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At least 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Exponential Approximations Using Fourier Series Partial Sums

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.

Banerjee, Nana S.↗
NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗
NASA NTRS1997

Formal Methods for Verification and Validation of Partial Specifications: A Case Study

This paper describes our work exploring the suitability of formal specification methods for independent verification and validation (IV&V) of software specifications for large, safety critical systems. An IV&V contractor often has to perform rapid analysis on incomplete specifications, with no control over how those specifications are represented. Lightweight formal methods show significant promise in this context, as they offer a way of uncovering major errors, without the burden of full proofs of correctness. We describe a case study of the use of partial formal models for V&V of the requirements for Fault Detection Isolation and Recovery on the space station. We conclude that the insights gained from formalizing a specification are valuable, and it is the process of formalization, rather than the end product that is important. It was only necessary to build enough of the formal model to test the properties in which we were interested. Maintenance of fidelity between multiple representations of the same requirements (as they evolve) is still a problem, and deserves further study.

Easterbrook, Steve↗
NASA NTRS1998

Reynolds-Averaged Navier-Stokes Simulations of Two Partial-Span Flap Wing Experiments

Structured Reynolds Averaged Navier-Stokes simulations of two partial-span flap wing experiments were performed. The high-lift aerodynamic and aeroacoustic wind-tunnel experiments were conducted at both the NASA Ames 7-by 10-Foot Wind Tunnel and at the NASA Langley Quiet Flow Facility. The purpose of these tests was to accurately document the acoustic and aerodynamic characteristics associated with the principle airframe noise sources, including flap side-edge noise. Specific measurements were taken that can be used to validate analytic and computational models of the noise sources and associated aerodynamic for configurations and conditions approximating flight for transport aircraft. The numerical results are used to both calibrate a widely used CFD code, CFL3D, and to obtain details of flap side-edge flow features not discernible from experimental observations. Both experimental set-ups were numerically modeled by using multiple block structured grids. Various turbulence models, grid block-interface interaction methods and grid topologies were implemented. Numerical results of both simulations are in excellent agreement with experimental measurements and flow visualization observations. The flow field in the flap-edge region was adequately resolved to discern some crucial information about the flow physics and to substantiate the merger of the two vortical structures. As a result of these investigations, airframe noise modelers have proposed various simplified models which use the results obtained from the steady-state computations as input.

Takalluk, M. A.↗
NASA NTRS1961

Effects of Surface Recombination on Heat Transfer to Bodies in a High Enthalpy Stream of Partially Dissociated Nitrogen

Heat-transfer rates to two surfaces having widely different catalytic effectiveness are compared at a Mach number of 6 in a low-density stream of partially dissociated nitrogen. The heat-transfer rate to a polished copper cylinder is twice as great as the heat-transfer rate to a silicon-monoxide-coated cylinder when the stream total energy content is 9000 Btu/lb. Various methods for determining the stream energy content, the stream velocity, and the stream Mach number have been developed and compared. It is shown that methods for estimating the stream energy content by means of purely aerodynamic concepts may neglect the sizable fraction of the stream energy contained in molecular dissociation.

Winkler, Ernest L..↗
NASA NTRS1959

A Transonic Wind-Tunnel Investigation of the Performance and of the Static Stability and Control Characteristics of a Model of a Fighter-Type Airplane which Embodies Partial Body Indentation

An investigation was conducted to obtain the aerodynamic characteristics of a model of a fighter-type airplane embodying partial body indentation. The wing had an aspect ratio of 4, taper ratio of 0.5, 35 deg sweepback of the 0.25-chord line, and a modified NACA 65A006 airfoil section at the root and a modified NACA 65A004 airfoil section at the tip. The fuselage has been indented in the region of the wing in order to obtain a favorable area distribution. The results reported herein consist of the performance and of the static longitudinal and lateral stability and control characteristics of the complete model. The Mach number range extended from 0.60 to 1.13, and the corresponding Reynolds number based on the wing mean aerodynamic chord varied from 1.77 x 10(exp 6) to 2.15 x 10(exp 6). The drag rise for both the cambered leading edge and symmetrical wing sections occurred at a Mach number of 0.95. Certain local modifications to the body which further improved the distribution of cross-sectional area gave additional reductions in drag at a Mach number of 1.00. The basic configuration indicated a mild pitch-up tendency at lift coefficients near 0.70 for the Mach number range from 0.80 to 0.90; however, the pitch-up instability may not be too objectionable on the basis of dynamic-stability considerations. The basic configuration indicated positive directional stability and positive effective dihedral through the angle-of-attack range and Mach number range with the exception of a region of negative effective dihedral at low lifts at Mach numbers of 1.00 and slightly above.

Bielat, Ralph P.↗
NASA NTRS1998

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

Lewis, Robert Michael↗
NASA NTRS1996

Vibration Characteristics of Partially Covered Double-Sandwich Cantilever Beam

The differential equations of motion together with the boundary conditions for a partially covered, double-sandwich cantilever beam are derived. Bending and extension, rotational and longitudinal inertia of damping layers, and shear deformation and rotational and longitudinal inertia of the constraining layers and the primary beam are included in the equations. The theory is applicable for long as well as short, soft, or stiff damping layer, double-sandwich beams. Also, the effects of different parameters on the system loss factor and resonance frequency are discussed. Differences are found to exist with the previous beam model (called the Euler beam model) when the damping layers are stiff, when the thickness of the damping layer is large compared to the primary-beam thickness, and in the case of higher modes of vibration.

