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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 379 records · Page 21
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NASA NTRS1975

Nonlinear acoustic behavior at a caustic - An approximate analytical solution

The present paper discusses an approximate analytical solution to the nonlinear behavior of a discontinuous acoustic signal near a caustic. The Seebass transformation (1970) is refined to provide results which satisfy the governing equation to any prescribed accuracy, except across the shock wave produced by reflection of the simple wave at the caustic. The solution is approximate in the sense that the basic equation is satisfied wherever the solution is continuous but can satisfy only one of the two jump conditions at the reflected shock. The results give essential geometric features of the exact solution and provide a quantitative estimate of the strength of the so-called superboom.

Gill, P. M.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) 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.↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
NASA NTRS1975

Approximate solutions of radiative transfer in dusty nebulae. 2: Hydrogen and helium

The ionization structure of hydrogen and helium in dusty nebulae is discussed. The general equations for pure hydrogen nebulae are modified to include helium. An approximate analytic solution is presented for Stroemgren radii of hydrogen and helium in the absence of dust. It is shown that these results, with simple modifications, are also applicable to dusty nebulae where the effective absorption cross section of dust grains varies slowly with frequency in the 1000 to 200A range. No analytic solutions are possible if this cross section varies rapidly with frequency. In this case, however, simple coupled differential equations are derived. Approximate analytic expressions are presented for evaluation of the variation of the fraction of ionizing radiation absorbed by dust and the ratio of the volume emission measures of He II to H II regions with the spectrum of the ionizing source, helium abundance, and absorption properties of dust. The effects of dust on the He III zone are discussed. Results are restricted to spherically symmetric nebulae, but nonuniform gas and dust distributions and clumpiness can be taken into account.

Dana, R. A.↗
NASA NTRS1976

Accuracy of decoupling approximations for rotational excitation - Low-energy CO-He collisions

Scattering calculations have been performed for low-energy collisions of CO with He using the 'effective potential' approximation of Rabitz (1972) and the 'coupled states' approximation of McGuire and Kouri (1973). These are compared with the accurate quantum close-coupling scattering results of Green and Thaddeus. All calculations employed a theoretical potential believed to represent accurately the true interaction. The effective potential method is found to be in qualitative agreement, and the coupled states method is found to be in semi-quantitative agreement, with close-coupling results for rotationally inelastic integral cross sections.

Green, S.↗
NASA NTRS1975

An examination of the adiabatic approximation in cosmic ray propagation theory

A theory for the pitch-angle scattering of cosmic rays in a turbulent magnetic field can be derived from first principles by applying both the quasi-linear and adiabatic approximations to the master equation for the ensemble averaged distribution function. A proof of the failure of these approximations, taken together, is given. Some predictions of the quasi-linear theory, are given. New wave-like propagation modes have been discovered.

Scudder, J.↗
NASA NTRS1976

Approximate statistics of random vector magnitudes

Simple, rough approximations are presented for the mean and 99% values for random vectors of up to three independent elements. The accuracy of the provided approximate expressions has been investigated with the aid of Monte Carlo simulations involving 15 different combinations of the three statistical parameters. The results of this investigation are discussed.

Hagar, H., Jr.↗
NASA NTRS1976

On the accuracy of the 'decoupled l-dominant' approximation for atom-molecule scattering

Cross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the 'decoupled l-dominant' (DLD) approximation and are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. DLD predictions of state-to-state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data.

Green, S.↗
NASA NTRS1976

Exponential approximation for daily average solar heating or photolysis

When incorporating formulations of instantaneous solar heating or photolytic rates as functions of altitude and sun angle into long range forecasting models, it may be desirable to replace the time integrals by daily average rates that are simple functions of latitude and season. This replacement is accomplished by approximating the integral over the solar day by a pure exponential. This gives a daily average rate as a multiplication factor times the instantaneous rate evaluated at an appropriate sun angle. The accuracy of the exponential approximation is investigated by a sample calculation using an instantaneous ozone heating formulation available in the literature.

