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NASA NTRS1986

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗

NASA NTRS1986

Boundary conditions for the paleoenvironment: Chemical and Physical Processes in dense interstellar clouds

The present research includes searches for important new interstellar constituents; observations relevant to differentiating between different models for the chemical processes that are important in the interstellar environment; and coordinated studies of the chemistry, physics, and dynamics of molecular clouds which are the sites or possible future sites of star formation. Recent research has included the detection and study of four new interstellar molecules; searches which have placed upper limits on the abundance of several other potential constituents of interstellar clouds; quantitative studies of comparative molecular abundances in different types of interstellar clouds; investigation of reaction pathways for astrochemistry from a comparison of theory and the observed abundance of related species such as isomers and isotopic variants; studies of possible tracers of energenic events related to star formation, including silicon and sulfur containing molecules; and mapping of physical, chemical, and dynamical properties over extended regions of nearby cold molecular clouds.

Irvine, W. M.↗

NASA NTRS1986

EISCAT velocity patterns for theoretical plasma convection models

Theoretical line-of-sight velocities, as would be observed by the EISCAT radar, are computed for idealized models of plasma convection in the polar ionosphere. The calculations give the velocity as a function of range and Universal Time. For several variants of the Volland and Heelis convection models, how the maxima, minima and reversals of velocity depend on beam azimuth is examined. The analysis is designed to be applied to data from the UK-POLAR experiment, an example of which is shown.

Rishbeth, H.↗

NASA NTRS1985

Continuous inline blending of antimisting kerosene

A continuous inline blender was developed to blend polymer slurries with a stream of jet A fuel. The viscosity of the slurries ranged widely. The key element of the blender was a static mixer placed immediately downstream of the slurry injection point. A positive displacement gear pump for jet A was employed, and a progressive cavity rotary screw pump was used for slurry pumping. Turbine flow meters were employed for jet A metering while the slurry flow rate was calibrated against the pressure drop in the injection tube. While using one of the FM-9 variant slurries, a provision was made for a time delay between the addition of slurry and the addition of amine sequentially into the jet A stream.

Parikh, P.↗

NASA NTRS1985

MHD modelling of the earth's magnetosphere

Attention is given to the shock capturing technique, nonuniform grid system, and multiple time scale problem aspects of a global MHD model of the earth's magnetosphere that uses numerical methods. Because of the fast Alfven waves near the earth, the model is more difficult to solve than problems of hydrodynamic flow past bodies. The Rusanov (1962) scheme, which is a variant of the Lax (1954) method that maintains viscosity at a minimum value except where a large one is required, is used. The magnetosphere shape obtained by these means is noted.

Wu, C. C.↗

NASA NTRS1985

Mass loss from red giants - Infrared spectroscopy

A discussion is presented of IR spectroscopy, particularly high-resolution spectroscopy in the approximately 1-20 micron band, as it impacts the study of circumstellar envelopes. The molecular bands within this region contain an enormous amount of information, especially when observed with sufficient resolution to obtain kinematic information. In a single spectrum, it is possible to resolve lines from up to 50 different rotational/vibrational levels of a given molecule and to detect several different isotopic variants. When high resolution techniques are combined with mapping techniques and/or time sequence observations of variable stars, the resulting information can paint a very detailed picture of the mass-loss phenomenon. To date, near-IR observations have been made of 20 molecular species. CO is the most widely observed molecule and useful information has been gleaned from the observed rotational excitation, kinematics, time variability and spatial structure of its lines. Examples of different observing techniques are discussed in the following sections.

Wannier, P. G.↗

NASA NTRS1986

Isotopic compositions of bismuth, lead, thallium, and mercury from mini r-processing

The yields of stable isotopes of Bi, Pb, Tl and Hg as well as yields of Pb-205 are calculated with a parametrized model for 'mini r-processing' in the Ne, O, C-rich zones of explosive burning in massive stars. The Pb isotopic compositions stand out by their comparatively low Pb-207 yields and by the fact that this r-process variant yields Pb-204 quite abundantly. The average Pb-205/Pb-204 yield ratio of 6.1 is the same order of magnitude as yield ratios deduced for s-processing. The Hg from this mini r-process looks like normal solar-system mercury, but with Hg-196 missing and the light s-isotopes A = 198, 199, 200 and 201 depleted (especially the odd-A species).

