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Results for “Smooth approximation”

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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NASA NTRS1990

Fuselage design for a specified Mach-sliced area distribution

A procedure for designing a fuselage having a prescribed effective area distribution computed from -90 deg Mach slices is described. This type of calculation is an essential tool in designing a complete configuration with an effective area distribution that corresponds to a desired sonic boom signature shape. Sample calculations are given for M=2 and M=3 designs. The examples include fuselages constrained to have circular cross sections and fuselages having cross sections of arbitrary shape. It is found that, for a prescribed effective area distribution having sharp variations, the iterative procedure converges to a smoothed approximation to the prescribed distribution. For a smooth prescribed area distribution, the solution is not unique.

Barger, Raymond L.↗

NASA NTRS1973

A method for digital image registration using a mathematical programming technique

A new algorithm based on a nonlinear programming technique to correct the geometrical distortions of one digital image with respect to another is discussed. This algorithm promises to be superior to existing ones in that it is capable of treating localized differential scaling, translational and rotational errors over the whole image plane. A series of piece-wise 'rubber-sheet' approximations are used, constrained in such a manner that a smooth approximation over the entire image can be obtained. The theoretical derivation is included. The result of using the algorithm to register four channel S065 Apollo IX digitized photography over Imperial Valley, California, is discussed in detail.

Yao, S. S.↗

NASA NTRS1951

Concerning the flow about ring-shaped cowlings Part II : annular bodies of infinite length with circulation for smooth entrance

The investigations carried out in a previous report (NACA TM 1325) concerning the flow about ring-shaped cowlings were extended by taking a circulation about the cowling into consideration. The present second report treats bodies of infinite length with approximately smooth entrance. The circulation was caused by distributing vortex rings of constant density over a stream surface extending to infinity. Furthermore, the influence of a hub body on such cowlings was dealt with. The examples treated are meant to give the designer a basis for his design.

FLOW, INCOMPRESSIBLE↗

NASA NTRS1985

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗

NASA NTRS1986

Multigrid method for nearly singular and slightly indefinite problems

Brandt, A.↗

NASA NTRS1995

Observations of the 3-D distribution of interplanetary electrons and ions from solar wind plasma to low energy cosmic rays

The 3-D Plasma and Energetic Particle instrument on the GGS Wind spacecraft (launched November 1, 1994) is designed to make measurements of the full three-dimensional distribution of suprathermal electrons and ions from solar wind plasma to low energy cosmic rays, with high sensitivity, wide dynamic range, good energy and angular resolution, and high time resolution. Three pairs of double-ended telescopes, each with two or three closely sandwiched passivated ion implanted silicon detectors measure electrons and ions from approximately 20 keV to greater than or equal to 300 keV. Four top-hat symmetrical spherical section electrostatic analyzers with microchannel plate detectors, a large and a small geometric factor analyzer for electrons and a similar pair for ions, cover from approximately 3 eV to 30 keV. We present preliminary observations of the electron and ion distributions in the absence of obvious solar impulsive events and upstream particles. The quiet time electron energy spectrum shows a smooth approximately power law fall-off extending from the halo population at a few hundred eV to well above approximately 100 keV The quiet time ion energy spectrum also shows significant fluxes over this energy range. Detailed 3-D distributions and their temporal variations will be presented.

Lin, R. P.↗

NASA NTRS1978

Wave propagation through a random medium - The random slab problem

The first-order smoothing approximation yields integral equations for the mean and the two-point correlation function of a wave in a random medium. A method is presented for the approximate solution of these equations that combines features of the eiconal approximation and of the Born expansion. This method is applied to the problem of reflection and transmission of a plane wave by a slab of a random medium. Both the mean wave and the covariance are calculated to determine the reflected and transmitted amplitudes and intensities.

Acquista, C.↗

NASA NTRS1987

Numerical studies of the thermal design sensitivity calculation for a reaction-diffusion system with discontinuous derivatives

The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.

Hou, Jean W.↗

NASA NTRS1991

Computer-Aided Design Of Sheet-Material Parts

Computer-aided-design system partly automates tedious process of designing and guiding assembly of small pieces of flat sheet material into large surfaces that approximate smoothly curved surfaces having complicated three-dimensional shapes. Capability provides for flexibility enabling designer to assess quickly and easily effects of changes in design in making engineering compromises among various sizes and shapes. Saves time and money in both design and fabrication. Used in rocket-engine application and other applications requiring design of sheet-material parts.