Chen, Qinghua↗
NASA NTRS2000

Mineralogy, Petrology, Chemistry, and Ar-39 - Ar-40 and Ages of the Caddo County IAB Iron: Evidence for Early Partial Melt Segregation of a Gabbro Area Rich in Plagioclase-Diopside

We found coarse-grained gabbroic material rich in plagioclase and diopside in the Caddo County IAB iron meteorite. The polished thin sections studied were made from areas rich in Al and Ca detected by a micro-focus X-ray fluorescence (XRF) mapping technique. The gabbro is not a clast within a breccia, but rather this area is located mainly at silicate-metal boundaries only a few cm away from an area with fine-grained, ultramafic silicate similar to winonaites. Medium-grained orthopyroxene and olivine are found in transitional areas showing no disturbance of their crystalline textures. A vein-like region, starting at the area rich in fine-grained mafic silicate, extends towards the gabbroic area with a gradual increase in abundance of plagioclase and diopside. This texture and our accumulated knowledge of the formation mechanism of IAB/winonaltes meteorites, suggest that the gabbroic materials were formed by inhomogeneous segregation of partial melts of chondritic source materials. Compositional data on two mineralogically distinct samples of the gabbro-rich portion of the inclusion were obtained by INAA. Compared to an average of LAB silicate inclusions or winonaites, the Caddo County gabbro is enriched in the incompatible lithophile elements Na, Ca, Sc, REE and Hf, which is consistent with a melt origin for the gabbro. The cosmogenic space exposure age of Caddo County (511 Ma) is significantly younger than exposure ages of some other IAB meteorites, An 39Ar-40Ar age determination of the gabbroic material indicates a series of upward steps in age from 4.516 Ga to 4.523 Ga, with a few high temperature ages up to 4.54 Ga. The older age could approximate the primary recrystallization age of silicates. The stepped Ar age spectrum may indicate differences in Ar closure temperatures during slow cooling of -2-20'C/Myr in the parent body. Alternatively, the younger Ar-Ar ages may date a shock event which occurred while Caddo County was hot and which also created textures such as a linear metal vein with rounded zigzag walls in a diopside crystal and slightly miss-oriented rounded plagioclase domain.

Takeda, Hiroshi↗
NASA NTRS2001

Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

Shertzer, J.↗
NASA NTRS2001

Upward Flame Spread Over Thin Solids in Partial Gravity

The effects of partial-gravity, reduced pressure, and sample width on upward flame spread over a thin cellulose fuel were studied experimentally and the results were compared to a numerical flame spread simulation. Fuel samples 1-cm, 2-cm, and 4-cm wide were burned in air at reduced pressures of 0.2 to 0.4 atmospheres in simulated gravity environments of 0.1-G, 0.16-G (Lunar), and 0.38-G (Martian) onboard the NASA KC-135 aircraft and in normal-gravity tests. Observed steady flame propagation speeds and pyrolysis lengths were approximately proportional to the gravity level. Flames spread more quickly and were longer with the wider samples and the variations with gravity and pressure increased with sample width. A numerical simulation of upward flame spread was developed including three-dimensional Navier-Stokes equations, one-step Arrhenius kinetics for the gas phase flame and for the solid surface decomposition, and a fuel-surface radiative loss. The model provides detailed structure of flame temperatures, the flow field interactions with the flame, and the solid fuel mass disappearance. The simulation agrees with experimental flame spread rates and their dependence on gravity level but predicts a wider flammable region than found by experiment. Some unique three-dimensional flame features are demonstrated in the model results.

Feier, I. I.↗
NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗
NASA NTRS2001

Partial Pressures of In-Se from Optical Absorbance of the Vapor

The optical absorbance of the vapor phase over various In-Se compositions between 33.3 and 61 atomic percent and 673 and 1418K has been measured and used to obtain the partial pressures of Se2(g) and In2Se(g). The results are in agreement with silica Bourdon gage measurements for compositions between 50 and 61 atomic percent but significantly higher than those from Knudsen cell and simultaneous Torsion-Knudsen cell measurements. The sequiselenide is found to sublime incongruently. Congruent vaporization occurs for the liquid above 1000 K between 50.08 and 56 at. percent Se. The Gibbs energy of formation of the liquid from its pure liquid elements between 1000 and 1300K is essentially independent of temperature and falls between -36 and -38 kJ per gram atomic weight for 50 and 56 percent Se at 1200 and 1300K.

Brebrick, R. F.↗
NASA NTRS1998

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

Waheed, Abdul↗
NASA NTRS2001

Thiols in Hydrothermal Solution: Standard Partial Molal Properties and Their Role in the Organic Geochemistry of Hydrothermal Environments

Modern seafloor hydrothermal systems are locations where great varieties of geochemistry occur due to the enormous disequilibrium between vent fluids and seawater. The disequilibrium geochemistry has been hypothesized to include reactions to synthesize organic compounds. Despite the incomplete understanding of the carbon budget in hydrothermal systems, the organic geochemistry of these sites has received little attention. Experimental simulations of these environments, however, indicate that organic compounds may have difficulty forming in a purely aqueous environment. On the other hand, thiols, thioesters and disulfides have been implicated as reaction intermediates between CO or CO2 in experiments of carbon reduction in hydrothermal environments, as well as in a variety of biological processes and other abiotic reactions. The reduction of CO2 to thesis, for example, is observed using the FeS-H2S/FeS2 couple to provide the reducing power. We have used recent advances in theoretical geochemistry to estimate the standard partial moral thermodynamic properties and parameters for the revised Helgeson-Kirkham-Flowers equation of state for aqueous straight-chain alkyl thesis. With these data and parameters we have evaluated the role that organic sulfur compounds may play as reaction intermediates during organic compound synthesis. We conclude that organic sulfur compounds may hold the key to the organic chemistry leading to the origin of life in hydrothermal settings. These results may also explain the presence of sulfur in a number of biomolecules present in ancient thermophilic microorganisms.

Schulte, Mitchell D.↗
NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