Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrices”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Moduli matrices of the vacua and walls on SO(2N)/U(N)

We construct parallel domain walls on the SO(2 N)/ U (N) manifold by using the moduli matrices, which were originally formulated on the Grassmann manifold. We propose a method to impose a quadratic constraint to the moduli matrices. This talk is based on [3]PRD83,125003(2011). This article is prepared for the proceedings of International Workshop on Supersymmetries and Quantum Symmetries-SQS 2011.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Computationally Efficient Decompositions of Oblique Projection Matrices

Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

±Characterization of Group V Dubnium Homologs on DGA Extraction Chromatography Resin from Nitric and Hydrofluoric Acid Matrices and Initial Investigation of Element 114 Homolog Ge

Studies of the chemical properties of superheavy elements (SHE) pose interesting challenges due to their short half-lives and low production rates. Chemical systems must have extremely fast kinetics, fast enough kinetics to be able to examine the chemical properties of interest before the SHE decays to another nuclide. To achieve chemistry on such time scales, the chemical system must also be easily automated. Most importantly however, a chemical system must be developed which provides suitable separation and kinetics before an on-line study of a SHE can be performed. Relativistic effects make studying the chemical properties of SHEs interesting due to the impact these effects could have on the SHEs chemical properties. Relativistic effects arise when the velocity of the s orbital electrons approach the speed of light. As this velocity increases, the Bohr radius of the inner electron orbitals decreases and there is an increase in the particles mass. This contraction results in a destabilization of the energy of the outer d and f electron orbitals (5f and 6d in the case of SHE), which can cause these to expand due to their increased shielding from the nuclear charge. Another relativistic effect is the spin-orbit splitting for p, d, and f orbitals into j = 1 1/2 states. This can lead most interestingly to a possible increased stability of element 114, which due to large spin-orbit splitting of the 7p orbital and the relativistically stabilized 7p 1/2 and 7s orbital gives rise to a closed shell ground state of 7s 2 7p 1/2 2 . The homologs of element 105, dubnium (Db), Ta and Nb and the pseudo-homolog Pa, are well known to hydrolyze and form both neutral and non-neutral monoatomic and polyatomic species that may cause issues with extraction from a given chemical system. Early ion-exchange and solvent-extraction studies show mixed results for the behavior of Db. Some studies show Db behaving most similar to Ta, while others show it behaving somewhere between Nb and Pa. Much more recent studies have examined the properties of Db from HNO 3 /HF matrices, and suggest Db forms complexes similar to those of Pa. Very little experimental work into the behavior of element 114 has been performed. Thermochromatography experiments of three atoms of element 114 indicate that the element 114 is at least as volatile as Hg, At, and element 112. Lead was shown to deposit on gold at temperatures about 1000 C higher than the atoms of element 114. Results indicate a substantially increased stability of element 114. No liquid phase studies of element 114 or its homologs (Pb, Sn, Ge) or pseudo-homologs (Hg, Cd) have been performed. Theoretical predictions indicate that element 114 is should have a much more stable +2 oxidation state and neutral state than Pb, which would result in element 114 being less reactive and less metallic than Pb. The relativistic effects on the 7p 1/2 electrons are predicted to cause a diagonal relationship to be introduced into the periodic table. Therefore, 114 2+ is expected to behave as if it were somewhere between Hg 2+ , Cd 2+ , and Pb 2+ . In this work two commercially available extraction chromatography resins are evaluated, one for the separation of Db homologs and pseudo?homologs from each other as well as from potential interfering elements such as Group IV Rf homologs and actinides, and the other for separation of element 114 homologs. One resin, Eichrom's DGA resin, contains a N,N,N',N'-tetra-n-octyldiglycolamide extractant, which separates analytes based on both size and charge characteristics of the solvated metal species, coated on an inert support. The DGA resin was examined for Db chemical systems, and shows a high degree of selectivity for tri-, tetra-, and hexavalent metal ions in multiple acid matrices with fast kinetics. The other resin, Eichrom's Pb resin, contains a di-t-butylcyclohexano 18-crown-6 extractant with isodecanol solvent, which separates analytes based on steric interactions between the cavity of the crown ether and electrostatic interactions between the oxygen's of the ether and cations in the mobile phase. This particular resin has been shown to have an extremely high uptake affinity for Pb, a direct homolog of element 114, and is thus a good initial extractant to examine for a potential element 114 chemical system. Figure 1.1 shows the respective extractant molecules from the DGA and Pb resins. Batch uptake experiments were conducted to examine the uptake behavior of Ta on the DGA resin. Batch uptake experiments were also conducted to examine the uptake behavior of Ge on the Pb resin. Column experiments were designed based on batch uptake experiments of Ta, Am, Pa, Np, Zr, and Nb to establish a sequential extraction of Group IV/V homologs as well as Am for potential use as a Db chemical system.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2011

