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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2010

Tridiagonal realization of the antisymmetric Gaussian {beta}-ensemble

The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter {beta}, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q{sub i}), the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and (q{sub i}). The third proof maps matrices from the antisymmetric Gaussian {beta}-ensemble to those realizing particular examples of the Laguerre {beta}-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Evaluation of the accuracy of an offline seasonally-varying matrix transport model for simulating ideal age

Newton-Krylov solvers for ocean tracers have the potential to greatly decrease the computational costs of spinning up deep-ocean tracers, which can take several thousand model years to reach equilibrium with surface processes. One version of the algorithm uses offline tracer transport matrices to simulate an annual cycle of tracer concentrations and applies Newton’s method to find concentrations that are periodic in time. Here we present the impact of time-averaging the transport matrices on the equilibrium values of an ideal-age tracer. We compared annually-averaged, monthly-averaged, and 5-day-averaged transport matrices to an online simulation using the ocean component of the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels. We found that increasing the time resolution of the offline transport model reduced a low age bias from 12% for the annually-averaged transport matrices, to 4% for the monthly-averaged transport matrices, and to less than 2% for the transport matrices constructed from 5-day averages. The largest differences were in areas with strong seasonal changes in the circulation, such as the Northern Indian Ocean. As a result, for many applications the relatively small bias obtained using the offline model makes the offline approach attractive because it uses significantly less computer resources and is simpler to set up and run.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Matrix effect on vibrational frequencies: Experiments and simulations for HCl and HNgCl (Ng = Kr and Xe)

We study the environmental effect on molecules embedded in noble-gas (Ng) matrices. The experimental data on HXeCl and HKrCl in Ng matrices is enriched. As a result, the H−Xe stretching bands of HXeCl are now known in four Ng matrices (Ne, Ar, Kr, and Xe), and HKrCl is now known in Ar and Kr matrices. The order of the H−Xe stretching frequencies of HXeCl in different matrices is ν(Ne) < ν(Xe) < ν(Kr) < ν(Ar), which is a non-monotonous function of the dielectric constant, in contrast to the “classical” order observed for HCl: ν(Xe) < ν(Kr) < ν(Ar) < ν(Ne). The order of the H−Kr stretching frequencies of HKrCl is consistently ν(Kr) < ν(Ar). These matrix effects are analyzed theoretically by using a number of quantum chemical methods. The calculations on these molecules (HCl, HXeCl, and HKrCl) embedded in single Ng{sup ′} layer cages lead to very satisfactory results with respect to the relative matrix shifts in the case of the MP4(SDQ) method whereas the B3LYP-D and MP2 methods fail to fully reproduce these experimental results. The obtained order of frequencies is discussed in terms of the size available for the Ng hydrides in the cages, probably leading to different stresses on the embedded molecule. Taking into account vibrational anharmonicity produces a good agreement of the MP4(SDQ) frequencies of HCl and HXeCl with the experimental values in different matrices. This work also highlights a number of open questions in the field.

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

Wall-crossing invariants: from quantum mechanics to knots

We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones (N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Approaches to optimization of SS/TDMA time slot assignment

Reduction techniques for traffic matrices are explored in some detail. These matrices arise in satellite switched time-division multiple access (SS/TDMA) techniques whereby switching of uplink and downlink beams is required to facilitate interconnectivity of beam zones. A traffic matrix is given to represent that traffic to be transmitted from n uplink beams to n downlink beams within a TDMA frame typically of 1 ms duration. The frame is divided into segments of time and during each segment a portion of the traffic is represented by a switching mode. This time slot assignment is characterized by a mode matrix in which there is not more than a single non-zero entry on each line (row or column) of the matrix. Investigation is confined to decomposition of an n x n traffic matrix by mode matrices with a requirement that the decomposition be 100 percent efficient or, equivalently, that the line(s) in the original traffic matrix whose sum is maximal (called critical line(s)) remain maximal as mode matrices are subtracted throughout the decomposition process. A method of decomposition of an n x n traffic matrix by mode matrices results in a number of steps that is bounded by n(2) - 2n + 2. It is shown that this upper bound exists for an n x n matrix wherein all the lines are maximal (called a quasi doubly stochastic (QDS) matrix) or for an n x n matrix that is completely arbitrary. That is, the fact that no method can exist with a lower upper bound is shown for both QDS and arbitrary matrices, in an elementary and straightforward manner.

