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NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗

NASA NTRS1991

SAM 2 measurements of the polar stratospheric aerosol. Volume 9: October 1982 - April 1983

The Stratospheric Aerosol Measurement (SAM) II sensor aboard Nimbus 7 is providing 1.0 micron extinction measurements of Antarctic and Arctic stratospheric aerosols with a vertical resolution of 1 km. Representative examples and weekly averages including corresponding temperature profiles provided by NOAA for the time and place of each SAM II measurement are presented. Contours of aerosol extinction as a function of altitude and longitude or time are plotted, and aerosol optical depths are calculated for each week. Typical values of aerosol extinction and stratospheric optical depth in the Arctic are unusually large due to the presence of material from the El Chichon volcano eruption in the Spring of 1982. For example, the optical depth peaked at 0.068, more than 50 times background values. Typical values of aerosol extinction and stratospheric optical depth in the Antarctic varied considerably during this period due to the transport and arrival of the material from the El Chichon eruption. For example, the stratospheric optical depth varied from 0.002 in October 1982, to 0.021 in January 1983. Polar stratospheric clouds were observed during the Arctic winter, as expected. A representative sample is provided of the ninth 6-month period of data to be used in atmospheric and climatic studies.

Mcmaster, L. R.↗

NASA NTRS1991

A summary of existing and planned experiment hardware for low-gravity fluids research

An overview is presented of (1) existing ground-based, low gravity research facilities, with examples of hardware capabilities, and (2) existing and planned space-based research facilities, with examples of current and past flight hardware. Low-gravity, ground-based facilities, such as drop towers and aircraft, provide the experimenter with quick turnaround time, easy access to equipment, gravity levels ranging from 10(exp -2) to 10(exp -6) G, and low-gravity durations ranging from 2 to 30 sec. Currently, the only operational space-based facility is the Space Shuttle. The Shuttle's payload bay and middeck facilities are described. Existing and planned low-gravity fluids research facilities are also described with examples of experiments and hardware capabilities.

Hill, Myron E.↗

NASA NTRS1990

Strike-slip faulting, wrinkle ridges, and time variable stress states in the Coprates Region of Mars

The existence of strike-slip faults was recently documented in two locations on Mars. Two clear examples are reviewed located southeast of Valles Marineris and preliminary evidence is presented for more widespread strike-slip deformation elsewhere in Coprates. The first two examples show that strike-slip faulting occurred in a broad zone east of the Coprates Rise spanning approximately 400 km east-west by perhaps 1000 km north-south. The last example suggests that the growth of major wrinkle ridges throughout Coprates may have been influenced by horizontally directed shear stresses and that more than one generation of ridges was produced. Thus, 'compressional' deformation of ridged plains south of Valles Marineris was spatially heterogeneous and a temporal change in stress may have been involved.

Schultz, Richard A.↗

NASA NTRS1991

Alternative smoothing algorithms for on-line estimation problems

In recent years, much emphasis has been placed on the Kalman filter to solve on-line estimation problems. Smoothers, which determine state estimates at a certain time t using measurements between 0 and T, have been used primarily in off-line estimation schemes. This paper presents alternative forms of smoothers that can be used for on-line estimation problems. The alternative smoothing algorithms provide state estimates which are more refined than Kalman filtered state estimates. The alternative smoothing algorithms are illustrated in two examples. The first example considers a linear discrete-time system while the second example considers a nonlinear continuous-time system with discrete-time measurements.

Baumgartner, Eric T.↗

NASA NTRS1990

A design algorithm using Z-plane closed loop pole placement

It is argued that the design of a single input single output (SISO) control system is simplified if the designer has direct control over the closed loop poles. A space-laser-communications design example utilizing a two-transform algorithm that constructs a generic discrete compensator is presented. The plant in the example has an anti-aliasing filter, a double integrator, a torquer time constant, and a sample-and-hold as continuous elements, and a discrete proportional plus integral module. This fifth-order system is representative of many instrument pointing control systems. Poles resulting from the compensator are placed near the origin of the Z-plane so that the response is dominated by the closed loop poles from the plant. Root locus, time response, and frequency response data are given. Normalization by the sample interval is used to provide a dimensionless example.

