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Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.
A genetic algorithm is used to select the inputs to a neural network function approximator. In the application considered, modeling critical parameters of the space shuttle main engine (SSME), the functional relationship between measured parameters is unknown and complex. Furthermore, the number of possible input parameters is quite large. Many approaches have been used for input selection, but they are either subjective or do not consider the complex multivariate relationships between parameters. Due to the optimization and space searching capabilities of genetic algorithms they were employed to systematize the input selection process. The results suggest that the genetic algorithm can generate parameter lists of high quality without the explicit use of problem domain knowledge. Suggestions for improving the performance of the input selection process are also provided.
Radial velocities have been obtained for six of nine stars identified on the basis of similar distances and common, extreme transverse velocities in the proper motion survey of Majewski (1992) as a candidate halo moving group at the north Galactic pole. These radial velocities correspond to velocities perpendicular to the Galactic plane which span the range -48 +/- 21 to -128 +/- 9 km/sec (but a smaller range, -48 +/- 21 to -86 +/- 19 km/sec, when only our own measurements are considered), significantly different than the expected distribution, with mean 0 km/sec, for a random sample of either halo or thick disk stars. The probability of picking such a set of radial velocities at random is less than 1%. Thus the radial velocity data support the hypothesis that these stars constitute part of a halo moving group or star stream at a distance of approximately 4-5 kpc above the Galactic plane. If real, this moving group is evidence for halo phase space substructure which may be the fossil remains of a destroyed globular cluster, Galactic satellite, or Searle & Zinn (1978) 'fragment.'
An approximate method for calculating heating rates on three-dimensional vehicles at angle of attack is presented. The method is based on the axisymmetric analog for three-dimensional boundary layers and uses a generalized body-fitted coordinate system. Edge conditions for the boundary-layer solution are obtained from an inviscid flowfield solution, and because of the coordinate system used, the method is applicable to any blunt body geometry for which an inviscid flowfield solution can be obtained. The method is validated by comparing with experimental heating data and with thin-layer Navier-Stokes calculations on the shuttle orbiter at both wind-tunnel and flight conditions and with thin-layer Navier-Stokes calculations on the HL-20 at wind-tunnel conditions.
We discuss the question of the form of the radiative transfer equation in an expanding envelope when a quasi-static approximation is applied. We find that the radiative transfer equation written in the fluid's rest frame must include the `advection' term.
The GEOTAIL satellite experienced several encounters with the magnetopause during the interval 0300 to 0600 hours on 27 October 1992 at a gsm location of (X,Y,Z) approximately (-81, -8, 7.5) R(sub e). Energetic ions of both solar wind and ionospheric origin (H(+), He(++), and O(+)) were observed streaming in the anti-solar direction on both the lobe and magnetosheath side of the plasma mantle-magnetosheath boundary, with maximum fluxes occuring at the boundary. Even though the mantle plasma had penetrated well into the lobe through convective drift, the energetic ions were observed only at the magnetopause and provided a clear signature of the boundary region. Using a measured convective drift velocity and observed ergetic particle anisotropies, we estimated that the maximum distance from GEOTAIL that the energetic ions could have been accelerated or made contact with the boundary field lines was less than 8 - 39 R(sub e), implying that both solar wind and ionospheric ions are accelerated and contact the magnetopause many tens of earth radii behind the earth. We further found that the unusual magnetopause positions encountered at this time could be explained in part by solar wind aberration effects. However additional processes (e. g., magnetospheric breathing modes, convoluted tail topologies) are required to fully explain these observations.
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.