Wade, T. O.↗
NASA NTRS1989

A gyroscope calibration analysis for the Gamma Ray Observatory (GRO)

Current documentation and software do not adequately address the calculation and use of the optimal weight matrices involved in calibrating inertial reference units (IRU). Several facets of the GRO IRU calibration as it relates to the bias and misalignment weighting matrices are investigated. The physical meaning and use of the bias and misalignment weight matrices in IRU calibration are examined. The relation of the weighting and the final biases, misalignments, and their corrections are pursued. Methods for determining reliable, realistic weighting matrices to be used in the GRO IRU calibration (IRUCAL) utility are determined. Possible correlations among observation uncertainties are also explored. For the undetermined case where the maneuvers are insufficient to identify all calibration parameters, the weighting matrices allow as much information as possible to be extracted from the measurements. Finally, applicable simulated flight data are used, incorporating the appropriate calibration maneuvers, to test the weighting matrices in the IRUCAL utility, and examine correlation effects.

Ketchum, Eleanor A.↗
NASA NTRS1996

The Infrared Spectra of Nitriles and Related Compounds Frozen in Ar and H2O

We present the 2320-2050/cm (4.31-4.88 micron) infrared spectra of 16 solid state nitrites, isonitriles, and related compounds in order to facilitate the assignment of absorption features in a spectral region now becoming accessible to astronomers for the first time through the Infrared Space Observatory (ISO). This frequency range spans the positions of the strong C(is congruent to)N stretching vibration of these compounds and is inaccessible from the ground due to absorption by CO2 in the terrestrial atmosphere. Band positions, profiles, and intrinsic strengths (A values) were measured for compounds frozen in Ar and H2O matrices at 12 K. The molecular species examined included acetonitrile, benzonitrile phenylcyanide) 9-anthracenecarbonitrile, dimethylcyanamide, isopropy1nitrile (isobutyronitrile), methylacrylonitrile, crotononitrile, acrylonitrile (vinyl cyanide), 3-aminocrotononitrile, pyr-uvonitrile, dicyandiamide, cyanamide, n-butyfisocyanide, methylisocyanoacetate, dilsopropylcarbodiimide, and hydrogen cyanide. The C(is congruent to)N stretching bands of the majority of nitrites fall in the 2300-2200/cm (4.35-4.55 micron) range and have similar positions in both Ar and H2O matrices, although the bands are generally considerably broader in the H2O matrices. In contest, the isonitriles and a few exceptional nitrites and related species produce bands at lower frequencies spanning the 2200-2080/cm (4.55-4.81 micron) range. These features also have similar positions in both Am and H2O matrices and the bands are broader in the H2O matrices. Three of the compounds (pyruvonitrile, dicyandiamide, and cyanamide) show unusually large shifts of their C(is congruent to)N stretching frequencies when changing from Ar to H2O matrices. We attribute these shifts to the formation of H2O:nitrile complexes with these compounds. The implications of these results for the identification of the 2165/cm (4.62 micron) "XCN" interstellar feature and the 4550/cm (2.2 micron) feature of various objects in the solar system are discussed.

