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NASA NTRS1994

Metal-line absorption at Z(sub abs) approximately Z(sub em) from associated galaxies

For a preliminary study of whether C IV absorption at Z(sub abs) approximately Z(sub em) is related to associated galaxy companions, we have collected data from a sample of 10 quasars with 0.15 less than z less than 0.65 for which high-resolution optical and UV spectroscopy is available from the literature, and for which we have deep optical images and limited spectroscopy. We also present new optical spectra for two of our samples. Four of these quasars have associated C IV absorption systems. In thes four fields, there are eight galaxies with M(sub r) less than -19.0 mag within 35 kpc of the quasar (projected distance, assuming they are at the quasar redshift), which may be candidates for the associated C IV absorption. This observed density of galaxies near quasars with associated C IV absorption is significantly greater than that for a control sample of quasars chosen from the literature. This result suggests that galaxies near the quasar line of sight may be linked with associated C IV absorption. None of these quasars show associated Mg II absorption, despite the presence of galaxies very near the line of sight, suggesting a Mg II 'proximity effect,' where ionizing flux from the quasar destroys the Mg(+) from at least the outer parts of the galaxies. Three quasars are located in rich galaxy clusters, but none of these quasars are found to have associated C IV absorption. This suggests that galaxies in rich clusters associated with quasars are less likely to be metal-line absorbers. It is plausible that the extended galaxy halos which may be responsible for the absorptions are stripped from galaxies in these dense environments. While it seems that at Z approximately 0.6 rich clusters do not cause them, associated C IV absorption systems at higher redshift may be explained by associated clusters if there has been evolution in the properties of galaxy halos in dense environments.

Ellingson, E.↗
NASA NTRS1994

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗
NASA NTRS1996

Approximate Analysis for Interlaminar Stresses in Composite Structures with Thickness Discontinuities

An efficient, approximate analysis for calculating complete three-dimensional stress fields near regions of geometric discontinuities in laminated composite structures is presented. An approximate three-dimensional local analysis is used to determine the detailed local response due to far-field stresses obtained from a global two-dimensional analysis. The stress results from the global analysis are used as traction boundary conditions for the local analysis. A generalized plane deformation assumption is made in the local analysis to reduce the solution domain to two dimensions. This assumption allows out-of-plane deformation to occur. The local analysis is based on the principle of minimum complementary energy and uses statically admissible stress functions that have an assumed through-the-thickness distribution. Examples are presented to illustrate the accuracy and computational efficiency of the local analysis. Comparisons of the results of the present local analysis with the corresponding results obtained from a finite element analysis and from an elasticity solution are presented. These results indicate that the present local analysis predicts the stress field accurately. Computer execution-times are also presented. The demonstrated accuracy and computational efficiency of the analysis make it well suited for parametric and design studies.

Rose, Cheryl A.↗
NASA NTRS1994

Coupled-Cluster Theory Employing Approximate Integrals: An Approach to Avoid the Input/Output and Storage Bottlenecks

By representing orbital products in an expansion basis, certain classes of two-electron integrals are approximated for use in CCSD(T) calculations (singles and doubles coupled-cluster plus a perturbational estimate of the effects of connected triple excitations). This leads to a very large reduction in disk storage and input/output requirements, with usually only a modest increase in computational effort. The new procedure will allow very large CCSD(T) calculations to be undertaken, limited only by available processor time. Using the molecular basis as the expansion basis, explicit numerical comparisons of equilibrium geometries, harmonic frequencies, and energy differences indicate that the error due to the use of approximate integrals is less than the error associated with truncation of the molecular basis set.

Rendell, Alistair P.↗
NASA NTRS1994

Rigorous Justification of the Localized Approximation to the Beam-Shape Coefficients in Generalized Lorenz-Mie Theory: On-Axis Beams - Part 1

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams.