Gilbert, Jeffrey L.↗

NASA NTRS1987

Structure and dynamics of amorphous water ice

Further insight into the structure and dynamics of amorphous water ice, at low temperatures, was obtained by trapping in it Ar, Ne, H2, and D2. Ballistic water-vapor deposition results in the growth of smooth, approximately 1 x 0.2 micrometer2, ice needles. The amorphous ice seems to exist in at least two separate forms, at T < 85 K and at 85 < T < 136.8 K, and transform irreversibly from one form to the other through a series of temperature-dependent metastable states. The channels formed by the water hexagons in the ice are wide enough to allow the free penetration of H2 and D2 into the ice matrix even in the relatively compact cubic ice, resulting in H2-(D2-) to-ice ratios (by number) as high as 0.63. The larger Ar atoms can penetrate only into the wider channels of amorphous ice, and Ne is an intermediate case. Dynamic percolation behavior explains the emergence of Ar and Ne (but not H2 and D2) for the ice, upon warming, in small and big gas jets. The big jets, each containing approximately 5 x 10(10) atoms, break and propel the ice needles. Dynamic percolation also explains the collapse of the ice matrix under bombardment by Ar , at a pressure exceeding 2.6 dyn cm-2, and the burial of huge amounts of gas inside the collapsed matrix, up to an Ar-to-ice of 3.3 (by number). The experimental results could be relevant to comets, icy satellites, and icy grain mantles in dense interstellar clouds.

NASA Program Exobiology↗

NASA NTRS1993

Experiment-specific cosmic microwave background calculations made easier - Approximation formula for smoothed delta T/T windows

Simple and easy to implement elementary function approximations are introduced to the spectral window functions needed in calculations of model predictions of the cosmic microwave backgrond (CMB) anisotropy. These approximations allow the investigator to obtain model delta T/T predictions in terms of single integrals over the power spectrum of cosmological perturbations and to avoid the necessity of performing the additional integrations. The high accuracy of these approximations is demonstrated here for the CDM theory-based calculations of the expected delta T/T signal in several experiments searching for the CMB anisotropy.

Gorski, Krzysztof M.↗

NASA NTRS1993

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗

NASA NTRS1994

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗

NASA NTRS1982

Synthesis of offset dual reflector antennas transforming a given feed illumination pattern into a specified aperture distribution

The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed which realizes an exact aperture phase distribution and an aperture amplitude distribution that is accurate to within an arbitrarily small numerical tolerance. However, this procedure does not always yield a smooth solution, i.e., the reflector surfaces thus realized may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, only the requirement for the aperture amplitude distribution is relaxed, and the condition on the aperture phase distribution is continued to be satisfied exactly.

Mittra, R.↗

NASA NTRS1995

Exponentially accurate approximations to piece-wise smooth periodic functions

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Greer, James↗

NASA NTRS1983

Method for compression testing of composite materials at high strain rates

A method is presented for testing composite materials in compression at strain rates up to approximately 500 per s. The method uses a thin ring specimen (4 in. in diameter, 1 in. wide, six-eight plies thick) loaded dynamically by an external pressure pulse applied explosively through a liquid. Strains in the specimen and in a steel calibration ring are recoorded with a digital processing oscilloscope. Results are plotted by an x-y plotter in the form of a dynamic stress-strain curve. Data analysis is based on a numerical solution of the equation of motion. A computer program is used which involves smoothing and approximation of the strain magnitude, strain rate, and strain acceleration. Dynamic stress-strain curves obtained for 0-deg and 90-deg specimens of two graphite/epoxy composites are presented.

Daniel, I. M.↗

NASA NTRS1979

Silicon-on-ceramic Process: Silicon Sheet Growth and Device Development for the Large-area Silicon Sheet and Cell Development Tasks of the Low-cost Solar Array Project

Significant progress is reported in fabricating a 4 sq cm cell having a 10.1 percent conversion efficiency and a 10 sq cm cell having a 9.2 percent conversion efficiency. The continuous (SCIM) coater succeeded in producing a 16 sq cm coating exhibiting unidirectional solidification and large grain size. A layer was grown at 0.2 cm/sec in the experimental coater which was partially dendritic but also contained a large smooth area approximately 100 micron m thick. The dark characteristic measurements of a typical SCC solar cell yield shunt resistance values of 10K ohms and series resistance values and 0.4 ohm. The production dip-coater is operating at over 50 percent yield in terms of good cell quality material. The most recent run yielded 13 good substrates out of 15.

Chapman, P. W.↗

NASA NTRS1988

Thermal measurements for jets in disturbed and undisturbed crosswind conditions

A direct comparison is made of the thermal field properties for a low-disturbance and a high-disturbance level condition affecting the low-temperature air jets introduced into gas turbine combustor aft sections in order both to cool the high-temperature gases and quench the combustion reactions. Sixty-four fast-response thermocouples were simultaneously sampled and corrected for their time constant effect at a downstream plane close to the jet exit. Histograms formed from independent samples were sufficiently smooth to approximate a pdf.

Wark, Candace E.↗