Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix Theory”

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 1,693 records · Page 94
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Measurement of t -channel production of single top quarks and antiquarks in pp collisions at 13 TeV using the full ATLAS Run 2 data sample

The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using 140 fb -1 of ATLAS data. The total cross-sections are determined to be σ(tq) = 137$^{+8}_{-8}$ pb and σ($\bar{t}q$) = 84$^{+6}_{-5}$ pb for top-quark and top-antiquark production, respectively. The combined cross-section is found to be σ(tq + $\bar{t}q$) = 221$^{+13}_{-13}$ pb and the cross-section ratio is R t = σ(tq) / σ($\bar{t}q$) = 1.636$^{+0.036}_{-0.034}$. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of R t using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: -0.37 < C$^{3,1}_{Qq}$ /Λ 2 < 0.06 and -0.87 < C$^{3}_{ΦQ}$ / Λ 2 < 1.42. The constraint |V tb | > 0.95 at the 95% confdence level is derived from the measured value of σ(tq + $\bar{t}q$), assuming that the Wtb interaction is a left-handed weak coupling and that |V tb | $\gg$ |V td |, |V ts |. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confdence contours in the corresponding two-dimensional parameter spaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Data-assimilated time-lapse visco-acoustic full-waveform inversion: Theory and application for injected CO 2 plume monitoring

Continuous seismic monitoring for quantifying CO 2 plume migration and detection of any potential leakages in the subsurface is essential for the security of long-term anthropogenic carbon dioxide geologic storage. Traditional time-lapse full-waveform inversion (TLFWI) methods aim to map the CO 2 distribution by estimating seismic velocity changes, but recent studies find that CO 2 -induced attenuation is an important complement to seismic velocity for tracking the CO 2 plumes and even quantifying the CO 2 saturation. We have developed a novel data-assimilated TLFWI method to construct high-resolution time-lapse velocity and attenuation changes from dense time-lapse monitoring data. This method consists of two theoretical developments: visco-acoustic full-waveform inversion (QFWI) and multiparameter hierarchical matrix-powered extended Kalman filter (mHiEKF). The method is capable of (1) posing temporal constraints to retrieve time-lapse information from dense monitoring data by using mHiEKF, (2) accurately recovering high-spatial-resolution velocity and attenuation perturbations using first-order equation system-based QFWI, and (3) providing the model uncertainty by estimating their model standard deviation. With numerical examples, we first find the effectiveness of the new QFWI on estimating accurate velocity and attenuation models simultaneously. Then, a CO 2 leakage case and a realistic Frio-II CO 2 monitoring case are presented to find the advantages and applicability of our data-assimilated QFWI method for estimating time-lapse changes using dense time-lapse monitoring surveys. Here, by assimilating time-lapse seismic monitoring data over time, our data-assimilated QFWI method can improve the resolution of velocity and attenuation changes and decrease their model uncertainties.

58 GEOSCIENCES↗
NASA NTRS1972

Short-range correlations in carbon-12, oxygen-16, and neon-20: Intrinsic properties

The Brueckner-Hartree-Fock (BHF) method has been applied to nuclei whose intrinsic structure is nonspherical. Reaction matrix elements were calculated as functions of starting energy for the Hamada-Johnston interaction using the Pauli operator appropriate to O-16 and a shifted oscillator spectrum for virtual excited states. Binding energies, single particle energies, radii, and shape deformations of the intrinsic state, in ordinary as well as renormalized BHF, are discussed and compared with previous HF studies and with experiment when possible. Results are presented for C-12, 0-16 and Ne-20. It is found that the binding energies and radii are too small, but that separation energies are well reproduced when the renormalized theory is used.

Braley, R. C.↗
NASA NTRS1988

Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing

The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.

Rodriguez, G.↗
NASA NTRS1990

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility.

Starbuck, J. Michael↗
NASA NTRS1992

Measurement of multiaxial ply strength by an off-axis flexure test

An off-axis flexure (OAF) test was performed to measure ply strength under multiaxial stress states. This test involves unidirectional off-axis specimens loaded in bending, using an apparatus that allows these anisotropic specimens to twist as well as flex without the complications of a resisting torque. A 3D finite element stress analysis verified that simple beam theory could be used to compute the specimen bending stresses at failure. Unidirectional graphite/epoxy specimens with fiber angles ranging from 90 deg to 15 deg have combined normal and shear stresses on their failure planes that are typical of 45 deg plies in structural laminates. Tests for a range of stress states with AS4/3501-6 specimens showed that both normal and shear stresses on the failure plane influenced cracking resistance. This OAF test may prove to be useful for generating data needed to predict ply cracking in composite structures and may also provide an approach for studying fiber-matrix interface failures under stress states typical of structures.

