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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately

The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.

Huang, Zhaofeng↗
NASA NTRS1995

An aspect ration bound for triangulating a d-grid cut by a hyperplane

We consider the problem of triangulating a d-dimensional uniform grid of d-cubes that is cut by a k-dimensional affine subspace. The goal is to obtain a triangulation with bounded aspect ratio. To achieve this goal, we allow some of the box faces near the affine subspace to be displaced. This problem has applications to finite element mesh generation. For general d and k, the bound on aspect ratio that we attain is double-exponential in d. For the important special case of d = 3, the aspect ratio bound is small enough that the technique is useful in practice.

Mitchell, Scott A.↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗
NASA NTRS2020

The Cl isotope composition and halogen contents of Apollo-return samples

Lunar mare basalts are depleted in F and Cl by approximately an order of magnitude relative to mid-ocean ridge basalts and contain two Cl-bearing components with elevated isotopic compositions relative to the bulk-Earth value of ∼0‰. The first is a watersoluble chloride constituting 65 ± 10% of total Cl with δ37Cl values averaging 3.0 ± 4.3‰. The second is structurally bound chloride with δ37Cl values averaging 7.3 ± 3.5‰. These high and distinctly different isotopic values are inconsistent with equilibrium fractionation processes and instead suggest early and extensive degassing of an isotopically light vapor. No relationship is observed between F/Cl ratios and δ37Cl values, which suggests that lunar halogen depletion largely resulted from the Moon-forming Giant Impact. The δ37Cl values of apatite are generally higher than the structurally bound Cl, and ubiquitously higher than the calculated bulk δ37Cl values of 4.1 ± 4.0‰. The apatite grains are not representative of the bulk rock, and instead record localized degassing during the final stages of lunar magma ocean (LMO) or later melt crystallization. The large variability in the δ37Cl values of apatite within individual thin sections further supports this conclusion. While urKREEP (primeval KREEP [potassium/rare-earth elements/phosphorus]) has been proposed to be the source of the Moon’s high Cl isotope values, the ferroan anorthosites (FANs) have the highest δ37Cl values and have a positive correlation with Cl content, and yet do not contain apatite, nor evidence of a KREEP component. The high δ37Cl values in this lithology are explained by the incorporation of a >30‰ HCl vapor from a highly evolved LMO.

The Moon↗
NASA NTRS1996

Generalized Bezout's Theorem and its applications in coding theory

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

Berg, Gene A.↗
NASA NTRS1984

Rapid single-axis torque-bounded slewing of SCOLE configuration

The first general research objective was to address control design challenges of the Spacecraft Control Laboratory Experiment (SCOLE) via the two stage approach: (1) slew the whole as if it were a rigid body about one Space Shuttle body axis each time using the onboard Reaction Control System (RCS) thrusters; and (2) damp out excited vibrations. The second objective was to examine the feasibility of applying the approach to shuttle-attached flexible space structures. The following was accomplished: (1) a standard bang-bang control technique was adapted; (2) a slew rate limit was imposed in the design; and (3) slew acceleration deviation was defined as the index of slew performance degradation.

Lin, Jiguan Gene↗
DOE OSTI2024

Convex optimization of contour deformations

We discuss various formal aspects of contour deformations used to alleviate sign problems; most importantly, relating these contour deformations to a certain convex optimization problem. As a consequence of this connection we describe a general method for proving upper bounds on the average phase achievable by the contour deformation method. Using this method we show that Abelian lattice Yang-Mills in two spacetime dimensions possesses, for many values of the complex coupling, an exponential sign problem that cannot be removed via any contour deformation. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1978

A global model for rain attenuation prediction

A model was developed for the prediction of rain attenuation statistics for 8 rain rate climate regions spanning all land regions from the equator to the poles. The model uses empirically determined rain rate distributions for each climate region and an empirical model to estimate path averaged rain rate for given values of point rain rate. Attenuation distribution observations were compared with model predictions. Good agreement was obtained for earth-space paths at 0.1 percent of the year. At the extremes, 0.01 and 1 percent of the year the observations were generally within the model estimate bounds but the agreement is not as good as at 0.1 percent of the year. The discrepancies are attributed to the limited duration of the attenuation observations and to the limited number of rain rate distribution observations.

Crane, R. K.↗
NASA NTRS1987

Magnetotails at unmagnetized bodies - Comparison of Comet Giacobini-Zinner and Venus

It is found that the near ionopause environs play a crucial role in the tail formation process at both Venus and G-Z and that draping at the two very different sized bodies occurs on ionopause scale sizes. On the other hand, ion densities, downtail mass fluxes, tailward J x B forces, and lobe betas are factors of about 10,000, 50, 100, and 20 times greater in the G-Z tail than in Venus', while bulk flow speeds and ion temperatures are factors of about 15 and 240 times lower. These large quantitative differences in the properties within the two magnetotails are attributable to the significantly greater upstream mass loading of the solar wind by the extended neutral atmosphere at G-Z (comets in general) compared to the gravitationally bound atmosphere of Venus.

Mccomas, D. J.↗
NASA NTRS1991

Optimal controllers for finite wordlength implementation

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold.

Liu, K.↗
NASA NTRS1990

Optimal controllers for finite wordlength implementation

There exist realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take into account the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the LQG (linear quadratic Gaussian) theory since they reduce to the standard LQG controller when infinite-precision computation is used, but for finite precision the separation principle does not hold.

Liu, K.↗
NASA NTRS1992

Extension theorems for homogenization on lattice structures

When applying homogenization techniques to problems involving lattice structures, it is necessary to extend certain functions defined on a perforated domain to a simply connected domain. This paper provides general extension operators which preserve bounds on derivatives of order l. Only the special case of honeycomb structures is considered.

Miller, Robert E.↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
DOE OSTI2024

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

What exactly does Bekenstein bound?

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spatial region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound that pertains to the decoder Bob. In contrast, even at high temperatures, the Unruh channel can transmit a significant number of zero-bits , which are quantum communication resources that can be used for quantum identification and many other primitive protocols. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are generally not constrained by the Bekenstein bound. However, we further show that when both the encoder and the decoder are restricted, the Bekenstein bound does constrain the channel capacities, including the zero-bit capacity.

Hayden, Patrick [Stanford University, CA (United S↗
NASA NTRS1990

Design of linear quadratic regulators with eigenvalue placement in a specified region

Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

Shieh, Leang-San↗