Bernstain, Max P.↗
NASA NTRS1997

The infrared spectra of nitriles and related compounds frozen in Ar and H2O

We present the 2320-2050 cm-1 (4.31-4.88 micrometers) infrared spectra of 16 solid-state nitriles, isonitriles, and related compounds in order to facilitate the assignment of absorption features in a spectral region now becoming accessible to astronomers for the first time through the Infrared Space Observatory (ISO). This frequency range spans the positions of the strong C triple bond N stretching vibration of these compounds and is inaccessible from the ground due to absorption by CO2 in the terrestrial atmosphere. Band positions, profiles, and intrinsic strengths (A values) were measured for compounds frozen in Ar and H2O matrices at 12 K. The molecular species examined included acetonitrile, benzonitrile (phenylcyanide), 9-anthracenecarbonitrile, dimethylcyanamide, isopropylnitrile (isobutyronitrile), methylacrylonitrile, crotononitrile, acrylonitrile (vinyl cyanide), 3-aminocrotononitrile, pyruvonitrile, dicyandiamide, cyanamide, n-butylisocyanide, methylisocyanoacetate, diisopropylcarbodiimide, and hydrogen cyanide. The C triple bond N stretching bands of the majority of nitriles fall in the 2300-2200 cm-1 (4.35-4.55 micrometers) range and have similar positions in both Ar and H2O matrices, although the bands are generally considerably broader in the H2O matrices. In contrast, the isonitriles and a few exceptional nitriles and related species produce bands at lower frequencies spanning the 2200-2080 cm-1 (4.55-4.81 micrometers) range. These features also have similar positions in both Ar and H2O matrices, and the bands are broader in the H2O matrices. Three of the compounds (pyruvonitrile, dicyandiamide, and cyanamide) show unusually large shifts of their C triple bond N stretching frequencies when changing from Ar to H2O matrices. We attribute these shifts to the formation of H2O:nitrile complexes with these compounds. The implications of these results for the identification of the 2165 cm-1 (4.62 micrometers) "XCN" interstellar feature and the 4550 cm-1 (2.2 micrometers) feature of various objects in the solar system are discussed.

NASA Center ARC↗
NASA NTRS2014

High Temperature Lightweight Self-Healing Ceramic Composites for Aircraft Engine Applications

The present research effort was undertaken to develop a new generation of SiC fiber- reinforced engineered matrix composites (EMCs) with sufficient high temperature plasticity to reduce crack propagation and self-healing capabilities to fill surface-connected cracks to prevent the oxygen ingress to the fibers. A matrix engineered with these capabilities is expected to increase the load bearing capabilities of SiCSiC CMCs at high temperatures. Several matrix compositions were designed to match the coefficient of thermal expansion (CTE) of the SiC fibers using a rule of mixture (ROM) approach. The CTE values of these matrices were determined and it was demonstrated that they were generally in good agreement with that of monolithic SiC between room temperature and 1525 K. The parameters to hot press the powders were optimized, and specimens were fabricated for determining bend strength, CTE, oxidation and microstructural characteristics of the engineered matrices. The oxidation tests revealed that some of the matrices exhibited catastrophic oxidation, and therefore, these were eliminated from further consideration. Two promising compositions were down selected based on these results for further development. Four-point bend tests were conducted on these two promising matrices between room temperature and 1698 K. Although theses matrices were brittle and failed at low stresses at room temperature, they exhibited high temperature ductility and higher stresses at the higher temperatures. The effects of different additives on the self-healing capabilities of these matrices were investigated. The results of preliminary studies conducted to slurry and melt infiltration trials with CrSi2 are described.

Silicides↗
DOE OSTI2016

Mathematical foundations of the GraphBLAS

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This study provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Finally, performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Covariance Shaping Over Riemannian Manifolds for Massive MIMO Communication

Acquiring accurate instantaneous channel state information (CSI) is a challenging aspect of massive multi-input multi-output (MIMO) communication. Utilizing statistical information, such as channel covariance matrix, to design statistical beamforming vectors is robust when compared to instantaneous CSI. In this paper, we propose a novel MIMO covariance shaping scheme over Riemannian manifolds. It serves as an effective statistical beamforming solution to a number of close proximity user equipment (UE) that are undergoing substantial channel correlation. Proposed algorithm exploits the Hermitian positive definite nature of covariance matrices lying over Riemannian manifold. We introduce Wasserstein distance function as a Riemannian metric to measure distances between channel covariance matrices. Furthermore, K-means clustering technique is utilized to effectively identify the optimal shape of effective optimal covariance matrices. Our findings suggest that maximizing the geodesic distance between covariance matrices ultimately leads to a corresponding increase in the network throughput, as determined by the beamforming vector used to shape the covariance matrices. Simulation results validate that the proposed solution converges faster than Euclidean-based state-of-the-art, while maintaining the same computational complexity. Finally, the sum rate performance asymptotically achieves full capacity for two-UE case and more than 96% of the upper bound exhaustive search benchmark for multi-UE scenario.