Crews, John H., Jr.↗
NASA NTRS2004

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Sullivan, Roy M.↗
NASA NTRS2009

The Principle of Energetic Consistency

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Cohn, Stephen E.↗
DOE OSTI2022

Helium interaction with solutes and impurities in neutron-irradiated nanostructured ferritic alloys: A first principles study

Density functional theory calculations are performed to explore the binding between He and alloying solutes, impurities, and transmutation products expected in neutron irradiated nanostructured ferritic alloys (NFAs), here 14YWT is taken as an example. Elements that exhibit significant binding (attraction) with an interstitial He are Y (binding energy = 0.46 eV), Mg (0.32), O (0.33), Ti (0.16), and C (0.15). Those that provide significant binding to a substitutional He are O (1.44), Y (1.24), N (0.73), H (0.56), Mg (0.52), Ti (0.34), Si (0.34), C (0.33), Al (0.32), Ni (0.26), Ta (0.23), and Mn (0.16). The presence of these elements in Fe matrix could reduce the transport of He towards oxide particles, dislocations, and internal boundaries, and could promote He bubble nucleation in the matrix. For convenience, we compile existing binding energy data of He with He n and He n V (He-vacancy) clusters. Dissociation pathway analysis reveals that, in general, the most likely dissociation of a He n V cluster is by a sequential emission of individual He atoms. Furthermore, larger bubbles are more prone to dissociation than smaller ones. In addition, we estimate the binding energy (segregation energy) of He in bulk Y 2 Ti 2 O 7 (YTO) single crystal, YTO/Fe interface, and YTO particle embedded in Fe, with respect to interstitial He in Fe, from existing formation energies of He in these structures. We also compile available data of He binding with Fe self-interstitial atom (SIA), SIA clusters, and edge and screw dislocations. Note that given the absence of DFT data, the binding with SIA clusters and dislocations are gathered from simulations with empirical potentials. Finally, the data presented in this paper is important to inform multiscale simulations of He bubble accumulation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Influence of gadolinium doping on structural, optical, and electronic properties of polymeric graphitic carbon nitride

Polymeric graphitic carbon nitride (gCN) materials have received great attention in the fields of photo and electrocatalysis due to their distinct properties in metal-free systems with high physicochemical stability. Nevertheless, the activity of undoped gCN is limited due to its relatively low specific surface area, low conductivity, and poor dispersibility. Doping Gd atoms in a gCN matrix is an efficient strategy to fine-tune its catalytic activity and its electronic structure. Herein, the influence of various wt% of gadolinium (Gd) doped in melon-type carbon nitride was systematically investigated. Gadolinium-doped graphitic carbon nitride (GdgCN) was synthesized by adding gadolinium nitrate to dicyandiamide during polymerization. The X-ray diffraction (XRD) and transmission electron microscopy (TEM) results revealed that the crystallinity and the morphological properties are influenced by the % of Gd doping. Furthermore, X-ray photoelectron spectroscopy (XPS) studies revealed that the gadolinium ions bonded with nitrogen atoms. Complementary density functional theory (DFT) calculations illustrate possible bonding configurations of Gd ions both in bulk material and on ultrathin melon layers and provide evidence for the corresponding bandgap modifications induced by gadolinium doping.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Transversity GPDs of the proton from lattice QCD

We present the first calculation of the x dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with nonlocal operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as 0.83, 1.25, and 1.67 GeV, and the values of the momentum transfer squared are 0.69 and 1.02 GeV 2 . These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of twisted-mass fermions with a clover term: two degenerate-mass light quarks, a strange quark, and a charm quark. The lattice results are renormalized nonperturbatively and finally matched to the light-cone GPDs using one-loop perturbation theory within the framework of large-momentum effective theory. The final GPDs are given in the $\overline{MS}$ scheme at a scale of 2 GeV. In addition to the individual GPDs, we form the combination of the transversity GPDs that is related to the transverse spin structure of the proton. Finally, we extract the lowest two moments of the GPDs and draw a number of important qualitative conclusions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1978

Modal analysis of turborotors using planar modes - Theory

The generalized dynamic equations of motion have been obtained by the direct stiffness method for multimass flexible rotor bearing systems including the effects of gyroscopic moments, disk skew, and rotor acceleration. A set of undamped critical speed mode shapes calculated from the average horizontal and vertical bearing stiffness is used to transform the equations of motion into a set of coupled modal equations of motion. The modal equations are coupled by the generalized bearing coefficients and the gyroscopic moments. An analysis using only undamped critical speeds or decoupled modal analysis assuming proportional damping may lead to erroneous results. This paper presents a rapid method of calculating rotor resonance speeds with their corresponding amplification factors, stability and unbalance response of turborotors. Examples of the application of this modal approach are presented and results are compared to those of other methods such as matrix transfer analysis.

