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At least 235 records · Page 13

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NASA NTRS1972

Digital modeling of human operator dynamics via class of Liapunov functions

A technique is described which is utilized for modeling human operator dynamics. The technique is based upon a model-reference system configuration and a class of Liapunov functions formulated for this purpose which possess variable characteristics. It is shown how such a class of Liapunov functions and their time derivatives is formulated. The crux of the formulation lies in three variable positive definite matrices used for the construction of the class of Liapunov functions. The form and order of these matrices depend upon the form and order of the error differential equation of the human operator model-reference system. These matrices can be modified to include nonlinear functions of the human operator model.

Mekel, R.↗

NASA NTRS1985

Derivation of jack movement influence coefficients as a basis for selecting wall contours giving reduced levels of interference in flexible walled test sections

This report covers work done in a transonic wind tunnel towards providing data on the influence of the movement of wall-control jacks on the Mach number perturbations along the test section. The data is derived using an existing streamline-curvature program, and in application is reduced to matrices of influence coefficients.

Goodyer, M. J.↗

NASA NTRS1985

Standard profiles of ozone from ground to 60 km obtained by combining satellite and ground based measurements

A study is reported based on four years of SBUV data and five years of published ozonesonde data. The Solar Backscatter Ultraviolet Experiment (SBUV), has been operating continuously since November 1978, providing some 1000 profiles per day. The data are of excellent quality from about 50 km down to the tropopause. By combining the satellite-derived data with ozonesonde data, a data base of standard ozone profiles and variance/covariance matrices has been developed, defining the observed variation of the atmospheric ozone around the mean profiles. Highlights of the data base are presented along with parameters of an analytical fit that describes the essential features of the data set. Although the data base was created specifically for use as a priori profiles for SBUV and Umkehr retrievals, it should be useful in other remote sensing applications and in modeling the UV radiation fields in the stratosphere. Another suggested application is in estimating ozone above the peak altitude of the ozone balloons.

Bhartia, P. K.↗

NASA NTRS1992

A comparison of the chemistry of pseudotachylyte breccias in the Archean Levack Gneisses of the Sudbury structure, Ontario

The Archean Levack Gneisses of the North Range host millimeter-thick veins and centimeter-thick lenses of pseudotachylyte, as well as substantially larger meter-wide, dykelike bodies of pseudotachylytic 'breccia'. The 'breccia' occurs up to several tens of kilometers away from the Sudbury Igneous Complex and is commonly sited within or near joints and other natural weaknesses such as bedding, dyke contacts, and lithological boundaries. The larger 'breccia' dykes comprise a generally dark matrix containing rounded to subrounded and occasionally angular rock fragments derived predominantly from Levack Gneiss. Selected samples of bulk Sudbury Breccia and Sudbury Breccia matrices were chemically analyzed and compared to existing data on the Levack Gneisses and Sudbury Breccia. The matrices are apparently enriched in Fe and, to a lesser extent, Mg, Ti, and Ca compared to the wallrocks and the majority of clasts. This enrichment can be partly explained by the preferential cataclasis and/or frictional melting of hydrous ferromagnesian wallrock minerals, but also appear to require contamination by more basic exotic lithologies. This suggests that certain components of pseudotachylitic Sudbury Breccia have undergone significant transport during their formation.

Thompson, Lucy M.↗

NASA NTRS1988

Derivatives of eigenvalues and eigenvectors of a general complex matrix

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Murthy, Durbha V.↗

NASA NTRS1973

Development of polyphenylquinoxaline graphite composites

The potential of polyphenylquinoxaline (PPQ)/graphite composites to serve as structural material at 316 C (600 F)has been demonstrated using a block copolymer, BlCo(13), PPQ derivative. Initially, thirteen polyphenylquinoxalines were evaluated. From this work, four candidate polymers were selected for preliminary evaluation as matrices for HMS graphite fiber reinforced composites. The preliminary composite evaluation enabled selection of one of the four polymers for advanced composite preparation and testing. Using an experimentally established cure schedule for each of the four polymers, preliminary laminates of 50% resin volume content, prepared without postcure, were tested for flexure strength and modulus, interlaminar shear strength (short beam), and tensile strength and modulus at ambient temperature. A block copolymer (Bl Co 13) derived from one mole p-bis (phenylglyoxalyl) benzene, one fourth mole 3,3'-diaminobenzidine and three-fourths mole 3,3', 4,4'-tetraminobenzophenone was selected for extensive study. Tensile, flexural, and interlaminar shear values were obtained after aging and testing postcured BlCo(13) laminates at 316 C (600 F). The potential of PPQ/graphite laminates to serve as short term structural materials at temperatures up to 371 C (700 F) was demonstrated through weight loss experiments.

