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At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2020

High spatial resolution thermal conductivity mapping of SiC/SiC composites

Herein, silicon carbide (SiC) ceramic matrix composites are being investigated as a new generation of fuel cladding materials due to its higher accident tolerance compared to Zircaloy. Characterization of the thermal conductivity of SiC constituents and their interfaces and interphases in SiC/SiC composites is needed as inputs to models of cladding performance. We used time-domain thermoreflectance (TDTR) to map the thermal conductivity with a spatial resolution of 2 µm. The SiC/SiC composite is comprised of Hi-Nicalon Type S fibers in a matrix made by chemical vapor infiltration (CVI matrix). The interphase material is a pyrolytic carbon/SiC multilayer. We report thermal conductivity maps of the SiC fiber and SiC matrix at temperatures of 25 °C, 90 °C, 164 °C, and 250 °C. The fiber has a uniform and isotropic thermal conductivity of 22 W m -1 K -1 at 25 °C; the thermal conductivity of fiber is approximately independent of temperature. The matrix thermal conductivity is not uniform and varies from 50 to 120 W m -1 K -1 at 25 °C; the thermal conductivity of the matrix scales approximately with the inverse of the square root of temperature, i.e., ∝ 1/T 1/2 . The thermal conductivity of the interphase at room temperature is 6 W m -1 K -1 . The calculated spatially averaged thermal conductivity of this SiC/SiC composite at 1000°C is 29 W m -1 K -1 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1975

The life and times of Big Bertha - Lunar breccia 14321

The assembly and metamorphic history of polymict breccia 14321 are reconstructed. The earliest formed fragmental component of 14321 (microbreccia-1) is dominated by KREEP-rich norite, extruded and subsequently brecciated and lithified in an ejecta blanket at approximately 1000 C in the general region of Mare Imbrium after the Serenitatis impact but prior to the Imbrium impact. This early microbreccia component and lesser amounts of mare-type basalt, microgranite, rhyolite glass, anorthosite and olivine microbreccia were assembled at the Apollo 14 site as part of the Fra Mauro ejecta blanket from the Imbrium impact. The resulting microbreccia-3 incorporates all the lithic types above and accretionary lapilli structures (microbreccia-2) in a dark matrix annealed at approximately 700 C. A later impact on the Fra Mauro excavated and mutually abraded microbreccia-3 and a local, 14321-type, basalt which were assembled into polymict breccia 14321. Final placement of 14321 at its sampling location was accomplished during the minor Cone Crater impact event.

Duncan, A. R.↗

NASA NTRS2006

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Patnaik, Surya N.↗

NASA NTRS1974

Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules

We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.

Cohen, S. C.↗

NASA NTRS2003

Isotopic Composition of Silicon Carbide in the CO3 Chondrite Colony

Presolar grains have been identified in primitive members of all chondrite classes. The isotopic compositions of presolar grains provide probes of galactic evolution and nucleosynthesis in stars, while the abundances and characteristics of presolar grains contain a record of thermal processing in the solar system. Most of the detailed isotopic work has been done on SiC from Murchison and Orgueil, supplemented by a few studies of ordinary and enstatite chondrites. This work investigates SiC in the Colony CO3.O meteorite. SiC is present in Colony at a matrix-normalized abundance of approximately 3.7 ppm, much less than in CI chondrites and the matrixes of CM and primitive ordinary and enstatite chondrites. The abundances of SiC and other presolar grains in Colony seem to correlate with the chemical processing that produced CO3 chondrites. This implies that the known presolar grains experienced the same processing as the bulk CO3 material and assumes that the parent material was the same as that for other chondrites, including CI. That parent material is most plausibly the average material in the sun s parent molecular cloud. One test of this idea is to look for primary differences between SiC in Colony (and other meteorites) and that in CI and CM chondrites. True differences not related to thermal processing would falsify the assumption that all chondrite classes originated from the same reservoir of presolar dust.

Smith, J. B.↗

NASA NTRS1979

Accuracy of an approximate static structural analysis technique based on stiffness matrix eigenmodes

Use of the stiffness matrix eigenmodes, instead of the vibration eigenmodes, as generalized coordinates is proposed for condensation of static load deflection equations in finite element stiffness method. The modes are selected by strain energy criteria and the resulting fast, approximate analysis technique is evaluated by applications to idealized built-up wings and a fuselage segment. The best results obtained are a two-order of magnitude reduction of the number of degrees of freedom in a high aspect ratio wing associated with less than one percent error in prediction of the largest displacement.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1987

The use of the QR factorization in the partial realization problem

The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction.