Computation of Large Covariance Matrices by SAMMY on Graphical Processing Units and Multicore CPUs

Computational power of Graphical Processing Units and multicore CPUs was harnessed by the nuclear data evaluation code SAMMY to speed up computations of large Resonance Parameter Covariance Matrices (RPCMs). This was accomplished by linking SAMMY to vendor-optimized implementations of the matrix-matrix multiplication subroutine of the Basic Linear Algebra Library to compute the most time-consuming step. The U-235 RPCM computed previously using a triple-nested loop was re-computed using the NVIDIA implementation of the subroutine on a single Tesla Fermi Graphical Processing Unit, and also using the Intel's Math Kernel Library implementation on two different multicore CPU systems. A multiplication of two matrices of dimensions 16,000 x 20,000 that had previously taken days, took approximately one minute on the GPU. Similar performance was achieved on a dual six-core CPU system. The magnitude of the speed-up suggests that these, or similar, combinations of hardware and libraries may be useful for large matrix operations in SAMMY. Uniform interfaces of standard linear algebra libraries make them a promising candidate for a programming framework of a new generation of SAMMY for the emerging heterogeneous computing platforms.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2018

Universality for 1d Random Band Matrices: Sigma-Model Approximation

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233–1260, 2016; Commun Math Phys 351:1009–1044, 2017). We consider random Hermitian block band matrices consisting of W×W random Gaussian blocks (parametrized by j,k∈Λ=[1,n]{sup d}∩ℤ{sup d}) with a fixed entry’s variance J{sub jk}=δ{sub j,k}W{sup −1}+βΔ{sub j,k}W{sup −2}, β>0 in each block. Taking the limit W→∞ with fixed n and β, we derive the sigma-model approximation of the second correlation function similar to Efetov’s one. Then, considering the limit β,n→∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β≫n, is determined by the classical Wigner–Dyson statistics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Radium-226 analysis methodology in Savannah River Site high activity waste matrices

Waste cleanup efforts currently underway at the Savannah River Site have created a need to characterize Radium-226 levels in the various high activity waste matrices currently in Site inventories. Here, the traditional method our laboratory used for analyzing Ra-226 in higher activity matrices was based on classic cation exchange methodology. Radiochemical separations were often initiated in remotely operated shielded analytical cells followed by additional hands-on separations in radiological hoods. Methodology based on IBC advanced technologies SuperLig 640 extractant, mounted in 3M Empore filter media has been developed to streamLine the radium analyses.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2018

Matrix Assisted and/or Laser Desorption Ionization Quadrupole Ion Trap Time-of-Flight Mass Spectrometry of WO{sub 3} Clusters Formation in Gas Phase. Nanodiamonds, Fullerene, and Graphene Oxide Matrices

The formation of W{sub x}O{sub y}{sup +●/-●} clusters in the gas phase was studied by laser desorption ionization (LDI) and matrix assisted laser desorption ionization (MALDI) of solid WO{sub 3}. LDI produced (WO{sub 3}){sub n}{sup +●/-●} (n = 1-7) clusters. In MALDI, when using nano-diamonds (NDs), graphene oxide (GO), or fullerene (C{sub 60}) matrices, higher mass clusters were generated. In addition to (WO{sub 3}){sub n}{sup -●} clusters, oxygen-rich or -deficient species were found in both LDI and MALDI (with the total number of clusters exceeding one hundred ≈ 137). This is the first time that such matrices have been used for the generation of(WO{sub 3}){sub n}{sup +●/-●} clusters in the gas phase, while new high mass clusters (WO{sub 3}){sub n}{sup -●} (n = 12-19) were also detected. .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Effective construction of eigenvectors for a class of singular sparse matrices

