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At least 1,261 records · Page 70

Approximate temperature distribution for a diffuse, highly reflecting material.

The application of a 'two-flux' technique is considered for determining the reflective characteristics and approximate temperature distribution in highly backscattering materials characterized by a very small absorption coefficient. With respect to the transmitted internal radiation fields, the internal radiative emission is assumed to be negligible. A comparison of theory and experiment is presented.

Weston, K. C.↗

Input noise approximation in tracker modeling

The validity of approximating random Gaussian distributed inputs used in human response modeling by sums of discrete sine waves is studied. An ideal rectangular power density spectrum is simulated using both filtered Gaussian white noise and sums-of-discrete sine waves with three different input cutoff frequencies in the same compensatory tracking task. Resulting normalized tracking error and quality operator observations are used to investigate apparent discrepancies in human operator characteristics. Results show that discrete and continuous input tracking data compare favorable when the power in the crossover region is taken into account.

Torrey, P. F.↗

Approximations to the plasma dispersion function

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.↗

Molecular collisions. 11: Semiclassical approximation to atom-symmetric top rotational excitation

In a paper of this series a distorted wave approximation to the T matrix for atom-symmetric top scattering was developed which 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.↗

Approximations to the mean surface of Mars and Mars atmosphere using Mariner 9 occultations

When the Mariner 9 spacecraft passed behind Mars in its orbiting phase, the radio beam was cut off by some physical feature. These occultations occurred during the months of November and December 1971 and again in April and May 1972. The fairly good global spread of these data was used to estimate the shape of the Martian globe, as definable by mathematical shapes (ellipsoidal and spherical harmonic). The refraction profiles allowed the estimation of pressure near the occultation point; these, corrected back to an arbitrary fixed value of pressure, chosen to be 6.1 mb, were used as radii to an isobaric surface. Preliminary results showed a figure displacement from the mass center with a best fit southeast by 2.85 km. There was also an equatorial displacement in the direction of about 100 deg W. Atmospheric approximations for the mass center to 6.1-mb pressure distances were fit to an ellipsoid.

Cain, D. L.↗

A simple analytic approximation for dusty stromgren spheres.

We interpret recent far-infrared observations of H II regions in terms of true absorption by internal dust of a significant fraction of the Lyman-continuum photons. We present approximate analytic expressions describing the effects of internal dust on the ionization structure of H II regions, and outline a procedure for deducing the properties of this dust from optical and infrared observations.

Petrosian, V.↗

Approximate analysis of containment/deflection ring responses to engine rotor fragment impact.

The transient responses of containment and/or deflection rings to impact from an engine rotor-blade fragment are analyzed. Energy and momentum considerations are employed in an approximate analysis to predict the collision-induced velocities which are imparted to the fragment and to the affected ring segment. This collision analysis is combined with the spatial finite-element representation of the ring and a temporal finite-difference solution procedure to predict the resulting large transient elastic-plastic deformations of containment/deflection rings. Some comparisons with experimental data are given.

Wu, R. W.-H.↗

Corner pressures and fillet shock locations for symmetrical corners by an approximate method.

Description of an approximate method for predicting the pressure in the immediate corner region and the shock structure on stream-aligned, sharp-leading-edge, symmetrical corner configurations. The method is basically the two-shock method developed by Charwat and Redekopp (1966), with the additional assumption that the corner fillet shock can be located from the calculated pressure in the corner. Corner pressures are correlated over a wide range of Mach numbers in air and helium for different corner wedge angles. The shock structure calculated by this method is compared with supersonic and hypersonic data.

Watson, R. D.↗

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

Somogyi, D.↗

Partition function for a two dimensional plasma in the random phase approximation

The partition function for a two-dimensional plasma is evaluated within the random phase approximation. The periodic boundary conditions are fully taken into account by including the periodic image interactions. In the guiding-center limit, the negative temperature threshold energy is evaluated, and a value different from previous calculations results. When an identical random phase evaluated, and a value different from previous calculations results. When an identical random phase evaluation is applied to the finite gyroradius plasma, the Salzberg-Prager-May equation of state is recovered.