Verhaegen, M. H.↗

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.↗

DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Optimal 1D Ly α forest power spectrum estimation – I. DESI-lite spectra

ABSTRACT The 1D Ly α forest flux power spectrum P1D is sensitive to scales smaller than a typical galaxy survey, and hence ties to the intergalactic medium’s thermal state, suppression from neutrino masses, and new dark matter models. It has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. In this work, we revisit the optimal quadratic estimator for P1D, which is robust against the relevant problems such as pixel masking, time evolution within spectrum, and quasar continuum errors. We further improve the estimator by introducing a fiducial power spectrum, which enables us to extract more information by alleviating the discreteness of band powers. We meticulously apply our method to synthetic Dark Energy Spectroscopic Instrument (DESI) spectra and demonstrate how the estimator overcomes each challenge. We further apply an optimization scheme that approximates the Fisher matrix to three elements per row and reduces computation time by 60 per cent. We show that we can achieve per cent precision in P1D with 5-yr DESI data in the absence of systematics and provide forecasts for different spectral qualities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

nuclear-score-maximization v1.0

This software library presents efficient and multithreaded implementations of matrix low rank approximation via column selection in C++17 code. The algorithms are described in Fornace, Mark, and Michael Lindsey. "Column and row subset selection using nuclear scores: algorithms and theory for Nystro m approximation, CUR decomposition, and graph Laplacian reduction." arXiv preprint arXiv:2407.01698 (2024). The presented methods are by-and-large ver novel, have provable approximation guarantees, multiple use-cases, and exhibit higher quality approximations on a variety of studied examples.

Fornace, Mark↗

NASA NTRS1978

Identification of the stability parameters of an aeroelastic airplane

The problem of the parameter identification of large scale dynamic systems involving a system matrix characterized by approximately 200 elements is addressed. By using phase variable transformations, a mathematical model of an aeroelastic airplane is described in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. A mathematical model of the U.S. Air Force Total In-Flight Simulator was computed using the FLEXSTAB digital computer program. As data became available during the progress of the flight test program, this data was processed and substituted in the mathematical model for parameters analytically obtained from the FLEXSTAB program. The results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.

Rynaski, E. G.↗

NASA NTRS1980

Shock Sensitivity of energetic materials

Viscoplastic deformation is examined as the principal source of hot energy. Some shock sensitivity data on a proposed model is explained. A hollow sphere model is used to approximate complex porous matrix of energetic materials. Two pieces of shock sensitivity data are qualitatively compared with results of the proposed model. The first is the p2 tau law. The second is the desensitization of energetic materials by a ramp wave applied stress. An approach to improve the model based on experimental observations is outlined.

Kim, K.↗

NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗

NASA NTRS1989

An implicit and stiffly stable finite element CFD algorithm for unsteady aerodynamics

A stable and accurate finite element CFD algorithm for hyperbolic/incompletely parabolic conservation law systems is described and verified. It combines a Taylor weak statement FEM, an optimal implicit Runge-Kutta time integration algorithm, and a matrix tensor product approximate factorization linear algebra procedure. The results of computational experiments show that the developed algorithm is robust.

Baker, A. J.↗

NASA NTRS1989

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Gallopoulos, E.↗

NASA NTRS1990

Efficient parallel solution of parabolic equations - Implicit methods on the Cedar multicluster

A class of implicit methods for the parallel solution of linear parabolic differential equations based on Pade and Chebyshev rational approximations to the matrix exponential are presented. It is pointed out that this approach incorporates both natural hierarchical parallelism, improved intrinsic efficiency, and fewer timesteps. These advantages lead to an extremely fast family of methods for the solution of certain time-dependent problems. These techniques are illustrated with numerical experiments on the University of Illinois Cedar multicluster architecture. The experiments indicate that implicit methods of very high degree offer great promise for the solution of certain parabolic problems when in computational environment with parallel resources. Hierarchically organized parallel computers, such as the Cedar multicluster, are found to be especially attractive for these schemes.

Gallopoulos, E.↗

NASA NTRS1991

Optimal control study for the Space Station Solar Dynamic power module

The authors present the design of an optimal control system for the Space Station Freedom's Solar Dynamic Fine Pointing and Tracking (SDFPT) module. A very large state model of six rigid body modes and 272 flexible modes is used in conjunction with classical LQG optimal control to produce a full-order controller which satisfies the requirements. The results obtained are compared with those of a classically designed PID (proportional plus integral plus derivative) controller that was implemented for a six-rigid-body-mode forty-flexible-mode model. A major difficulty with designing LQG controllers for large models is solving the Riccati equation that arises from the optimal formulation. A Riccati solver based on a Pade approximation to the matrix sign function is used. A symmetric version of this algorithm is derived for the special class of Hamiltonion matrices, thereby yielding, for large problems, a nearly twofold speed increase over a previous algorithm.

Papadopoulos, P. M.↗