Gunter, E. J.↗
DOE OSTI2021

Reactivity of CO 2 with Utica, Marcellus, Barnett, and Eagle Ford Shales and Impact on Permeability

We report that in order to reduce greenhouse gas emissions while recovering hydrocarbons from unconventional shale formations, processes that make use of carbon dioxide to enhance oil recovery while storing carbon dioxide (CO 2 ) should be considered. Here, we examine samples from three shale basins across the United States (Utica and Marcellus Shales in the Appalachian Basin, Barnett Shale in the Bend Arch-Ft. Worth Basin, and Eagle Ford in the Western Gulf Basin) to address the following questions: (1) do changes from reaction with CO 2 and fluids at the micrometer and nanometer scale alter flow pathways and, in turn, impact hydrocarbon production, CO 2 storage, and seal integrity and (2) can CO 2 or fluid reactivity be predicted based on physical or chemical properties of shale formations? Experiments were conducted at 40 °C and 10.3 MPa to characterize the interaction between CO 2 and shale using X-ray diffraction (XRD), carbon and sulfur analysis, in situ Fourier transform infrared spectroscopy (FT-IR), feature relocation scanning electron microscopy coupled with energy-dispersive spectroscopy (SEM-EDS), mercury (Hg) intrusion porosimetry, and Brunauer-Emmett-Teller (BET) surface area and pore size analysis coupled with density functional theory (DFT) methods. Changes in mechanical, physical, and flow properties of shale cores due to CO 2 exposure were addressed using a New England Research Autolab 1500 and Xenon X-ray computed tomography (CT) scanning. Results showed that CO 2 did not promote significant reactivity with the shale if water was not present; only shales with swelling clays or residual interstitial pore water reacted with dry CO 2 to promote reactivity in shale. When water was added as a reactant, CO 2 formed carbonic acid and reacted with the shale to dissolve carbonate pockets, etched and pitted the shale matrix surfaces, and increased the microporosity and decreased nanoporosity. Porosity and permeability increased appreciably in core shale samples after exposure to CO 2 saturated fluid due to dissolution of carbonate. Shale mechanical properties were not altered. Trends were not observed that could tie CO 2 or fluid reactivity to physical or chemical properties of the shale formations at the basin scale from the samples we examined. However, if the shale contained significant amounts of carbonate and water was available to react with the CO 2 , pore sizes were altered in the matrix and permeability and porosity increased.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2021

Partial deconfinement at strong coupling on the lattice

We provide evidence for partial deconfinement — the deconfinement of a SU(M) subgroup of the SU(N) gauge group — by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the M × M submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Island for gravitationally prepared state and pseudo entanglement wedge

We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

2D gravity↗
DOE OSTI2025

Extending Orbital-Optimized Density Functional Theory to L-Edge XPS and Beyond: Spin–Orbit Coupling via Nonorthogonal Quasi-Degenerate Perturbation Theory

Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.

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

Degradation in interfacial shear strength of carbon fiber/ vinyl ester composites due to long-term exposure to seawater using push-out tests

Here, in this study, single fiber (~7-μm diameter) push-out tests are conducted to evaluate hygrothermal effects on the interfacial shear strength (IFSS) of carbon fiber/vinyl ester (CF/VE) composites. Hygrothermal conditioning is achieved by saturating samples in simulated seawater at 40 °C for two years. An investigation has been conducted on the preparation, validity, and interpretation of the push-out test results. First, the authors present a polishing methodology that results in thin films of CF/VE composites in the thickness range of 15–120 μm and produces an average 41.2% drop in IFSS due to long-term hygrothermal exposure. Using scanning electron microscopy (SEM), we show that during the push-out tests, the failure initiates locally at the zone of minimum bond strength at the bottom (away from the indenter), then propagates along the length of the interface. The influence of radial tensile stresses originating due to bending is found to be negligible. Using the SEM imaging of the pushed-out fibers, we validate the failure of the interface to be the primary source of failure. The associated results are found to depend on the thickness of the interface. We then reevaluate the results using the Weibull distribution, knowing that the failure mechanism is analogous to the weakest link theory. The results show a 25.5% drop in the IFSS of the CFVE composite, measured at an infinitesimal scale due to long-term to hygrothermal conditioning at 40 °C. A significant drop in IFSS was observed after reheating above glass transition temperature (T g ) and cooling.

36 MATERIALS SCIENCE↗