42 ENGINEERING↗
DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The R-matrix bootstrap for the 2d O( N ) bosonic model with a boundary

The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

High performance sparse multifrontal solvers on modern GPUs

Here, we have ported the numerical factorization and triangular solve phases of the sparse direct solver STRUMPACK to GPU. STRUMPACK implements sparse LU factorization using the multifrontal algorithm, which performs most of its operations in dense linear algebra operations on so-called frontal matrices of various sizes. Our GPU implementation off-loads these dense linear algebra operations, as well as the sparse scatter–gather operations between frontal matrices. For the larger frontal matrices, our GPU implementation relies on vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs and rocBLAS and rocSOLVER for AMD GPUs. For the smaller frontal matrices we developed custom CUDA and HIP kernels to reduce kernel launch overhead. Overall, high performance is achieved by identifying submatrix factorizations corresponding to sub-trees of the multifrontal assembly tree which fit entirely in GPU memory. The multi-GPU setting uses SLATE (Software for Linear Algebra Targeting Exascale) as a modern GPU-aware replacement for ScaLAPACK. On 4 nodes of SUMMIT the code runs ~10X faster when using all 24 V100 GPUs compared to when it only uses the 168 POWER9 cores. On 8 SUMMIT nodes, using 48 V100 GPUs, the sparse solver reaches over 50TFlop/s. Compared to SuperLU, on a single V100, for a set of 17 matrices our implementation is faster for all but one matrix, and is on average 5X (median 4X) faster

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Influence of silica matrix composition and functional component additives on the bioactivity and viability of encapsulated living cells

The remarkable impact encapsulation matrix chemistry can have on the bioactivity and viability of integrated living cells is reported. Two silica chemistries (aqueous silicate and alkoxysilane), and a functional component additive (glycerol), are employed to generate three distinct silica matrices. These matrices are used to encapsulate living E. coli cells engineered with a synthetic riboswitch for cell-based biosensing. Following encapsulation, membrane integrity, reproductive capability, and riboswitch-based protein expression levels and rates are measured over a 5 week period. Striking differences in E. coli bioactivity, viability, and biosensing performance are observed for cells encapsulated within the different matrices. E. coli cells encapsulated for 35 days in aqueous silicate-based (AqS) matrices showed relatively low membrane integrity, but high reproductive capability in comparison to cells encapsulated in glycerol containing sodium silicate-based (AqS + g) and alkoxysilane-based (PGS) gels. Further, cells in sodium silicate-based matrices showed increasing fluorescence output over time, resulting in a 1.8-fold higher fluorescence level, and a faster expression rate, over cells free in solution. Furthermore, this unusual and unique combination of biological properties demonstrates that careful design of the encapsulation matrix chemistry can improve functionality of the biocomposite material, and result in new and unexpected physiological states.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2011

Physicochemical controls on absorbed water film thickness in unsaturated geological media

Adsorbed water films commonly coat mineral surfaces in unsaturated soils and rocks, reducing flow and transport rates. Therefore, it is important to understand how adsorbed film thickness depends on matric potential, surface chemistry, and solution chemistry. Here, the problem of adsorbed water film thickness is examined through combining capillary scaling with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Novel aspects of this analysis include determining capillary influences on film thicknesses, and incorporating solution chemistry-dependent electrostatic potential at air-water interfaces. Capillary analysis of monodisperse packings of spherical grains provided estimated ranges of matric potentials where adsorbed films are stable, and showed that pendular rings within drained porous media retain most of the 'residual' water except under very low matric potentials. Within drained pores, capillary contributions to thinning of adsorbed films on spherical grains are shown to be small, such that DLVO calculations for flat surfaces are suitable approximations. Hamaker constants of common soil minerals were obtained to determine ranges of the dispersion component to matric potential-dependent film thickness. The pressure component associated with electrical double layer forces was estimated using the compression and linear superposition approximations. The pH-dependent electrical double layer pressure component is the dominant contribution to film thicknesses at intermediate values of matric potential, especially in lower ionic strength solutions (< 10 mol m{sup -3}) on surfaces with higher magnitude electrostatic potentials (more negative than - 50 mV). Adsorbed water films are predicted to usually range in thickness from 1 to 20 nm in drained pores and fractures of unsaturated environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). Furthermore, this work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Grassmann interpolation method for spin-unrestricted open-shell systems

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice—one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg–Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Chemistry↗