Gatlin, James A.↗

NASA NTRS1992

An introduction to high speed aircraft noise prediction

The Aircraft Noise Prediction Program's High Speed Research prediction system (ANOPP-HSR) is introduced. This mini-manual is an introduction which gives a brief overview of the ANOPP system and the components of the HSR prediction method. ANOPP information resources are given. Twelve of the most common ANOPP-HSR control statements are described. Each control statement's purpose and format are stated and relevant examples are provided. More detailed examples of the use of the control statements are presented in the manual along with ten ANOPP-HSR templates. The purpose of the templates is to provide the user with working ANOPP-HSR programs which can be modified to serve particular prediction requirements. Also included in this manual is a brief discussion of common errors and how to solve these problems. The appendices include the following useful information: a summary of all ANOPP-HSR functional research modules, a data unit directory, a discussion of one of the more complex control statements, and input data unit and table examples.

Wilson, Mark R.↗

NASA NTRS1991

Spatial vision within egocentric and exocentric frames of reference

It is remarkable that we are able to perceive a stable visual world and judge the directions, orientations, and movements of visual objects given that images move on the retina, the eyes move in the head, the head moves on the body, and the body moves in space. An understanding of the mechanisms underlying perceptual stability and spatial judgements requires precise definitions of relevant coordinate systems. An egocentric frame of reference is defined with respect to some part of the observer. There are four principal egocentric frames of reference, a station-point frame associated with the nodal point of the eye, an retinocentric frame associated with the retina, a headcentric frame associated with the head, and a bodycentric frame (torsocentric) associated with the torso. Additional egocentric frames can be identified with respect to any segment of the body. An egocentric task is one in which the position, orientation, or motion of an object is judged with respect to an egocentric frame of reference. A proprioceptive is a special kind of egocentric task in which the object being judged is also part of the body. An example of a proprioceptive task is that of directing the gaze toward the seen or unseen toe. An exocentric frame of reference is external to the observer. Geographical coordinates and the direction of gravity are examples of exocentric frames of reference. These various frames are listed in tabular form, together with examples of judgements of each type.

Howard, Ian P.↗

NASA NTRS1991

Extracting fuzzy rules under uncertainty and measuring definability using rough sets

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we live in consists of problems which fail to fall into this category, i.e., uncertainty is all too common. A problem is looked at which involves uncertainty. To be specific, attributes are dealt with which are fuzzy sets. Under this condition, knowledge is acquired by looking at examples. In each example, a condition as well as a decision is made available. Based on the examples given, two sets of rules are extracted, certain and possible. Furthermore, measures are constructed of how much these rules are believed in, and finally, the decisions are defined as a function of the terms used in the conditions.

Culas, Donald E.↗

NASA NTRS1991

A parallel-vector equation solver for unsymmetric matrices on supercomputers

A parallel-vector unsymmetric equation solver is presented. The solver exploits both vector and parallel capabilities provided by modern, high-performance supercomputers. A special storage scheme and loop-unrolling technique are used to optimize the vector performance. A parallel FORTRAN language is used to develop the solver on the CRAY 2 and CRAY Y-MP multiple processing computer environment. Three numerical examples are presented which demonstrate the efficiency and accuracy of this equation solver. The first two examples demonstrate the improved performance, and the third example utilizes the proposed solver to solve a highly nonlinear, unsymmetric finite element formulation for panel flutter.

Qin, J.↗

NASA NTRS1992

Error analysis of finite element results on plates with nonuniform grids

Discrete Dirac delta functions in two dimensions and the governing plate differential equations are used to produce continuous approximations from discrete finite-element data on nonuniform grids. The resulting continuous approximation when compared to the discrete data provides an error analysis. Moreover, the continuous approximation can be differentiated to compute continuous stresses needed for component failure prediction. Stresses can then be calculated accurately at boundaries and at interfaces where finite-element analysis alone may not provide reliable results. The continuous solution along with the differential equations also provides a residual error which is used in the error analysis. This is a unique feature of this approach. Two application examples of the procedure are provided. One example involves the linear response of a clamped square plate under uniform transverse load. Results from finite-element analysis and the continuous solution from the present analysis are compared to a closed-form elasticity solution. The continuous solution is used in a Zienkiewicz-Zhu error estimator to assess the performance of the present analysis. The continuous solution is observed to dramatically correct the finite-element results. In a second example, results for the nonlinear response of a stiffened panel are compared to the finite-element solution.

