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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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NASA NTRS1981

Shape determination and control for large space structures

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Weeks, C. J.↗
NASA NTRS1981

Static shape determination and control for a large space antenna

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and quadratic performance criteria for the comparison of estimates or control forces. Results are illustrated by simulations with a finite element model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic model. These expansions provide approximate solutions in the event that a closed form analytical solution to the system boundary value problem is not available.

Weeks, C.↗
NASA NTRS1986

A canonical expansion for nonlinear systems

The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

Su, R.↗
NASA NTRS2000

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Dydson, Roger W.↗
NASA NTRS2005

The Growth, Polarization and Motion of the Radio Afterglow from the Giant Flare from SGR 1806-20

The extraordinary giant flare (GF) of 2004 December 27 from the soft gamma repeater (SGR) 1806-20 was followed by a bright radio afterglow. We present an analysis of VLA observations of this radio afterglow from SGR 1806-20, consisting of previously reported 8.5 GHz data covering days 7 to 20 after the GF, plus new observations at 8.5 and 22 GHz from day 24 to 81. We find a deceleration in the expansion, from approximately 4.5 mas/day to less than 2.5 mas/day. The time of deceleration is roughly coincident with the rebrightening in the radio light curve, as expected to result when the ejecta from the GF sweeps up enough of the external medium, and transitions from a coasting phase to the Sedov-Taylor regime. The radio afterglow is elongated and maintains a 2:l axis ratio with an average position angle of -40 degrees (north through east), oriented perpendicular to the average intrinsic linear polarization angle. We also report on the discovery of motion in the flux centroid of the afterglow, at an average velocity of 0.26 plus or minus 0.03 c (assuming a distance of 15 kpc) at a position angle of -40 degrees. This motion, in combination with the growth and polarization measurements, suggests an initially asymmetric outflow, mainly from one side of the magnetar.

Taylor, G. B.↗
NASA NTRS2005

Solving Nonlinear Euler Equations with Arbitrary Accuracy

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Dyson, Rodger W.↗
NASA NTRS1972

Optimum Three Impulse Trajectory Generator with Patched Conic Trajectory Model

Optimal multi-impulse trajectories were investigated as a nominal about which asymptotic expansion was used to obtain approximations of optimal low thrust trajectories. The work consisted of the analysis and description of an optimal 3-impulse trajectory program. A patched-conic trajectory model was specifically designed for compatibility with the subsequent addition of the low thrust expansion approximation.

Payne, M. H.↗
NASA NTRS2022

Solar Temperature Variations Computed from SORCE SIM Irradiances Observed During 2003-2020

NASA’s Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) instrument produced about 17 years of daily average Spectral Solar Irradiance ( SSI ) data for wavelengths 240 nm – 2416 nm. We choose a day of minimal solar activity, 2008-08-24, during the 2008 − 2009 minimum between cycles 23 and 24, and compute the brightness temperature (𝑇 o ) from that day’s solar spectral irradiance (𝑆𝑆𝐼 o ). We consider small variations of T and SSI about these reference values, and derive linear and quadratic analytic approximations by Taylor expansion about the reference day values. To determine approximation accuracy, we compare to exact brightness temperatures T computed from the Planck spectrum, by solving analytically for T , or equivalent root-finding in Wolfram Mathematica. We find that the linear analytic approximation overestimates, while the quadratic underestimates the exact result. This motivates search for statistical “fit” models “in between” the two analytic models, with minimum root-mean-square-error RMSE. We make this search using open-source statistical R software, determine coefficients for linear and quadratic fit models, and compare statistical with analytic RMSE’s. When only linear analytic and fit models are compared, the fit model is superior at ultraviolet, visible, and near infrared wavelengths. This again holds true when comparing only quadratic models. Quadratic is superior to linear for both analytic and statistical models, and statistical fits give smallest RMSE’s. Lastly, we use linear analytic and fit models to find an interpolating function in wavelength, useful in case the SIM results need adjustment to another choices of wavelengths, to compare or extend to any other instrument.

SORCE↗
NASA NTRS1986

More on the expansion of a collisionless plasma into the wake of a body

Recent laboratory measurements of plasma expansion in a plasma wake experiment (Wright et al., 1985) are compared with analytical expressions which approximate the plasma expansion model of Crow et al. (1975). Good quantitative agreement is found between the data and theory for the velocity and position of the ion expansion front. These results provide an important insight into the behavior of the expansion early in its development.