Hoggatt, J. T.↗

DOE OSTI2020

Nucleophilic Thiols Reductively Cleave Ether Linkages in Lignin Model Polymers and Lignin

Lignin may serve as a renewable feedstock for the production of chemicals and fuels if mild, scalable processes for its depolymerization can be devised. The use of small organic thiols represents a bioinspired strategy to cleave the β–O–4 bond, the most common linkage in lignin. In the present study, synthetic β–O–4 linked polymers were treated with organic thiols, yielding up to 90 % cleaved monomer products. Lignin extracted from poplar was also treated with organic thiols resulting in molecular weight reductions as high as 65 % (Mn) in oxidized lignin. Thiol–based cleavage of other lignin linkages was also explored in small–molecule model systems to uncover additional potential pathways by which thiols might depolymerize lignin. The success of thiol–mediated cleavage on model dimers, polymers, and biomass–derived lignin illustrates the potential utility of small redox–active molecules to penetrate complex polymer matrices for depolymerization and subsequent valorization of lignin into fuels and chemicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Quantum Fourier transform revisited

Summary The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank‐1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix‐2 QFT decomposition to a radix‐ d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view.

Camps, Daan↗

DOE OSTI2024

Square Root Statistics of Density Matrices and Their Applications

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Modal identification using single-mode projection filters and comparison with ERA and MLE results

The Single-Mode Projection Filter (SPF) is a newly developed algorithm for eigensystem parameter identification from both analytical results and test data. The SPF is formulated with a single mode only and practical for parallel processing implementation. Explicit formulations of SPF are derived for the multi-input multi-output (MIMO) system by using the orthogonal matrices of the controllability and observability matrices in the general sense. The modal parameters of SPF are initially obtained from an analytical model in modal space. The experimental data are then processed through SPF to update its modal parameters and to minimize a cost function defined by the norm of an error matrix. The updated modal parameters represent the characteristics of the test data. A two-dimensional global minimum optimization algorithm is developed and applied for the filter update by using the interval analysis method. The SPF is developed based on a single-mode subsystem and identifies only one modal frequency and one modal damping within a specified region. For an n-modes structure, n SPF can be implemented for parallel processing to reduce the computational burden. The SPF is applied to analyze the simulated data for the MAST beam structure. The estimated modal parameters are comparable to those from the Eigensystem Realization Algorithm (ERA) and repeated modal frequencies are identified. The modal analysis of the Spacecraft Control Laboratory Experiment (SCOLE) data is also performed by using the ERA and the Maximum Likelihood Estimate (MLE). The result shows that the first five modal frequencies are very close from ERA and MLE. However, there are slight disparities in the damping rates and the computational burdens are quite different among these two algorithms.

Huang, Jen-Kuang↗

NASA NTRS1997

Recursive Deadbeat Controller Design

This paper presents a recursive algorithm for a deadbeat predictive controller design. The method combines together the concepts of system identification and deadbeat controller designs. It starts with the multi-step output prediction equation and derives the control force in terms of past input and output time histories. The formulation thus derived satisfies simultaneously system identification and deadbeat controller design requirements. As soon as the coefficient matrices are identified satisfying the output prediction equation, no further work is required to compute the deadbeat control gain matrices. The method can be implemented recursively just as any typical recursive system identification techniques.

