Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

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 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

LISA Parameter Estimation using Numerical Merger Waveforms

Coalescing supermassive black holes are expected to provide the strongest sources for gravitational radiation detected by LISA. Recent advances in numerical relativity provide a detailed description of the waveforms of such signals. We present a preliminary study of LISA's sensitivity to waveform parameters using a hybrid numerical/analytic waveform describing the coalescence of two equal-mass, nonspinning black holes. The Synthetic LISA software package is used to simulate the instrument response and the Fisher information matrix method is used to estimate errors in the waveform parameters. Initial results indicate that inclusion of the merger signal can significantly improve the precision of some parameter estimates. For example, the median parameter errors for an ensemble of systems with total redshifted mass of 10(exp 6) deg M solar mass at a redshift of z is approximately 1 were found to decrease by a factor of slightly more than two when the merger was included.

Thorpe, J. I.↗
NASA NTRS2017

Quantitative EPMA Compositional Mapping of NWA 2995: Characterization, and Petrologic Interpretation of Mafic Clasts

We present the first fully quantitative compositional maps of lunar meteorite NWA 2995 using electron microprobe stage mapping, and compare selected clast mineralogy and chemistry. NWA 2995 is a feldspathic fragmental breccia containing numerous highland fine grained lithologies, including anorthosite, norite, olivine basalt, subophitic basalt, gabbro, KREEP-like basalt, granulitic and glassy impact melts, coarse-grained mineral fragments, Fe-Ni metal, and glassy matrix [1]. Chips of NWA 2995, representing these diverse materials, were analyzed by INAA and fused-bead electron-probe microanalysis (EPMA); comparison of analytical data suggests grouping of lunar meteorites NWA 2995, 2996, 3190, 4503, 5151, and 5152. The mean composition of NWA 2995 corresponds to a 2:1 mixture of feldspathic and mare material, with approximately 5% KREEP component [2]. Clast mineral chemistry and petrologic interpretation of paired stone NWA 2996 has been reported by Mercer et al. [3], and Gross et al. [4]. This study combines advances in quantitative EPMA compositional mapping and data analysis, as applied to selected mafic clasts in a polished section of NWA 2995, to investigate the origin of mafic lithic components and to demonstrate a procedural framework for petrologic analysis.

Carpenter, P. K.↗
DOE OSTI2021

Development of an optimized and scalable method for isolation of umbilical cord blood-derived small extracellular vesicles for future clinical use

Abstract Extracellular vesicles (EV) are a promising therapeutic tool in regenerative medicine. These particles were shown to accelerate wound healing, through delivery of regenerative mediators, such as microRNAs. Herein we describe an optimized and upscalable process for the isolation of EV smaller than 200 nm (sEV), secreted by umbilical cord blood mononuclear cells (UCB-MNC) under ischemic conditions and propose quality control thresholds for the isolated vesicles, based on the thorough characterization of their protein, lipid and RNA content. Ultrafiltration and size exclusion chromatography (UF/SEC) optimized methodology proved superior to traditional ultracentrifugation (UC), regarding production time, standardization, scalability, and vesicle yield. Using UF/SEC, we were able to recover approximately 400 times more sEV per mL of media than with UC, and upscaling this process further increases EV yield by about 3-fold. UF/SEC-isolated sEV display many of the sEV/exosomes classical markers and are enriched in molecules with anti-inflammatory and regenerative capacity, such as hemopexin and miR-150. Accordingly, treatment with sEV promotes angiogenesis and extracellular matrix remodeling, in vitro. In vivo, UCB-MNC-sEV significantly accelerate skin regeneration in a mouse model of delayed wound healing. The proposed isolation protocol constitutes a significant improvement compared to UC, the gold-standard in the field. Isolated sEV maintain their regenerative properties, whereas downstream contaminants are minimized. The use of UF/SEC allows for the standardization and upscalability required for mass production of sEV to be used in a clinical setting.