Wright, K. H., Jr.↗
NASA NTRS1992

The effects of Venusian mantle convection with multiple phase transitions

Recently there was a flurry of activities in studying the effects of phase transitions in the Earth's mantle. From petrological and geophysical considerations, phase-transitions would also play an important role in venusian dynamics. The basic differences between the two planets are the surface boundary conditions, both thermally and mechanically. In this vein we have studied time-dependent mantle convection with multiple phase transitions and depth-dependent thermal expansivity (alpha is approximately rho(exp -6)), based on high-pressure and temperature measurements. Both the olivine-spinel and spinel-perovskite transitions were simulated by introducing an effective thermal expansivity, as described. Used together with the extended Boussinesq Approximation this method serves as a powerful tool to examine the effects of phase transitions on convection at relatively low computational costs.

Steinbach, V.↗
NASA NTRS1985

A model of the planetary nebula NGC 2392 determined from velocity observations

High-resolution slit spectra are combined with published photometric and velocity data to develop a model of the double-ring planetary nebula NGC 2392. The inner ring is due to an incomplete, prolate spheroid shell with most of the material concentrated near the minor axis circumference. The spheroid is seen almost pole-on, open at the sharp ends, and the formal velocity of expansion (93 km/s) at the ends is a record high for planetary nebulae. The outer ring is a nearly round spheroid of approximately 16 km/s expansion velocity and a different tilt angle than the inner shell. It is surrounded by rapidly expanding material with velocities of at least 75 km/s. A high-velocity stream of material is formed at the open ends of the inner shell and is accelerated by the central star's stellar wind to velocities of at least + or - 190 km/s, providing the first direct evidence for the kinematic role of a strong stellar wind. The inner shell age is approximately 800 yr, arguing that the shell material was preferentially ejected from the equator of the parent star, in contradiction with the usual predictions of theory.

Odell, C. R.↗
NASA NTRS1992

Resolution properties of the Fourier method for discontinuous waves

In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.

Gottlieb, David↗
NASA NTRS1976

Observations of the Gum Nebula with a Fabry-Perot spectrometer

Scans have been made of H-alpha, 6584-A forbidden N II, 5007-A forbidden O III, and 5876-A He I emissions in selected directions in the Gum Nebula. Analyses of the line profiles and line intensities indicate that much of the emitting gas in the Gum Nebula is confined to an expanding shell which has a radius of about 125 pc, an expansion velocity of approximately 20 km/s, an emission measure which ranges from about 15 units to about 500 units, and a temperature near 11,000 K. The ultraviolet flux from zeta Pup and gamma-2 Vel appears to be capable of producing most of the observed ionization, although the origin of the shell structure and high expansion velocity is not certain.-

Reynolds, R. J.↗
NASA NTRS1981

Plane-polar Fresnel and far-field computations using the Fresnel-Wilcox and Jacobi-Bessel expansions

It is pointed out that the computation of the Fresnel fields for large aperture antennas is significant for many applications. The present investigation is concerned with an approach for the effective utilization of the coefficients of the Jacobi-Bessel series for the far-field to obtain an analytically continuous representation of the antenna field which is valid from the Fresnel region into the far field. Attention is given to exact formulations and closed form solutions, Fresnel and Fresnel small angle approximations, aspects of field expansion, the accuracy of the Fresnel and Fresnel small angle approximations, and the Jacobi-Bessel expansion applied to the Fresnel small angle approximation.

Rahmat-Samii, Y.↗
NASA NTRS1975

Thermal diffuse X-ray scattering in simple metals

Calculations are reported for the ionic structure factor and X-ray scattering cross section of sodium (at T=0 K and 90 K) and lithium (both isotopes at T=0 K) within the harmonic approximation. An evaluation of the appropriate displacement- displacement correlation function by the special point method circumvents the need for a multiphonon expansion. In the case of sodium, the structure in the one-phonon scattering was straightforwardly accounted for, and an approximate expansion was obtained for all multiphonon scattering. By treating core and conduction electrons on an equal footing, it is shown that information on the conduction electron system is present in the forward scattering component. In lithium the one-phonon cross section at small angles aids in the determination of the effective electron-ion interaction.

Straus, D. M.↗
NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