Lock, James A.↗
NASA NTRS1998

Rocket Propellant Ducts (Cryogenic Fuel Lines): First Cut Approximations and Design Guidance

The design team has to set parameters before analysis can take place. Analysis is customarily a thorough and time consuming process which can take weeks or even months. Only when analysis is complete can the designer obtain feedback. If margins are negative, the process must be repeated to a greater or lesser degree until satisfactory results are achieved. Reduction of the number of iterations thru this loop would beneficially conserve time and resources. The task was to develop relatively simple, easy to use, guidelines and analytic tools that allow the designer to evaluate what effect various alternatives may have on performance as the design progresses. "Easy to use" is taken to mean closed form approximations and the use of graphic methods. "Simple" implies that 2-d and quasi 3-d approximations be exploited to whatever degree is useful before more resource intensive methods are applied. The objective is to avoid the grosser violation of performance margins at the outset. Initial efforts are focused on thermal expansion/contraction and rigid body kinematics as they relate to propellant duct displacements in the gimbal plane loop (GPL). The purpose of the loop is to place two flexible joints on the same two orthogonal intersecting axes as those of the rocket motor gimbals. This supposes the ducting will flex predictably with independent rotations corresponding to those of the motor gimbal actions. It can be shown that if GPL joint axes do not coincide with motor gimbal axes, displacement incompatibilities result in less predictable movement of the ducts.

Brewer, William V.↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
NASA NTRS1999

Gain-Scheduled Approximations to H-Infinity Controllers for the F/A-18 Active Aeroelastic Wing

The Active Aeroelastic Wing will demonstrate technologies related to aeroservoelastic effects such as wing twist and load minimization. This paper presents a control design based on H-infinity synthesis that simultaneously considers the multiple objectives associated with handling qualities, actuator limitations, and loads. The controller is realized as a filter and gain set approximation to a state-space H-infinity controller. This approximation allows scheduling of the controller over a flight envelope.

Lind, Rick↗
NASA NTRS1999

Accuracy of the Independent Pixel Approximation at Absorbing Wavelengths

In order to correctly interpret shortwave cloud radiation measured by satellites and ground-based radiometers, or by two aircraft flying above and below clouds, we need to better understand interactions between inhomogeneous clouds and solar radiation. The discrepancies between shortwave absorption inferred from measurements and predicted by models, between cloud optical depths estimated from satellites and ground measurements, between single scattering albedo retrieved from in situ radiation measurements and computed from measured droplet size distribution, among others, are strongly affected by cloud horizontal inhomogeneity. Net horizontal photon transport (i. e., horizontal fluxes) are a direct consequence of the inhomoqeneity in cloud structure. Horizontal fluxes and their effect on the accuracy of the pixel-by-pixel one-dimensional (1 D) radiative transfer calculations has recently undergone close scrutiny for conservative scattering. However, the properties and magnitude of horizontal fluxes in absorbing wavelengths are still poorly understood. As far as we are aware, only Ackerman and Cox and Titov discussed correlations between horizontal fluxes at absorbing wavelengths, though these were far from comprehensive. This paper partly fills this gap. We discuss here of whether the accuracy of the Independent Pixel Approximation (IPA), a 1 D radiative transfer approximation for each pixel, is a better model for multiple scattering at conservative or at absorbing wavelengths. Issues addressed here are: (1) dependence of net horizontal fluxes on single scattering albedo; (2) connection between pixel-by-pixel accuracy of the IPA and horizontal fluxes and (3) radiative smoothing and horizontal fluxes at absorbing wavelengths. In contrast to the traditional understanding of IPA, we study IPA accuracies not only for reflectance but also for transmittance and absorptance at both conservative and absorbing wavelengths. In spite of the apparent similarity between the three processes, dependence of IPA accuracies on single-scattering albedo is completely different. As a result, cloud optical properties retrieved from high resolution satellite images and ground-based measurements using IPA at absorbing channels will have different accuracies.

Marchak, Alexander↗
NASA NTRS2000

Photogrammetrically Measured Distortions of Composite Structure Microwave Reflectors at Approximately 90 K

The Microwave Anisotropy Probe (MAP) Observatory, scheduled for a fall 2000 launch, is designed to measure temperature fluctuations (anisotropy) and produce a high sensitivity and high spatial resolution (better than 0.3 deg.) map of the cosmic microwave background (CMB) radiation over the entire sky between 22 and 90 GHz. MAP utilizes back-to-back composite Gregorian telescopes supported on a composite truss structure to focus the microwave signals into 10 differential microwave receivers. Proper position and shape of the telescope reflectors at the operating temperature of approximately 90 K is a critical element to ensuring mission success. We describe the methods and analysis used to validate the in-flight position and shape predictions for the reflectors based on photogrammetric (PG) metrology data taken under vacuum with the reflectors at approximately 90 K. Contour maps showing reflector distortion analytical extrapolations were generated. The resulting reflector distortion data are shown to be crucial to the analytical assessment of the MAP instrument's microwave system in-flight performance.

