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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Polynomial Compensation, Inversion, And Approximation

New criterion introduced for design of discrete-time compensator. Method devised for polynomial compensation, inversion, and approximation of discrete-time linear systems. Involves quadratic measure of difference between response of compensated system and desired response. Impulse response of compensated system improves as degree of polynomial increases. Compensator emphasizes matching of large initial response. Compensators used in variety of applications, including navigation systems for spacecraft, aircraft, ships, and automated manufacturing equipment.

Baram, Yoram↗
NASA NTRS1990

New pole placement algorithm - Polynomial matrix approach

A simple and direct pole-placement algorithm is introduced for dynamical systems having a block companion matrix A. The algorithm utilizes well-established properties of matrix polynomials. Pole placement is achieved by appropriately assigning coefficient matrices of the corresponding matrix polynomial. This involves only matrix additions and multiplications without requiring matrix inversion. A numerical example is given for the purpose of illustration.

Shafai, B.↗
NASA NTRS1991

Polynomial optimization techniques for activity scheduling. Optimization based prototype scheduler

Polynomial optimization techniques for activity scheduling (optimization based prototype scheduler) are presented in the form of the viewgraphs. The following subject areas are covered: agenda; need and viability of polynomial time techniques for SNC (Space Network Control); an intrinsic characteristic of SN scheduling problem; expected characteristics of the schedule; optimization based scheduling approach; single resource algorithms; decomposition of multiple resource problems; prototype capabilities, characteristics, and test results; computational characteristics; some features of prototyped algorithms; and some related GSFC references.

Reddy, Surender↗
NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS1994

Multivariable Hermite polynomials and phase-space dynamics

The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.

Dattoli, G.↗
NASA NTRS1991

Polynomials

In this 'Project Mathematics! series, sponsored by California Institute for Technology (CalTech), the mathematical concept of polynomials in rectangular coordinate (x, y) systems are explored. sing film footage of real life applications and computer animation sequences, the history of, the application of, and the different linear coordinate systems for quadratic, cubic, intersecting, and higher degree of polynomials are discussed.

Apostol, Tom M.↗
NASA NTRS1995

Tables of properties of airfoil polynomials

This monograph provides an extensive list of formulas for airfoil polynomials. These polynomials provide convenient expansion functions for the description of the downwash and pressure distributions of linear theory for airfoils in both steady and unsteady subsonic flow.

Desmarais, Robert N.↗
NASA NTRS1996

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

Johnson, Duane↗
NASA NTRS1997

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗
NASA NTRS2005

Polynomial Expressions for Estimating Elastic Constants From the Resonance of Circular Plates

Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.

Salem, Jonathan A.↗
NASA NTRS2012

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Crespo, Luis G.↗
NASA NTRS2012

Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties

This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.

Crespo, Luis G.↗
NASA NTRSDate not supplied

Cryogenic Extension of NASA Species Polynomials Using Hydrogen and Oxygen at Stoichiometry

The Helmholtz free energy for a mixture has been used in many chemistry and combustion studies for mixtures. An approach is described where polynomial fits intended for a thermally perfect ideal gases can be modified and implemented into a Helmholtz free energy model, such as those used by NIST in their REFPROP program. However, the limitation of the polynomial fits must be respected and should only used in a valid temperature interval where the flow field can be treated as a thermally perfect ideal gas when these species are present. This approach can allow a CFD simulation to have cryogenic regions of a flow field where high fidelity cryogenic species models are needed and allows for the use of species in other areas at higher temperatures where combustion species do not have such a model available or is not needed. Presented in the paper are CFD 1D detonation wave and species mass fraction simulation results which have cryogenic upstream conditions of Hydrogen and Oxygen at stoichiometry.

Combustion↗
DOE OSTI2026

Spectra-to-exposure conversion using polynomial response models for gamma-ray field characterization

Accurate measurement of exposure rate from gamma-ray spectral data remains a critical challenge during radiological emergency response operations. Conventional methods rely on pre-defined static conversion factors derived from fixed geometries and isotopic compositions, which often fail to capture real-world environmental variability. This study presents a generalized approach as a "next-step" for converting gamma-ray spectral data into exposure rate using polynomial response models. The method introduces a flexible weighting scheme based on the in-situ detector response to distributed sources, enabling a pathway towards improved correspondence between measured spectra and "ground-truth" exposure rates. Experimental data from sodium iodide NaI(Tl) detectors were used to validate the approach as, at least equivalent to the current count-to-exposure method employed in emergency response CONOPS. Results show that the polynomial weighting model is sufficiently equal to the count-to-exposure method and may help improve accuracy given its adaptability to real-world conditions.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2026

Bayesian Adaptive Polynomial Chaos Expansions

Polynomial chaos expansions (PCEs) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare—especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that the Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis and ordinal regression tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