Fundamental results and an efficient algorithm for constructing eigenvectors corresponding to non-zero eigenvalues of matrices with zero rows and/or columns are developed. The formulation is built on the relation between eigenvectors of such matrices and the eigenvectors of their submatrices after removing all zero rows and columns. While being easily utilized, the algorithm decreases the computation time needed for numerical eigenanalysis, and resolves potential numerical eigensolver instabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of φ $-$functions of matrices via quadrature

Here, in this article, we propose an algorithm for approximating the action of φ $-$ functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the φ $-$ functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Bayesian Evaluation Including Covariance Matrices of Neutron-induced Reaction Cross Sections of {sup 181}Ta

A new evaluation of neutron-induced reactions on {sup 181}Ta using a consistent procedure based on Bayesian statistics is presented. Starting point of the evaluation is the description of nuclear reactions via nuclear models implemented in TALYS 1.4. A retrieval of experimental data was performed and covariance matrices of the experiments were generated from an extensive study of the corresponding literature. All reaction channels required for a transport file up to 200 MeV have been considered and the covariance matrices of cross section uncertainties for the most important channels are determined. The evaluation has been performed in one step including all available experimental data. A comparison of the evaluated cross sections and spectra with experimental data and available evaluations is performed. In general the evaluated cross section reflect our best knowledge and give a fair description of the observables. However, there are few deviations from expectation which clearly indicate the impact of the prior and the need to account for model defects. Using the results of the evaluation a complete ENDF-file similarly to those of the TENDL library is generated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A data analysis method to rapidly characterize gallium concentration in plutonium matrices using LIBS

The processing of actinide samples is a complex and costly endeavor that requires compositional analysis at various stages. Laser-induced breakdown spectroscopy (LIBS) has been used to analyze actinide-containing samples in many nuclear applications including waste management, fuel processing and forensics. The LIBS spectrum obtained from actinide materials are generally extremely complex, exhibiting many thousands of strong emission lines. This makes it difficult to identify other elements within the sample of interest, given the rich and dominant actinide spectrum. Here, in this article, we describe a recent effort to identify and quantify impurities and alloying constituents in plutonium matrices using a hand-held LIBS instrument that is used to rapidly and efficiently measure an emission spectrum from a material sample. We tabulate the emission line positions and intensities of plutonium. We report the development of machine-learning software that can identify gallium and quantify its concentration in plutonium matrices. This work has the potential to provide a rapid and nearly non-destructive technique that allows more confidence in characterizing the composition of materials that are present within complex actinide associated targets. We describe how our LIBS measurements and data analysis methods have successfully quantified the gallium concentration in a variety of samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Current and future federal and state sampling guidance for per- and polyfluoroalkyl substances in environmental matrices

Per- and polyfluoroalkyl substances (PFAS) are a class of emerging contaminants composed of an estimated 5000 to 10,000 human-made, fluorinated, organic chemicals. Due to the complexity of PFAS, the need for multiple environmental matrix considerations and the absence of a promulgated federal standard for environmental sampling and analysis, U.S. states have begun developing health-based regulatory and/or guidance values for a limited number of PFAS in environmental matrices. As there is a growing body of science to inform PFAS sampling guidance standard development, it is important to understand which U.S. states are implementing sampling guidelines and how they plan to handle emerging PFAS. This critical review discusses the current and impending federal and state sampling guidelines for PFAS in environmental matrices, the data gaps surrounding PFAS sampling guidance in U.S. states, and the future impacts of impending guidance documents and regulations. Ten federal guidance documents are available for PFAS sampling guidance and analysis. The maximum number of PFAS covered in these guidance documents is 25 analytes spanning across 8 unique media. While the EPA has developed several different sampling and analytical guidelines for PFAS, there is no formal regulation of PFAS or requirements of states to enforce these guidelines. Consequently, only 31 states have informally adopted sampling guidelines, while the other 19 states have no guidance documentation in place for PFAS. The introduction of new PFAS sampling guidelines by the EPA, as well as updated analytical guidelines that target more PFAS or total organofluoride, is expected to continuously shift the landscape of federal and state guidance for PFAS sampling moving forward.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices

