wild 2, the mechanism for this apparent selectivity is poorly understood. We use a statistical approach to explain this distribution in terms of relative contributions from different chondrite forming regions. Samples and Analyses: We have made a particular effort to obtain the best possible analyses of both major and minor elements in Wild 2 olivine and the 5-30 micrometer population in chondrite matrix. Previous studies of chondrite matrix either include larger isolated grains (not found in the Wild 2 collection) or lack minor element abundances. To overcome this gap in the existing data, we have now compiled greater than 10(exp 3) EPMA analyses of matrix olivine in CI, CM, CR, CH, Kakangari, C2-ungrouped, and the least equilibrated CO, CV, LL, and EH chondrites. Also, we are acquiring TEM/EDXS analyses of the Wild 2 olivine with 500s count times, to reduce relative errors of minor elements with respect to those otherwise available. Results: Using our Wild 2 analyses and those from [2], the revised major element distribution is more similar to anhydrous IDPs than previous results, which were based on more limited statistics (see figure below). However, a large frequency peak at Fa(sub 0-1) still persists. All but one of these grains has no detectable Cr, which is dissimilar to the Fa(sub 0-1) found in the CI and CM matrices. In fact, Fa(sub 0-1) with strongly depleted Cr content is a composition that appears to be unique to Kakangari and enstatite (highly reduced) chondrites. We also note the paucity of Fa(sub greater than 58), which would typically indicate crystallization in a more oxidizing environment [3]. We conclude that, relative to the bulk of anhydrous IDPs, Wild 2 may have received a larger contribution from the Kakangari and/or enstatite chondrite forming regions. Alternatively, Wild 2 may have undergone accretion in an anomalously reducing region, marked by nebular condensation of this atypical forsterite. In [4], a similar conclusion was reached with an Fe-XANES study. We will also use similar lines of reasoning, and our previous conclusions in [5], to constrain the relative contributions of silicates that appear to have been radially transported from different ordinary and carbonaceous chondrite forming regions to the Kuiper Belt. In addition, the widespread depletion of Cr in these FeO-rich (Fa(sub greater than 20)) fragments is consistent with mild thermal metamorphism in Wild 2.

Frank, D. R.↗

NASA NTRS1984

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Casasent, D.↗