Cardoso, Renato M. S.↗
DOE OSTI2023

Quantum Gauge Networks: A New Kind of Tensor Network

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of tensor network ansatz for which the computation cost of simulations does not explicitly increase for larger spatial dimensions. We take inspiration from the gauge picture of quantum dynamics, which consists of a local wavefunction for each patch of space, with neighboring patches related by unitary connections. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We describe how a QGN can be obtained from a generic wavefunction or matrix product state (MPS). All 2k-point correlation functions of any wavefunction for M many operators can be encoded exactly by a QGN with bond dimension O(M k ). In comparison, for just k = 1, an exponentially larger bond dimension of 2 M/6 is generically required for an MPS of qubits. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension. The approximate dynamics can achieve exact energy conservation for time-independent Hamiltonians, and spatial symmetries can also be maintained exactly. We benchmark the algorithm by simulating the quantum quench of fermionic Hamiltonians in up to three spatial dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Kinematics of the CS method for the treatment of molecular collisions

The problem of the quantum treatment of nonreactive collisions of two simple molecules or of an atom and a molecule is considered mathematically. Kinematical structure theorems analogous to the Wigner-Eckart theorem for scalar operators are derived for the transition operator (T-operator) of a two-molecule system, where, in addition to the usual conservation laws, certain additional conservation laws are presumed satisfied in a collision. The additional conservation laws were examined in order to develop a testable approximation scheme (CS method) for the specification of the kinematics of a system of two rigid diatomic molecules. The rand p-helicity basis states for a two-rigid rotor system are defined and unitary transformations established between these and conventional bases. It is found that only questionable criteria exist for testing the on-the-energy-shell matrix of a T(energy) operator for the presence of properties of two of the additional conservation laws.

Hahne, G. E.↗
NASA NTRS1993

Thermoviscoplastic analysis of fibrous periodic composites using triangular subvolumes

The nonlinear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each step of the loading history, the total strain increment at any point is governed by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and strains to be determined within a unit cell of the periodic lattice. The nonlinearity arising from the viscoplastic behavior of the constituent materials comprising the composite is treated as fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungsten/copper metal matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loading history perpendicular to the fibers is found to be highly heterogeneous, and typical homogenization techniques based on treating the stress and strain distributions within the constituent phases as homogeneous result in large errors under inelastic loading conditions.

Walker, Kevin P.↗
NASA NTRS2002

Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites

A research program is underway to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Under these types of loading conditions, the material response can be highly strain rate dependent and nonlinear. State variable constitutive equations based on a viscoplasticity approach have been developed to model the deformation of the polymer matrix. The constitutive equations are then combined with a mechanics of materials based micromechanics model which utilizes fiber substructuring to predict the effective mechanical and thermal response of the composite. To verify the analytical model, tensile stress-strain curves are predicted for a representative composite over strain rates ranging from around 1 x 10(exp -5)/sec to approximately 400/sec. The analytical predictions compare favorably to experimentally obtained values both qualitatively and quantitatively. Effective elastic and thermal constants are predicted for another composite, and compared to finite element results.

Goldberg, Robert K.↗
NASA NTRS2013

A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field

Producing fluid structural interaction estimates of panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. It is a useful practice to simulate the spatial correlation of the applied pressure field over a 2d surface using a matrix of small patch area regions on a finite element model (FEM). Use of a fitted function for the spatial correlation between patch centers can result in an error if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Several patch density assumptions to approximate the fitted spatial correlation function are first evaluated using both qualitative and quantitative illustrations. The actual response of a typical vehicle panel system FEM is then examined in a convergence study where the patch density assumptions are varied over the same model. The convergence study results illustrate the impacts possible from a poor choice of patch density on the analytical response estimate. The fitted correlation function used in this study represents a diffuse acoustic field (DAF) excitation of the panel to produce vibration response.

Smith, Andrew↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Decay amplitudes to three hadrons from finite-volume matrix elements

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g - 2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Post-irradiation examination of the Sirius-1 nuclear thermal propulsion fuel test

Nuclear Thermal Propulsion (NTP) systems hold promise in reducing transit times for exploration of the solar system by both crewed and uncrewed missions. NTP systems currently under investigation include a once-through high-temperature gas-cooled fission reactor to provide thermal energy to heat the coolant, which also serves as the propellant. The fuel system consists of angular UN fuel particles dispersed in a matrix of W/Re, creating a ceramic and metallic composite or cermet, which has been irradiated in Idaho National Laboratory's (INL) Transient Reactor Test Facility (TREAT). This enabled evaluation of these materials under representative nuclear heating rates (~95 K/s) and peak surface temperatures (~2527 K). Further, these surface conditions were indicative of achievement of the target peak internal temperature of approximately 2850 K. These tests named Sirius-1 (UN–W/Re), have been irradiated and this paper will present post-irradiation examination results. The Sirius-1 test produced minor, stable cracks in the fuel specimen and spalling of surface material. Volatilized uranium ‘soot’ was found deposited on the inner wall of the irradiation capsule indicating loss of some fissile material from the fuel specimen. Spalling from the surfaces was also noted upon visual inspection. Uranium diffusion from the fuel particles resulted in the formation of U/Re phases and the production of a laminar microstructure on the edge of the fuel system. Overall, the specimen was stable and remained within a coolable geometry upon conclusion of multiple thermal cycles to prototypical operating temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A2Σ+) by H2

