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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Evaluation of Jacobian determinants by Monte Carlo methods - Application to the quasiclassical approximation in molecular scattering.

Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.

La Budde, R. A.↗
NASA NTRS1972

Methods and approximations for the computation of transmission profiles in the v4 band of methane in the atmosphere of Jupiter.

This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.

Taylor, F. W.↗
NASA NTRS1973

Approximate thermochemical tables for some C-H and C-H-O species

Approximate thermochemical tables are presented for some C-H and C-H-O species and for some ionized species, supplementing the JANAF Thermochemical Tables for application to finite-chemical-kinetics calculations. The approximate tables were prepared by interpolation and extrapolation of limited available data, especially by interpolations over chemical families of species. Original estimations have been smoothed by use of a modification for the CDC-6600 computer of the Lewis Research Center PACl Program which was originally prepared for the IBM-7094 computer Summary graphs for various families show reasonably consistent curvefit values, anchored by properties of existing species in the JANAF tables.

Bahn, G. S.↗
NASA NTRS1973

A high frequency correction to the Kirchhoff approximation, with application to rough surface EM wave scattering

A high frequency correction to the Kirchhoff approximation is developed for application to rough surface scattering. An approximate solution to the magnetic field integral equation for perfect conductivity and plane wave excitation yields a perturbed surface current expressed as a linear function of the second derivatives of surface height. The corrected surface current vector is substituted into the far field Stratton-Chu integral and average backscattered powers for the four polarization combinations are computed on the assumption that the surface is describable as a stationary Gaussian random process. The strength of this scattering solution is that it can account for height curvature correlation without requiring small height and slope.

Jackson, F. C.↗
NASA NTRS1972

Use of the Glauber approximation in atomic collisions - A progress report.

Recent progress in the use of the Glauber (1970) theory for estimating atomic collision cross sections is reviewed. It appears that the Glauber approximation is reliable for electron-hydrogen elastic scattering and excitation at incident energies exceeding 30 eV. For more complicated atomic collisions, the usefulness of the Glauber approximation has not yet been significantly tested.

Gerjuoy, E.↗
NASA NTRS1973

Some approximation concepts for structural synthesis.

An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss example problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.

Schmit, L. A., Jr.↗
NASA NTRS1973

An improved separability approximation for line radiative transport in nonhomogeneous media.

A simple modification to the constant half-width approximation of Wilson and Greif, which is an extension of the well-known Curtis-Godson method to the treatment of temperature variations along the integration path, is introduced which permits a more accurate evaluation of line radiative transport in nonhomogeneous gases. To demonstrate the method's accuracy, comparisons are made with Wilson and Greif and numerical frequency integrated results for the line equivalent width and radiative flux in a planar slab with prescribed Planck function and line half-width spatial variations. These variations are chosen to represent typical shock layer conditions. It is found that the modified procedure reduces the inaccuracies inherent in Wilson and Greif's approximation by factors ranging from 5 to 10, while retaining the latter method's ease of application.

Boughner, R. E.↗
NASA NTRS1973

A thick-thin approximation for radiative transfer.

First- and second-order formulations of a thick-thin approximate technique for application to the solution of energy transport when nongray radiation is important are presented. The virtue of the technique is that it eliminates the cumbersome integral terms which usually appear. It is shown that the temperature distributions calculated with the technique agree well with the results of more rigorous calculations if a proper value of the critical optical depth, which separates the thick and thin regions of the spectrum, is used. The proper value of the critical optical depth is less than one and may be less than 0.5. It is also shown that the jump boundary conditions which are frequently employed with the Rosseland, or diffusion, approximation should incorporate the Planck mean absorption coefficient for a nongray gas. This is in contradiction to suggestions appearing in the literature.

Olstad, W. B.↗
NASA NTRS1973

Approximation for maximum centerline heating on lifting entry vehicles.

A centerline heating approximation is proposed in which only three basic equations need be solved. The heat rates correlate well with those obtained by more complex procedures. The approximation is readily adaptable to existing trajectory optimization programs to provide realistic surface temperature constraint capability with little increase in computer storage capacity and computer time. It is based on an analysis of heat-rate data computed for altitudes from 36,000 to 122,000 m, velocities from 600 to 7900 m/sec, and angles of attack from 0 to 60 degrees.

Helms, V. T., III↗
NASA NTRS1973

Note on the modified two-stream approximation of Sagan and Pollack.

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order l equal to or greater than 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic scattering.

Lyzenga, D. R.↗
NASA NTRS1973

Molecular collisions 21: Semiclassical approximation to atom-symmetric top rotational excitation

A distorted wave approximation to the T matrix for atom-symmetric top scattering was developed. The approximation is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.

Russell, D.↗
NASA NTRS1974

Use of a pitot-static probe for determining wing section drag in flight at Mach numbers from 0.5 to approximately 1.0

The use of a pitot-static probe to determine wing section drag at speeds from Mach 0.5 to approximately 1.0 was evaluated in flight. The probe unit is described and operational problems are discussed. Typical wake profiles and wing section drag coefficients are presented. The data indicate that the pitot-static probe gave reliable results up to speeds of approximately 1.0.

Montoya, L. C.↗
NASA NTRS1973

New methods of fragmentary approximation of a function

Certain special methods of fragmentary approximation of a function are examined and the properties of the most widespread elementary functions for such approximation methods are investigated, for the purpose of developing useful characteristics and properties for practical realization, in particular, for their reproduction by analog functional converters, with a significantly smaller number of controlable or adjustable parameters than in known ones.

Kolesnichenko, S. G.↗
NASA NTRS1974

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

Phillips, D. H.↗
NASA NTRS1974

An approximate inviscid radiating flow-field analysis for sphere-cone Venusian entry vehicles

A computational method based on the earlier work of one of the authors has been improved and modified to provide an accurate and rapid prediction of the radiating flow about blunt conical probes entering the atmosphere of Venus. Special features include a more general approximate equation of state, a more rapidly converging iteration scheme, a 38-step absorption coefficient model for a Venus atmosphere gas mixture model, and a shock-shape formula which yields a computed body shape in excellent agreement with the desired body. The method was used to calculate distributions of radiative heating for a large spherically blunted conical probe vehicle (1.219 m base diameter) and for three small spherically blunted conical probe vehicles (0.724 m base diameter). Solutions obtained with the presently developed approximate method required short computing times of the order of 1 to 3 minutes for each complete solution and gave agreements of 10% to 15% with the more exact predictions.

Falanga, R. A.↗
NASA NTRS1974

Approximations to and local properties of diffusions with discontinuous controls

The paper discusses several properties of control systems defined by stochastic differential equations, which are defined by the method of Girsanov, using a transformation of measures, and where the controls are discontinuous. Uniqueness of the multivariate distributions of the process is proved, and it is shown that the process is a limit, in a natural sense, of a certain discrete time approximation. Other questions, concerning the effects on the distributions of the paths, and of the cost of approximating the control by a smooth control and concerning local properties of the solution, are discussed.

Kushner, H. J.↗
NASA NTRS1974

Some approximation concepts for structural synthesis

An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.

Schmit, L. A., Jr.↗
NASA NTRS1974

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