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At least 217 records · Page 12

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NASA NTRS1992

A subspace iteration for eigenvector derivatives

An iterative procedure for calculating eigenvector derivatives has been developed based on the subspace iteration concept. The basic formulation is derived directly from the first variation of the resulting equations of subspace iteration for solving eigenvalue problems. Since the basic formulation conserves the convergence properties of the original subspace iteration for eigen-problems, an overrelaxation scheme similar to Bathe's approach is employed to accelerate the subspace iteration process for calculating eigenvector derivatives.

Ting, T.↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Attosecond time delays at Cooper minima in valence-shell photoionization of alkali-metal and alkaline-earth-metal atoms

Ji et al. [New J. Phys. 26, 093014 (2024)] established a direct link between the photoionization cross section and the attosecond time delay near Cooper minima (CM) in the valence shells of noble-gas atoms. This link is based on the analytic properties of the ionization amplitude in the complex plane of the photoelectron energy, and is particularly sensitive to the winding number of the amplitude around the origin of the complex energy plane. Here, in this study, we demonstrate an analogous relation for photoionization of the valence 𝑛⁢𝑠 shells of alkali-metal atoms (AMA), from Na (𝑛 = 3) to Cs (𝑛 = 6), as well as alkaline-earth-metal atoms (AEMA), from Mg (𝑛 = 3) to Ba (𝑛 = 6). To this end, we employ a fully relativistic formalism that separates the two complementary 𝑛⁢𝑠 1/2 → 𝐸⁢𝑝 1/2 and 𝐸⁢𝑝 3/2 ionization channels. Each of these channels exhibits a phase variation close to 𝜋, but in opposite directions, near their respective Cooper minima. This phase variation vanishes in a nonrelativistic formulation, where the two channels become degenerate. For AMA, due to the threshold proximity of the CM, the universal Coulomb contribution to the time delay must be subtracted. The remaining component of the time delay is target-specific, angular-dependent, and accessible through comparative measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Quantum computing for heavy quarkonium spectroscopy

Here, we report a first demonstration for the application of quantum computing to heavy quarkonium spectroscopy study. Based on a Cornell-potential model for the heavy quark and antiquark system, we show how this Hamiltonian problem can be formulated and solved with the variational quantum eigensolver (VQE) approach on the IBM cloud quantum computing platform. Errors due to a global depolarizing noise channel are corrected with a zero-noise extrapolation method, resulting in good agreement with the expected value. We also generalize the VQE method for solving excited states by orthogonalization with respect to the ground state. This new approach is demonstrated to be successful for the quarkonium system on a noiseless quantum simulator and can easily be adapted for solving similar excited state problems in many other physical systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Constraint of pionless EFT using two-nucleon spectra from lattice QCD

Finite-volume pionless effective field theory (FVEFT π/ ) at next-to-leading order (NLO) is used to analyze the two-nucleon lattice QCD spectrum of Ref. [1], performed at quark masses corresponding to a pion mass of approximately 800 MeV. Specifically, the effective theory is formulated in finite volume, and variational sets of wave functions are optimized using differential programming. Using these wave functions projected to the appropriate finite-volume symmetry group, variational bounds from FVEFT π/ are obtained for the ground state, as well as excited states. By comparison with the lattice QCD GEVP spectrum, different low energy constants (LECs) are constrained. Furthermore, relativistic corrections are incorporated, allowing for the s-d-wave mixing term in the deuteron channel.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1972

Analysis of instrumentation error effects on the identification accuracy of aircraft parameters

An analytical investigation is presented of the effect of unmodeled measurement system errors on the accuracy of aircraft stability and control derivatives identified from flight test data. Such error sources include biases, scale factor errors, instrument position errors, misalignments, and instrument dynamics. Two techniques (ensemble analysis and simulated data analysis) are formulated to determine the quantitative variations to the identified parameters resulting from the unmodeled instrumentation errors. The parameter accuracy that would result from flight tests of the F-4C aircraft with typical quality instrumentation is determined using these techniques. It is shown that unmodeled instrument errors can greatly increase the uncertainty in the value of the identified parameters. General recommendations are made of procedures to be followed to insure that the measurement system associated with identifying stability and control derivatives from flight test provides sufficient accuracy.

Sorensen, J. A.↗

NASA NTRS1978

The STAGS computer code

Basic information about the computer code STAGS (Structural Analysis of General Shells) is presented to describe to potential users the scope of the code and the solution procedures that are incorporated. Primarily, STAGS is intended for analysis of shell structures, although it has been extended to more complex shell configurations through the inclusion of springs and beam elements. The formulation is based on a variational approach in combination with local two dimensional power series representations of the displacement components. The computer code includes options for analysis of linear or nonlinear static stress, stability, vibrations, and transient response. Material as well as geometric nonlinearities are included. A few examples of applications of the code are presented for further illustration of its scope.