Seyler, C. E., Jr.↗

Calculation of the total electron excitation cross section in the Born approximation using Slater wave functions for the Li (2s yields 2p), Li (2s yields 3p), Na (3s yields 4p), Mg (3p yields 4s), Ca (4s yields 4p) and K (4s yields 4p) excitations

Excitation of neutral atoms by inelastic scattering of incident electrons in gaseous nebulae were investigated using Slater Wave functions to describe the initial and final states of the atom. Total cross sections using the Born Approximation are calculated for: Li(2s yields 2p), Na(3s yields 4p), k(4s yields 4p). The intensity of emitted radiation from gaseous nebulae is also calculated, and Maxwell distribution is employed to average the kinetic energy of electrons.

Simsic, P. L.↗

Scattering in liquid haze - Analytic approximations

An analytic formula is derived which describes approximately the scattering of electromagnetic waves in a haze. This formula is compared, and found to agree well, with the exact results from Mie theory that are available in the literature. The formula is used to arrive at a simple, nonredundant, but complete parametrization of the aerosol model.

Kuriyan, J. G.↗

Limitations to the small scale yielding approximation for crack tip plasticity

Recent finite-element results by S. G. Larsson and A. J. Carlsson suggest a limited range of validity to the 'small scale yielding approximation,' whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor. It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting parallel to the crack at its tip, which accompanies the inverse square-root elastic singularity. Further implications of the non-singular stress term for crack tip deformations and fracturing are examined. It is suggested that its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than its effect on the yield zone size.

Rice, J. R.↗

Partition function for a two-dimensional plasma in the random-phase approximation

The partition function for a two-dimensional plasma is evaluated within the random-phase approximation. The periodic boundary conditions are taken fully into account by including the periodic image interactions. In the guiding-center limit, the 'negative temperature' threshold energy is evaluated, and a value different from previous calculations results. When an identical random-phase evaluation is applied to the finite-gyroradius plasma, the Salzberg-Prager-May equation of state is recovered.

Seyler, C. E., Jr.↗

Evidence for an approximately 4.5 aeon age of plagioclase clasts in a lunar highland breccia

Argon from neutron-irradiated mineral separates and whole rock samples of a metamorphosed breccia (65015) from Apollo 16 has been analyzed with a large number of gas extraction steps in order to obtain a high resolution in the apparent ages and to identify the gas released from different sources. The results on plagioclase show a Ar-40/Ar-39 plateau age of 3.98 b.y. which is attributed to the time of metamorphism, and an age of about 4.5 b.y. in the high-temperature fraction. Correlation of the release pattern with Ar-37 instead of Ar-39 permits the association of the approximate 4.5 b.y. age with relict plagioclasts which were demonstrated in previous petrographic and Rb-Sr studies as being unequilibrated. This result suggests that it is possible to identify lithic components which represent the early lunar crust.

Jessberger, E. K.↗

Least squares adjustment with relatively large observation errors, inaccurate initial approximations, or both

Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.

Eichhorn, H.↗

An approximate method of analysis for notched unidirectional composites

An approximate method is proposed for the analysis of unidirectional, filamentary composite materials having slit notches perpendicular to the fibers and subjected to tension parallel to the fibers. The approach is based on an engineering model which incorporates important effects of material heterogeneity by considering average extensional stresses in the fibers and average shear stresses in the matrix. Effects of interfacial failure and matrix plasticity at the root of the notch are considered. Predictions of the analysis are in reasonably good agreement with previous analytical models and experimental data for graphite/epoxy.

Zweben, C.↗

Applicability of the diffusion approximation

Several methods using an approximate form of the scattering indicatrix are discussed for simplifying the calculation of radiation transport in planetary atmospheres.

Biryukov, Y. L.↗