Cogley, A. C.↗
NASA NTRS1976

Approximate solutions of radiative transfer in dusty nebulae. II - Hydrogen and helium

The ionization structure of hydrogen and helium in dusty nebulae is discussed. General equations for pure hydrogen nebulae have been modified to include helium. An approximate analytical solution is presented for Stroemgren radii of hydrogen and helium in the absence of dust. It is shown that these results, with simple modifications, are also applicable to dusty nebulae where the effective absorption cross section of dust grains varies slowly with frequency in the range from 1000 to 200 A. No analytical solutions are possible if this cross section varies rapidly with frequency. In this case, however, simple coupled differential equations are derived which can easily be solved numerically. Approximate analytical expressions are given for evaluating the variation of the fraction of ionizing radiation absorbed by dust and the ratio of the volume emission measures of He II to H II regions with the spectrum of the ionizing source, helium abundance, and absorption properties of dust. The effects of dust on the He III zone are discussed. The present results are restricted to spherically symmetric nebulae, but nonuniform gas and dust distributions and clumpiness can be taken into account by the general results.

Dana, R. A.↗
NASA NTRS1977

Total Born approximation cross sections for single electron loss by atoms and ions colliding with atoms

The first born approximation (FBA) is applied to the calculation of single electron loss cross sections for various ions and atoms containing from one to seven electrons. Screened hydrogenic wave functions were used for the states of the electron ejected from the projectile, and Hartree-Fock elastic and incoherent scattering factors were used to describe the target. The effect of the target atom on the scaling of projectile ionization cross sections with respect to the projectile nuclear charge was explored in the case of hydrogen-like ions. Scaling of the cross section with respect to the target nuclear charge for electron loss by Fe (+25) in collision with neutral atoms ranging from H to Fe is also examined. These results were compared to those of the binary encounter approximation and to the FBA for the case of ionization by completely stripped target ions.

Rule, D. W.↗
NASA NTRS1976

A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response

A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN.

Everstine, G. C.↗
NASA NTRS1977

An improved digital algorithm for fast amplitude approximations of quadrature pairs

A computationally fast algorithm for approximating the amplitude (A) of a quadrature pair (I,Q) has been discovered. The piecewise linear formula, the unbiased estimate of A=X+1/8y when X or = 3Y and 7/8X + 1/2Y when X or = 3Y applies where X is congruent to the maximum absolute value of (I,Q) and Y is congruent to the minimum absolute value of (I,Q). This algorithm has been proven to be far more accurate then currently used approximations. An immediate application is the wideband digital spectrum analyzer under development for monitoring radio frequency interference at Deep Space Network stations.

Levitt, B. K.↗
NASA NTRS1976

A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.

Mitchell, D. G.↗
NASA NTRS1977

Approximations for proton excitation of coronal ion fine structure

Explicit approximations that yield proton excitation cross sections and rate coefficients for fine-structure transitions in a wide variety of ions over the low and intermediate energy ranges are obtained in terms of the electric quadrupole transition probability and quadrupole radial integral of a given ion. The range of applicability of these approximations is discussed, and comparisons are made with available cross sections and rate coefficients. Values of quadrupole radial integrals are given for ground configurations of even-Z elements in higher stages of ionization. Proton excitation rate coefficients are computed for coronal transitions involving fine-structure levels in the ions Fe XIII, Fe XV, Fe XVIII, Fe XXI, and Ca XIII.

Kastner, S. O.↗
NASA NTRS1977

Computational tests of angular momentum decoupling approximations for pressure broadening cross sections

The utility of several approximate scattering methods for predicting collision induced spectral pressure broadening has been tested by comparison with accurate close coupling results. In particular, broadening of the pure rotational spectra of HD, HCl, CO, and HCN - all perturbed by low energy collisions with He atoms - has been computed using the effective potential formalism of Rabitz, the decoupled l-dominant approximation of DePristo and Alexander, and the j(2)-conserving coupled states method of McGuire and Kouri. For this last method, pressure broadening cross sections have been obtained with the new, correct expression recently derived by Goldflam and Kouri as well as with an earlier formalism based on an incorrect labeling of the scattering matrices. These methods were found to be generally diasppointing for predicting pressure broadening with the exception of the new, correctly formulated j(2)-conserving coupled states method which was found to agree quantitatively (better than 5%) with close coupling values for all cases studied.

Green, S.↗
NASA NTRS1977

Note on the forward-scatter approximation

An asymptotic expansion in inverse powers of the wave number is derived for an integral of a type often encountered in the theory of wave propagation in inhomogeneous media. The procedure, which is essentially a forward-scatter approximation, yields all the terms of the expansion. In contrast, the conventional forward-scatter approximation is found to yield correctly only the first term of the expansion.

Wenzel, A. R.↗