Abstract The Born–Oppenheimer approximation, assuming separable nuclear and electronic motion, is widely adopted for characterizing chemical reactions in a single electronic state. However, the breakdown of the Born–Oppenheimer approximation is omnipresent in chemistry, and a detailed understanding of the non-adiabatic dynamics is still incomplete. Here we investigate the non-adiabatic quenching of electronically excited OH(A 2 Σ + ) molecules by H 2 molecules using full-dimensional quantum dynamics calculations for zero total nuclear angular momentum using a high-quality diabatic-potential-energy matrix. Good agreement with experimental observations is found for the OH(X 2 Π) ro-vibrational distribution, and the non-adiabatic dynamics are shown to be controlled by stereodynamics, namely the relative orientation of the two reactants. The uncovering of a major (in)elastic channel, neglected in a previous analysis but confirmed by a recent experiment, resolves a long-standing experiment–theory disagreement concerning the branching ratio of the two electronic quenching channels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Matrix element corrections in the PYTHIA8 parton shower in the context of matched simulations at next-to-leading order

We discuss the role of matrix element corrections (MEC) to parton showers in the context of MC@NLO-type matchings for processes that feature unstable resonances, where MEC are liable to result in double-counting issues, and are thus generally not employed. By working with PYTHIA8 , we show that disabling all MEC is actually unnecessary in computations based on the narrow-width approximation, and we propose alternative MEC settings which, while still avoiding double counting, allow one to include hard-recoil effects in the simulations of resonance decays. We illustrate our findings by considering $t\overline{t}$ production at the LHC, and by comparing MadGraph5-aMC@NLO predictions with those of POWHEG-BOX and standalone PYTHIA8 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗
NASA NTRS2015

Materials, Manufacturing, and Test Development of a Composite Fan Blade Leading Edge Subcomponent for Improved Impact Resistance

Application of polymer matrix composite materials for jet engine fan blades is becoming attractive as an alternative to metallic blades; particularly for large engines where significant weight savings are recognized on moving to a composite structure. However, the weight benefit of the composite is offset by a reduction of aerodynamic efficiency resulting from a necessary increase in blade thickness; relative to the titanium blades. Blade dimensions are largely driven by resistance to damage on bird strike. Further development of the composite material is necessary to allow composite blade designs to approximate the dimensions of a metallic fan blade. The reduction in thickness over the state of the art composite blades is expected to translate into structural weight reduction, improved aerodynamic efficiency, and therefore reduced fuel consumption. This paper presents test article design, subcomponent blade leading edge fabrication, test method development, and initial results from ballistic impact of a gelatin projectile on the leading edge of composite fan blades. The simplified test article geometry was developed to realistically simulate a blade leading edge while decreasing fabrication complexity. Impact data is presented on baseline composite blades and toughened blades; where a considerable improvement to impact resistance was recorded.

Materials↗
NASA NTRS2014

Materials, Manufacturing and Test Development of a Composite Fan Blade Leading Edge Subcomponent for Improved Impact Resistance

Application of polymer matrix composite materials for jet engine fan blades is becoming attractive as an alternative to metallic blades; particularly for large engines where significant weight savings are recognized on moving to a composite structure. However, the weight benefit of the composite of is offset by a reduction of aerodynamic efficiency resulting from a necessary increase in blade thickness; relative to the titanium blades. Blade dimensions are largely driven by resistance to damage on bird strike. Further development of the composite material is necessary to allow composite blade designs to approximate the dimensions of a metallic fan blade. The reduction in thickness over the state of the art composite blades is expected to translate into structural weight reduction, improved aerodynamic efficiency, and therefore reduced fuel consumption. This paper presents test article design, subcomponent blade leading edge fabrication, test method development, and initial results from ballistic impact of a gelatin projectile on the leading edge of composite fan blades. The simplified test article geometry was developed to realistically simulate a blade leading edge while decreasing fabrication complexity. Impact data is presented on baseline composite blades and toughened blades; where a considerable improvement to impact resistance was recorded.

Ballistic Impact↗
DOE OSTI2020

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