The axis ratio distribution of faint galaxies observed by the Hubble Space Telescope (HST) as part of the Medium Deep Survey (MDS) key project suggests that a very large fraction of the total population at magnitudes I greater than or equal to 20 mag consists of a class of galaxies with luminosity profile, axis ratio distribution, angular size, and color that resemble local dwarfs. We find that galaxies with exponential light profiles and small angular sizes (half-light radius less than 0.6 sec) have an axis ratio distribution that is incompatible with their being intrinsically flattened objects and is instead consistent with local elliptical galaxies. We call these objects 'Small Exponential Ellipticals.' They are most likely dwarf galaxies, and they are numerous enough that, together with irregular galaxies, they can account for most if not all of the excess in the number counts at I approximately 20-21 mag with respect to the standard no-evolution models. This may suggest that the excess number counts are best explained by dwarf-rich models with strong luminosity evolution of the dwarf galaxies. Our data also supports a very mild luminosity evolution of the giant galaxy populations, which contributes little to the excess number counts.
We present high-quality spectra covering the K window at a resolving power of 340 for a sample of 13 ultraluminous (L(sub IR) approximately greater than 10(exp 12) solar luminosity) infrared-selected galaxies, and line fluxes for a comparison sample of 24 lower luminosity galaxies. The 2 micrometers spectra of 10 of the ultraluminous galaxies are characterized by emission and absorption features commonly associated with stars and star formation; two others have the red power-law spectra and Br gamma line widths of Seyfert 1 galaxies; the final galaxy has strong emission from hot dust. We have found no broad-line active nuclei not already known from optical observations, despite the fact that the extinction at 2 micrometers is 1/10 that at optical wavelengths; any putative Seyfert 1 nuclei must be deeply buried. Powerful continua and emission lines from H2 and Br gamma are detected in all the ultraluminous galaxies. Comparing the H2 1-0 S(1), Br gamma, and 2 micrometers and far-infrared luminosities to those of the lower luminosity galaxies yields several major results. First, the dereddened Br gamma emission, relative to the far-infrared luminosity is significantly depressed in the ultraluminous sample, when compared to the lower luminosity galaxies. Five of the ultraluminous galaxies have L(sub Br gamma)L(sub IR) ratios lower than for any of the comparison objects. Second, the H2 1-0 S(1) luminosity is also responsible, directly or indirectly, for producing the excited H2, and that the H2 apparently comes from optically thin regions in both classes of objects. Third, eight of the 13 ultraluminous systems have lower 2 micrometers/far-infrared luminosity ratios than any of the lower luminosity galaxies, and five of these are the galaxies also deficient in Br gamma. These three findings may be understood if the the H2, Br gamma, and 2 mircometers continua in the ultraluminous galaxies arise from spatially distinct regions, with the continuum and Br gamma largely coming from volumes optically thick even at 2 micrometers, and obscured in such a fashion that the extinctions measured using optical spectroscopy do not properly measure the true optical depths. If this is the case, then even near-infrared spectroscopy may be unable to exclude the presence of undetected powerful active galactive nuclei in the ultraluminous galaxies.
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.
Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.
A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.
An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.
In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.
An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.
Astronauts often experience back pain during spaceflight. It was found that during spaceflight, 14 of 19 Shuttle crewmembers experienced back pain, which they described as dull (62%), localized to the lower back (500/6), and with an intensity of 2 on a 5-point scale. Further, the spine lengthens 4-7 cm in microgravity. Our objective was to compare back pain and spinal lengthening (body height increase) during simulated microgravity (6 deg head-down tilt, HDT) with the some parameters during actual microgravity. Eight male subjects completed a modified McGill pain questionnaire with intensity graded from zero (no pain) to five (intense and incapacitating gain) each day at 7.-OO pm during 2 d pre-HDT control, 16 d HDT, and I d post-HDT recovery periods. Only 2 subjects reported any pain after day 9 of HDT and during recov- ery. Heights increased 2.1 t 0.5 cm by day 3 of HDT and re- mained at that level until the end of the HDT period. Although spinal lengthening in space is greater than that during HDT, the HDT model approximates the level, type, distribution, and time course of back pain associated with actual microgrovity. In the HDT model, pain subsides in intensity when spinal lengthening stops. Therefore, back pain in actual and simulated microgravity may result from stretching of spinal andlor paraspinal tissues until a new spinal length is reached.