One-particle transition density matrices and natural transition orbitals enable quantitative description of electronic transitions and interstate properties involving correlated many-body wave functions within molecular orbital framework. In this work we extend the formalism to the analysis of tensor properties, such as spin–orbit couplings (SOCs), which involve states of different spin projection. By using spinless density matrices and Wigner–Eckart’s theorem, the approach allows one to treat the transitions between states with arbitrary spin projections in a uniform way. In addition to a pictorial representation of the transition, the analysis also yields quantitative contributions of hole-particle pairs into the overall many-body matrix elements. Specifically, it helps to rationalize the magnitude of computed SOCs in terms of El-Sayed’s rules. The capabilities of the new tool are illustrated by the analysis of the equation-of-motion coupled-cluster calculations of two transition metal complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Carbamoylation as an Effective Tool in the Analysis of the Soman Nerve Agent Marker Pinacolyl Alcohol in Soil Matrices by EI-GC-MS and LC-HRMS

Pinacolyl alcohol (PA) is a Schedule 2 chemical commonly featured in most proficiency tests (PTs) administered by the Organisation for the Prohibition of Chemical Weapons (OPCW) due to its direct as well as forensic link to the nerve agent Soman. Therefore, its detection by Chemical Weapons Convention (CWC) inspection teams during on-site investigations is a strong indicator of the past or latent presence of Soman in the environment. Its small molecular weight (102), early elution time, and poor ionization profile make PA a challenging analyte to detect particularly at low concentrations (∼1–10 μg/g). In this work, 1,1′-carbonyldimidazole (CDI) has been used to effectively modify PA for the first time in two different soil matrices (Virginia type A soil and silt sediment) at two separate concentrations (1 and 10 μg/g) for its subsequent detection by EI-GC-MS and LC-HRMS methods. For the EI-GC-MS analysis, the PA carbamate derivative (PIC) exhibits improved chromatography relative to PA such as improved peak shape, increased molecular weight (196 for PIC and 102 for PA) and increased retention time (16.9 min for PIC and ∼4.1 min for PA). In addition, the derivatization also improves the detection of PA by LC-HRMS as the PIC product possesses protonation sites (i.e., imidazole ring) relative to none exhibited by PA. More importantly, the carbamoylation proceeds under mild conditions (55 °C, no base) and rapidly (3 h), characteristics that make it an appealing protocol for the analysis of PA during OPCW PTs or real case scenarios particularly in instances where it is present at low concentrations. It is anticipated that the protocol can be applied to the forensic analysis of this important Soman marker in various environmental matrices.

Chemistry↗
DOE OSTI2013

Very Stable Electron Field Emission From Strontium Titanate Coated Carbon Nanotube Matrices With Low Emission Thresholds

PMMA-STO-CNT matrices were created by opened-tip vertically-aligned multiwalled carbon nanotubes (VA-MWCNTs) with conformal coating of strontium titanate and Poly(methyl methacrylate). Emission threshold of 0.8 V/μm was demonstrated, about five-fold lower than that of the as-grown VAMWCNTs. Theoretical simulation and modeling suggest that PMMA-STO-CNT matrices have suppressed screening effects and Coulombs’ repulsion forces between electrons in adjacent CNTs, leading to low emission threshold, high emission density, and prolong emission stability. These findings are important for practical application of VA-MWCNTs in field emission devices.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2012

Dirac matrices for Chern-Simons gravity

A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The multifacet graphically contracted function method. II. A general procedure for the parameterization of orthogonal matrices and its application to arc factors

Practical algorithms are presented for the parameterization of orthogonal matrices Q ∈ R {sup m×n} in terms of the minimal number of essential parameters (φ). Both square n = m and rectangular n < m situations are examined. Two separate kinds of parameterizations are considered, one in which the individual columns of Q are distinct, and the other in which only Span(Q) is significant. The latter is relevant to chemical applications such as the representation of the arc factors in the multifacet graphically contracted function method and the representation of orbital coefficients in SCF and DFT methods. The parameterizations are represented formally using products of elementary Householder reflector matrices. Standard mathematical libraries, such as LAPACK, may be used to perform the basic low-level factorization, reduction, and other algebraic operations. Some care must be taken with the choice of phase factors in order to ensure stability and continuity. The transformation of gradient arrays between the Q and (φ) parameterizations is also considered. Operation counts for all factorizations and transformations are determined. Numerical results are presented which demonstrate the robustness, stability, and accuracy of these algorithms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Boundary transfer matrices and boundary quantum KZ equations

A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