Almroth, B. O.↗

NASA NTRS1982

Dynamic response of lined tunnels by boundary elements

The dynamic stress concentration manifested around a lined cylindrical tunnel buried in an infinitely extending linear elastic or viscoelastic medium due to the passage of transient disturbances was investigated. Plane strain is assumed to hold and the transient disturbances can be of any arbitrary time variation. The boundary element method formulated in the Laplace transform domain is employed. Isoparametric boundary elements are used in the discretization of the liner and tunnel surfaces. Viscoelastic material behavior can be readily obtained from the linear elastic case in the Laplace transform domain through the use of the correspondence principle. The transient solution is recovered by numerical inversion of the solution obtained in the transformed domain.

Manolis, G. D.↗

NASA NTRS1984

Free-Edge Failures of Composite Laminates

The free-edge delamination of graphite/epoxy laminates under static loading is being analyzed to obtain fundamental understanding of the continuum mechanics involved. The analyses are conducted by idealizing the material response of each ply in the laminate as homogenous, linear elastic, and anisotropic. A generalized plane strain elastic boundary value problem was formulated to investigate the energy variation of such a body.

Source record↗

NASA NTRS1985

On a variational approach to some parameter estimation problems

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Banks, H. T.↗

NASA NTRS1985

On a variational approach to some parameter estimation problems

Banks, H. T.↗

NASA NTRS1987

The role and behavior of spin in gravitational physics

A self-consistent method of introducing spin into any Lagrangian based theory of gravitation was developed. The metric variation of the Lagrangian in the theory leads to an improved energy-momentum tensor which represents the source term in the gravitational field equations. The goal of the research is the construction of a theory general enough to be used to investigate spin effects in astrophysical objects and cosmology, and also to serve as a basis for discussion of the theoretical ideas tested by the NASA Gyroscope Experiment (aboard Gravity Probe B). Specific accomplishments in the following areas are summarized: the inclusion of electromagnetism into the variational principle for spinning matter, formulation of a self-consistent theory for the case of a fluid in which particle production processes occur, and the derivation of the Raychaudhuri equation in the case of spinning matter.

Ray, John R.↗

NASA NTRS1987

Nearly two-dimensional solutions of Euler's equations

Motivated by a stretched version of the Taylor-Green initial-value problem for the Euler and Navier-Stokes equations, nearly two-dimensional incompressible flows are considered involving a single direction of slow spatial variation. A multiple-scale formulation of the problem leads by contour averaging to a system that determines the slow development in space and time. It is shown that the latter system is equivalent to an axisymmetric problem with nonstandard connection between circulation, cylindrical radius, and angular velocity component. Special solutions of the system in the exact axisymmetric case suggest that near-two-dimensionality is lost in finite time.

Childress, Stephen↗

NASA NTRS1988

Non-Newtonian gravity or gravity anomalies?

Geophysical measurements of G differ from laboratory values, indicating that gravity may be non-Newtonian. A spherical harmonic formulation is presented for the variation of (Newtonian) gravity inside the Earth. Using the GEM-10B Earth Gravitational Field Model, it is shown that long-wavelength gravity anomalies, if not corrected, may masquerade as non-Newtonian gravity by providing significant influences on experimental observation of delta g/delta r and G. An apparent contradiction in other studies is also resolved: i.e., local densities appear in equations when average densities of layers seem to be called for.

Rubincam, David P.↗

NASA NTRS1988

An analytic treatment of gravitational microlensing for sources of finite size at large optical depths

Statistical methods are developed for gravitational lensing in order to obtain analytic expressions for the average surface brightness that include the effects of microlensing by stellar (or other compact) masses within the lensing galaxy. The primary advance here is in utilizing a Markoff technique to obtain expressions that are valid for sources of finite size when the surface density of mass in the lensing galaxy is large. The finite size of the source is probably the key consideration for the occurrence of microlensing by individual stars. For the intensity from a particular location, the parameter which governs the importance of microlensing is determined. Statistical methods are also formulated to assess the time variation of the surface brightness due to the random motion of the masses that cause the microlensing.

Deguchi, Shuji↗

NASA NTRS1990

Parallel computation using boundary elements in solid mechanics

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

Chien, L. S.↗

NASA NTRS1991

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

NASA NTRS2009

Thermal and Electrical Conductivity Measurements of CDA 510 Phosphor Bronze

Many cryogenic systems use electrical cables containing phosphor bronze wire. While phosphor bronze's electrical and thermal conductivity values have been published, there is significant variation among different phosphor bronze formulations. The James Webb Space Telescope (JWST) will use several phosphor bronze wire harnesses containing a specific formulation (CDA 510, annealed temper). The heat conducted into the JWST instrument stage is dominated by these harnesses, and approximately half of the harness conductance is due to the phosphor bronze wires. Since the JWST radiators are expected to just keep the instruments at their operating temperature with limited cooling margin, it is important to know the thermal conductivity of the actual alloy being used. We describe an experiment which measured the electrical and thermal conductivity of this material between 4 and 295 Kelvin.

Tuttle, James E.↗