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NASA NTRS1974

Influence of rotation on the maximum mass of pulsationally stable stars

The critical mass for stability against radial pulsations in rotating, homogeneous main-sequence stars is found to be greater than in the case of no rotation. Analytic and detailed numerical models show that the critical mass rises steeply with increasing concentration of angular momentum to the center of the star. For uniform rotation near breakup velocity at the star's equator the critical mass is about 850 solar masses if an electron-scattering opacity is used, or about 5000 solar masses if the opacities of Cox and Stewart are used. For nonuniform rotation with a constant ratio of centrifugal force to gravity in the star, the critical mass becomes 'infinite' long before breakup velocity is attained. The relevance of the present results to several observational problems is noted.

Stothers, R.↗

NASA NTRS1975

Two-photon stimulated emission and pulse amplification

Threshold conditions are given for the sustained operation of standing-wave and long-pulse traveling-wave two-photon lasers. Pulse shortening in long-pulse two-photon amplification, a behavior absent in the one-photon case, is also demonstrated analytically.

Yuen, H. P.↗

NASA NTRS1977

Satellite-based thunderstorm intensity parameters

Thunderstorm growth rates are investigated through use of infrared data furnished by the Synchronous Meteorological Satellite. Blackbody temperature isotherms provide an accurate method of delineating the areal expansion of cold areas; the blackbody temperature isotherms are valuable analytical tools even in cases when there is very little decrease with time of the minimum cloud top temperature. In an application of the severe storm monitoring technique, the origin of tornadoes is found to be closely linked to a rapid expansion of cold areas in seven out of eight cases.

Adler, R. F.↗

NASA NTRS1981

Sound diffraction around screens and wedges for arbitrary point source locations

A development is presented for the Green's function for a point source in the vicinity of a rigid wedge. The diffraction contributions to the Green's function for arbitrary source and listener location is expressed in a form which can be readily evaluated using the Laguerre technique for numerical integration. The present approach offers the advantages of efficient numerical evaluation and of relatively straightforward reduction to well-known analytical approximations in limiting cases. Comparisons with previously obtained experimental and numerical results obtained by Ambaud and Bergassoli (1972) are presented. The comparison with the experimental results is excellent; the advantages of the present numerical technique, vis a vis that of Ambaud and Bergassoli, are pointed out.

Hadden, W. J., Jr.↗

NASA NTRS1982

Topics in strong Langmuir turbulence

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Nicholson, D. R.↗

NASA NTRS1983

Topics in strong Langmuir turbulence

Nicholson, D. R.↗

NASA NTRS1985

A preliminary study of a cryogenic equivalence principle experiment on Shuttle

The Weak Equivalence Principle is the hypothesis that all test bodies fall with the same acceleration in the same gravitational field. The current limit on violations of the Weak Equivalence Principle, measured by the ratio of the difference in acceleration of two test masses to their average acceleration, is about 3 parts in one-hundred billion. It is anticipated that this can be improved in a shuttle experiment to a part in one quadrillion. Topics covered include: (1) studies of the shuttle environment, including interference with the experiment, interfacing to the experiment, and possible alternatives; (2) numerical simulations of the proposed experiment, including analytic solutions for special cases of the mass motion and preliminary estimates of sensitivity and time required; (3) error analysis of several noise sources such as thermal distortion, gas and radiation pressure effects, and mechanical distortion; and (4) development and performance tests of a laboratory version of the instrument.

Everitt, C. W. F.↗

NASA NTRS1986

Methods for computing comet core temperatures

The temperature profile within the comet nucleus provides the key to an understanding of the history of the volatiles within a comet. Certain difficulties arise in connection with current cometary temperature models. It is shown that the constraint of zero net heat flow can be used to derive general analytical expressions which will allow for the determination of comet core temperature for a spherically symmetric comet, taking into account information about the surface temperature and the thermal conductivity. The obtained results are compared with the expression for comet core temperatures considered by Klinger (1981). Attention is given to analytical results, an example case, and numerical models. The formalization developed makes it possible to determine the core temperature on the basis of the numerical models of the surface temperature.

Mckay, C. P.↗

NASA NTRS1989

Space vehicle thermal testing: Principles, practices and effectiveness

Component qualification and acceptance temperatures are derived from worst case thermal analyses and analytic uncertainty margin subject to certain specified temperature extremes. Temperature requirements are shown for equipment operation within specification and for survival and turn-on (need not operate within specification, but must not experience any degradation when returned to operational range). Temperature excursions for most equipment are seen to be 20 to 50 C above and below room temperature. Components without active electronics which are mounted outboard, such as solar arrays and antennas, are usually designed to withstand wider temperature excursions, particularly at the cold end. Batteries are tightly controlled at cold temperatures to increase life. Payload components such as extremely accurate clocks for precise navigation are controlled over a relatively narrow temperature range.

Gluck, Donald F.↗

NASA NTRS1988

The topology of fractal universes

It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.