Mule, Peter↗
NASA NTRS2000

Approximation Model Building for Reliability & Maintainability Characteristics of Reusable Launch Vehicles

This paper describes the development of parametric models for estimating operational reliability and maintainability (R&M) characteristics for reusable vehicle concepts, based on vehicle size and technology support level. A R&M analysis tool (RMAT) and response surface methods are utilized to build parametric approximation models for rapidly estimating operational R&M characteristics such as mission completion reliability. These models that approximate RMAT, can then be utilized for fast analysis of operational requirements, for lifecycle cost estimating and for multidisciplinary sign optimization.

Unal, Resit↗
NASA NTRS1997

Optimal Approximation of Quadratic Interval Functions

Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

Koshelev, Misha↗
NASA NTRS2000

Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing

A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.

He, Gouwei↗
NASA NTRS1994

The Monostatic/Bistatic Approximation

Many Radar Cross Section (RCS) prediction codes are limited to one monostatic return per run. However, such codes can calculate multiple bistatic returns per incident angle for a relatively small amount of additional computer resources. This note describes a method of using bistatic returns to generate multiple monostatic predictions for each incident angle computed. Typical results are presented and show the accuracy is initially good and then degrades as the separation angle between the incident and viewing angles becomes large. Introduction Since 1990, the monostatic/bistatic approximation has been used to reduce the number of runs required by finite-volume time-domain (FVTD) codes for making RCS versus azimuth plots. This approximation was spawned by the observation of a range test where the transmit and receive antennas were separated by a few degrees to prevent cross talk between the antennas. The measurements from this range are presented as monostatic RCS rather than bistatic: RCS. The procedure of reporting experimental bistatic RCS as the monostatic RCS at the angle bisecting the transmit and receive antennas was extended to FVTD codes and produces excellent results.

Schuh, Michael J.↗
NASA NTRS1998

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Barth, Timothy J.↗
NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗
NASA NTRS1961

An Approximate Analysis of Film Cooling on Blunt Bodies by Gas Injection Near the Stagnation Point

An approximate method for the estimation of laminar heat transfer to blunt bodies with gaseous film cooling i s developed. Attention is focused on the parameters which are important for the design of an attractive heat protection system. Application of the analysis is made to calculate the approximate coolant weight requirement for both a circular and a parabolic entry.

Swenson, Byron L.↗
NASA NTRS2003

The Achromatic Light Curve of the Optical Afterglow of GRB 030226 at a Redshift of z Approximately 2

Abstract. We report on optical and near-infrared (NIR) follow-up observations of the afterglow of GRB 030226, mainly performed with the telescopes at ESO La Silla and Paranal, with additional data obtained at other places. Our first observations started 0.2 days after the burst when the afterglow was at a magnitude of R approximately equal to 19 . One week later the magnitude of the afterglow had fallen to R=25, and at two weeks after the burst it could no longer be detected (R > 26). Our VLT blueband spectra show two absorption line systems at redshifts z = 1.962 +/- 0.001 and at z = 1.986 +/- 0.001, placing the redshift of the burster close to 2. Within our measurement errors no evidence for variations in the line strengths has been found between 0.2 and 1.2 days after the burst. An overabundance of alpha-group elements might indicate that the burst occurred in a chemically young interstellar region shaped by the nucleosynthesis from type II supernovae. The spectral slope of the afterglow shows no signs for cosmic dust along the line of sight in the GRB host galaxy, which itself remained undetected (R > 26.2). At the given redshift no supernova component affected the light from the GRB afterglow, so that the optical transient was essentially only powered by the radiation from the GRB fireball, allowing for a detailed investigation of the color evolution of the afterglow light. In our data set no obvious evidence for color changes has been found before, during, or after the smooth break in the light curve approximately 1 day after the burst. In comparison with investigations by others, our data favor the interpretation that the afterglow began to develop into a homogeneous interstellar medium before the break in the light curve became apparent.

Klose, S.↗