Heymann, D.↗

NASA NTRS1986

Development of a prototype automated on-orbit contact heat exchanger

An automated contact heat exchanger is being developed for use aboard the manned Space Station, serving as an interface heat exchanger between the pressurized module internal thermal buses and the central external thermal bus. The concept makes use of an array of flattened, thin-walled, flexible tubes that expand or contract to make or break the thermal connection as the internal pressure changes. Because of its simplicity, it permits on-orbit assembly by the remote manipulator system, thus eliminating the need for expensive EVA to make connections. A design methodology based on stress and thermal analyses has been developed and used to perform trade-offs between performance and cost, and to optimize design parameters. Simple verification tests have been performed to confirm the stress analysis model. Two conceptual variants of the contact heat exchanger are described, each designed for a 25 kW total heat load and a minimum uniform heat flux of 2.15 W/sq cm.

Lee, C. Y.↗

NASA NTRS1985

'Meatball searching' - The adversarial approach to online information retrieval

It is proposed that the different styles of online searching can be described as either formal (highly precise) or informal with the needs of the client dictating which is most applicable at a particular moment. The background and personality of the searcher also come into play. Particular attention is focused on meatball searching which is a form of online searching characterized by deliberate vagueness. It requires generally comprehensive searches, often on unusual topics and with tight deadlines. It is most likely to occur in search centers serving many different disciplines and levels of client information sophistication. Various information needs are outlined as well as the laws of meatball searching and the adversarial approach. Traits and characteristics important to sucessful searching include: (1) concept analysis, (2) flexibility of thinking, (3) ability to think in synonyms and (4) anticipation of variant word forms and spellings.

Jack, R. F.↗

NASA NTRS1985

Reducing the number of variational equations in the implementation of multiple shooting

The standard method of multiple shooting for a system of n first-order differential equations with k unknown initial conditions requires the integration of k sets of variational equations on the first shot and n sets of variational equations on every shot thereafter. This paper describes a variant of multiple shooting that requires the solution of k sets of variational equations on every shot. The technique applies to both linear and nonlinear boundary-value problems. Techniques to deal with difficulties unique to the solution of nonlinear problems are suggested.

Krogh, F. T.↗

NASA NTRS1987

Control-System Design Program

Control-theory design package, Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), developed to aid in design of controllers and optimal filters for systems modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, Linear-Quadratic-Gaussian (LQG) problem, most widely accepted method of determining optimal control policy. Provides for solution to time-in-variant continuous or discrete LQG problems. Attractive to control-system designer providing rigorous tool for dealing with multi-input and multi-output dynamic systems in continuous and discrete form. CDO version written in FORTRAN IV. VAX version written in FORTRAN 77.

Frisch, Harold P.↗

NASA NTRS1987

Measuring Viscosities of Gases at Atmospheric Pressure

Variant of general capillary method for measuring viscosities of unknown gases based on use of thermal mass-flowmeter section for direct measurement of pressure drops. In technique, flowmeter serves dual role, providing data for determining volume flow rates and serving as well-characterized capillary-tube section for measurement of differential pressures across it. New method simple, sensitive, and adaptable for absolute or relative viscosity measurements of low-pressure gases. Suited for very complex hydrocarbon mixtures where limitations of classical theory and compositional errors make theoretical calculations less reliable.

Singh, Jag J.↗

NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗

NASA NTRS1986

Fourier analysis of the SOR iteration

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants.

Leveque, R. J.↗

NASA NTRS1986

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗

NASA NTRS1987

Estimability and regulability of linear systems

A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

Baram, Yoram↗

NASA NTRS1987

Synchronization trigger control system for flow visualization

The use of cinematography or holographic interferometry for dynamic flow visualization in an internal combustion engine requires a control device that globally synchronizes camera and light source timing at a predefined shaft encoder angle. The device is capable of 0.35 deg resolution for rotational speeds of up to 73 240 rpm. This was achieved by implementing the shaft encoder signal addressed look-up table (LUT) and appropriate latches. The developed digital signal processing technique achieves 25 nsec of high speed triggering angle detection by using direct parallel bit comparison of the shaft encoder digital code with a simulated angle reference code, instead of using angle value comparison which involves more complicated computation steps. In order to establish synchronization to an AC reference signal whose magnitude is variant with the rotating speed, a dynamic peak followup synchronization technique has been devised. This method scrutinizes the reference signal and provides the right timing within 40 nsec. Two application examples are described.

Chun, K. S.↗

NASA NTRS1985

The SIFT hardware/software systems. Volume 2: Software listings

This document contains software listings of the SIFT operating system and application software. The software is coded for the most part in a variant of the Pascal language, Pascal*. Pascal* is a cross-compiler running on the VAX and Eclipse computers. The output of Pascal* is BDX-390 assembler code. When necessary, modules are written directly in BDX-390 assembler code. The listings in this document supplement the description of the SIFT system found in Volume 1 of this report, A Detailed Description.

Palumbo, Daniel L.↗