Hamilton, A. J. S.↗

NASA NTRS1989

Beam instability of the z mode in the solar wind

The instability of the slow extraordinary wave (z mode) caused by a tenuous population of energetic electrons, n(e), in the presence of a weak magnetic field and a cold plasma background, n(0), is investigated. The growth rate of the z mode was calculated within linear Vlasov theory and assuming that, for a weak magnetic field, the growth rate coincides with that of the electrostatic Langmuir wave, i.e., when the magnetic field is neglected for the cold background but retained for the energetic electrons. The analytical expression for the case of a thermal beam is deduced and numerically evaluated for some typical solar wind plasma conditions. The effects of the beam density, direction of propagation, and magnetic field on the observable polarization is discussed.

Krauss-Varban, D.↗

NASA NTRS1991

On the solution of a lubrication problem with particulate solids

The lubrication characteristic of a fluid with solid particles is studied using the continuum theory of mixtures. The governing equations are formulated and appropriate boundary conditions are introduced for an arbitrary-shaped lubricant film thickness. As a special case, closed-form analytical perturbation solutions for pressure and shear stress are obtained for a mixture of a conventional oil and solid particles with small values of solid-volume fraction sheared in the clearance space of an infinitely long slider bearing. It is found that when compared with a pure fluid, the mixture of the fluid and solid generates a higher pressure and therefore a higher load-carrying capacity with the added advantage of a reduction in the coefficient of friction.

Dai, F.↗

NASA NTRS1951

Approximate methods for calculating the flow about nonlifting bodies of revolution at high supersonic airspeeds

Explicit expressions are developed which yield the Mach number and pressure distributions on the surfaces of pointed nonlifting bodies of revolution operating at high supersonic airspeeds and at values of the hypersonic similarity parameter (ratio of free-stream Mach number to slenderness ratio) greater than 1. Very simple explicit expressions are obtained for these distributions in the special case of slender bodies. In the case of cones, the analytic solutions accurately define the entire flow field over a wide range of free-stream Mach numbers and apex angles.

Eggers, A J , Jr↗

NASA NTRS1990

Design sensitivity derivatives for isoparametric elements by analytical and semi-analytical approaches

This paper presents an analytical approach for incorporating design sensitivity calculations directly into the finite element analysis. The formulation depends on the implicit differentiation approach and requires few additional calculations to obtain the design sensitivity derivatives. In order to evaluate this approach, it is compared with the semi-analytical approach which is based on commonly used finite difference formulations. Both approaches are implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the accuracy and robustness of the developed analytical approach compared to the semi-analytical approach, some test cases using different structural and continuum element types are presented.

Zumwalt, Kenneth W.↗

NASA NTRS1993

Mesoscale simulations of the November 25-26 and December 5-6 cirrus cases using the RAMS model

The Regional Atmospheric Modeling System (RAMS), developed at Colorado State University, was used during the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment (FIRE) 2 (13 Nov. through 6 Dec. 1991) to provide real time forecasts of cirrus clouds. Forecasts were run once a day, initializing with the 0000 UTC dataset provided by NOAA (Forecast Systems Laboratory (FSL) Mesoscale Analysis and Prediction System (MAPS)). In order to obtain better agreement with observations, a second set of simulations were done for the FIRE 2 cases that occurred on 25-26 Nov. and 5-6 Dec. In this set of simulations, a more complex radiation scheme was used, the Chen/Cotton radiation scheme, along with the nucleation of ice occurring at ice supersaturations as opposed to nucleation occurring at water supersaturations that was done in the actual forecast version. The runs using these more complex schemes took longer wall clock time (7-9 hours for the actual forecasts as compared to 12-14 hrs for the runs using the more complex schemes) however, the final results of the simulations were definitely improved upon. Comparisons between these two sets of simulations are given. Now underway are simulations of these cases using a closed analytical solution for the auto-conversion of ice from a pristine ice class (sizes less than about 50 microns in effective diameter) to a snow class (effective diameters on the order of several hundred microns). This solution is employed along with a new scheme for the nucleation of ice crystals due to Meyers et al and Demott et al. The scheme is derived assuming complete gamma distributions for both the pristine and snow classes. The time rate of change of the number concentration and mass mixing-ratio of each distribution is found by calculating either the flux of crystals that grow beyond a certain critical diameter by vapor deposition in an ice supersaturated regime or by calculating the flux of crystals that evaporate to sizes below that same critical effective diameter.

Harrington, J. L.↗

NASA NTRS1994

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Filyushkin, V. V.↗

NASA NTRS2012

The High-Resolution Wave-Propagation Method Applied to Meso- and Micro-Scale Flows

The high-resolution wave-propagation method for computing the nonhydrostatic atmospheric flows on meso- and micro-scales is described. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The method uses a flux-based wave decomposition in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The two advantages of the technique are: 1) the need for an explicit definition of the Roe matrix is eliminated and, 2) the inclusion of source term due to gravity does not result in discretization errors. The resulting flow solver is conservative and able to resolve regions of large gradients without introducing dispersion errors. The methodology is validated against exact analytical solutions and benchmark cases for non-hydrostatic atmospheric flows.

Ahmad, Nashat N.↗

NASA NTRS2015

Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation

To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.

Seebeck Effect↗