Juang, Jer-Nan↗

NASA NTRS1999

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

Liu, Chao-Qun↗

NASA NTRS2022

In Situ Measurements of Surface Texture with Virtual Environments Support Science-Driven Human Surface Operations on the Moon and Beyond

Visualization tools enabling real-time scientific analysis are important for supporting future astronaut operations on the lunar surface. Such tools can be built into virtual environments to support scientific investigations, as well as situational awareness, real-time decision making, and efficient communication between astronauts and ground and support systems. Understanding how these tools can be optimized for science is essential for upcoming Artemis missions. In this contribution, we discuss how measurements of surface texture at multiple length scales can greatly enhance in situ science on/of the Moon, and eventually Mars, asteroids, and beyond. Roughness measurements at various wavelengths directly support objectives defined in the Artemis Science Plan, including (O1) “understanding planetary processes,” (O2) “understanding volatile cycles,” and (O3) “interpreting the impact history of the Earth-Moon system” . Key scientific analyses enabled by texture measurements at different length scales include: ● Sub-centimeter scales: Texture measurements can help constrain lava flow crystallinity, lava rheology, emplacement flow dynamics, and cooling histories (O1). Measurements of lacunarity (voids in fractal fill space) can shed light on eruptive volatile content, residence time of migrating volatiles, and near-surface volume available for micro-cold trapping of volatiles (O1, O2). ● Centimeter–meter scales: Texture measurements can be used for the differentiation of individual lava flows, the reconstruction of local stratigraphies and emplacement sequences, characterization of post-emplacement surface modification processes (O1, O3). Derived roughness (polarization) metrics can be used in the detection of water ice and characterization of ice properties (e.g., purity, grade, depth, abundance). ● Hectometer–Kilometer scales: Texture measurements can be used to differentiate major geologic surface units and surface structures (O1), constrain the presence of abundant ground ices (O2), and analyze surface modification and estimate surface age (O3). Real-time measurements of surface texture across these multiple length scales will enable efficient sample identification and scientific investigations by future astronauts. To support these investigations and the objective classification of surface texture, virtual environments employed by astronauts should be able to instantaneously convert raw data into processed data (e.g., digital terrain and elevation models) and derived metrics (e.g., RMS, std, Hurst, CPR) and perform statistical analyses (e.g., PCA, outliers, correlation matrices). Such tools are being developed and tested by the Resource Exploration and Science of our Cosmic Environment (RESOURCE) team, a node of NASA’s Solar System Exploration Research Virtual Institute (SSERVI), and are an excellent example of the powerful synergies of human and robotic ground assets critical in the return of humans to the Moon.

Ariel N. Deutsch↗

NASA NTRS1994

Electronic absorption spectroscopy of matrix-isolated polycyclic aromatic hydrocarbon cations. II. The phenanthrene cation (C14H10+) and its 1-methyl derivative

The ultraviolet, visible, and near infrared absorption spectra of phenanthrene (C14H10), 1-methylphenanthrene [(CH3)C14H9], and their radical ions [C14H10+; (CH3)C14H9+], formed by vacuum-ultraviolet irradiation, were measured in neon matrices at 4.2 K. The associated vibronic band systems and their spectroscopic assignments are discussed. The oscillator strengths were calculated for the phenanthrene ion and found lower than the theoretical predictions. This study presents the first spectroscopic data for phenanthrene and its methyl derivative trapped in a neon matrix where the perturbation of the isolated species by its environment is minimum; a condition crucial to astrophysical applications.

NASA Discipline Exobiology↗

NASA NTRS1985

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. A type of differentiating matrix based on local approximation on a sequence of sliding subgrids is considered. Previous derivations of this type of matrix have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The new formulation allows grids which have arbitrarily space points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids which include near-boundary points. Use of the differentiating matrix as an operator to solve eigenvalue problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗

DOE OSTI2020

Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

The paper reports development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), a new relativistic quantum-chemical method for treating spin-orbit coupling in molecules. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. In conclusion, to demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1977

Chemiluminescent reactions of sulfur /3P2/ atoms in cryogenic matrices - S + O2 yields SO2 /a3 B1/

Results are reported for thermoluminescence studies of reactions of sulfur atoms in cryogenically deposited solid argon through in situ photolysis of OCS. Analysis of the thermoluminescence spectrum that resulted from photolysis and heating of matrices in which O2 was codeposited with an OCS/Ar mixture shows that the emitter contained oxygen derived from the added O2 and that little SO2 accumulated during photolysis. The observed absence of thermoluminescence or fluorescence in either of the allowed transitions of excited SO2 is taken as definitive evidence that ground-state sulfur atoms can insert into the oxygen molecule with effectively zero activation energy.

Long, S. R.↗