Sistla, Rajaram↗

NASA NTRS1991

Earth benefits from NASA research and technology. Life sciences applications

This document provides a representative sampling of examples of Earth benefits in life-sciences-related applications, primarily in the area of medicine and health care, but also in agricultural productivity, environmental monitoring and safety, and the environment. This brochure is not intended as an exhaustive listing, but as an overview to acquaint the reader with the breadth of areas in which the space life sciences have, in one way or another, contributed a unique perspective to the solution of problems on Earth. Most of the examples cited were derived directly from space life sciences research and technology. Some examples resulted from other space technologies, but have found important life sciences applications on Earth. And, finally, we have included several areas in which Earth benefits are anticipated from biomedical and biological research conducted in support of future human exploration missions.

Source record↗

NASA NTRS1992

Extra high speed modified Lundell alternator parameters and open/short-circuit characteristics from global 3D-FE magnetic field solutions

The combined magnetic vector potential - magnetic scalar potential method of computation of 3D magnetic fields by finite elements, introduced in a companion paper, is used for global 3D field analysis and machine performance computations under open-circuit and short-circuit conditions for an example 14.3 kVA modified Lundell alternator, whose magnetic field is of intrinsic 3D nature. The computed voltages and currents under these machine test conditions were verified and found to be in very good agreement with corresponding test data. Results of use of this modelling and computation method in the study of a design alteration example, in which the stator stack length of the example alternator is stretched in order to increase voltage and volt-ampere rating, are given here. These results demonstrate the inadequacy of conventional 2D-based design concepts and the imperative of use of this type of 3D magnetic field modelling in the design and investigation of such machines.

Wang, R.↗

NASA NTRS1990

Using finite volume methods for aeroacoustics

This paper is concerned with the application of unsteady finite volume methods to the numerical calculation of aeroacoustic problems. Some discussion is made of how the acoustic analogy of Lighthill has led to a separation between the calculation of acoustic source, or flow, and the subsequent sound field. It is pointed out that for transonic flow this separation is not necessarily useful. The example problem of an impulsively started cylinder is given for speed of Mach .1 and .5. In the Mach .5 case a strong shock is followed as it develops. A further example of the cylinder stopping impulsively is given as well. MacCormack's explicit predictor-corrector method is used for all the examples.

Brentner, Kenneth S.↗

NASA NTRS1934

The effect of trim angle on the take-off performance

Data obtained at the N.A.C.A. tank from tests on the models of three flying-boat hulls - N.A.C.A. models 11-A, 16, and 22 - are used to demonstrate the effect of trim angle on water resistance. A specific example is taken, and data from Model 11-A are used to show that the trim angle giving the minimum water resistance will give minimum total air-plus-water resistance. Total-resistance curves for best trimmed angles and other angles are compared for the same example. The effect of wind on best trim angles and upon the take-off and run is shown by the working of an example. The possibility of using tank data on trim angles as aid in piloting is discussed, and an instrument for use in determining the trim angle of seaplanes is described. The importance of maintaining the best trim angle throughout the take-off is indicated.

Shoemaker, James M↗

NASA NTRS1986

Secondary impact hazard assessment

A series of light gas gun shots (4 to 7 km/sec) were performed with 5 mg nylon and aluminum projectiles to determine the size, mass, velocity, and spatial distribution of spall and ejecta from a number of graphite/epoxy targets. Similar determinations were also performed on a few aluminum targets. Target thickness and material were chosen to be representative of proposed Space Station structure. The data from these shots and other information were used to predict the hazard to Space Station elements from secondary particles resulting from impacts of micrometeoroids and orbital debris on the Space Station. This hazard was quantified as an additional flux over and above the primary micrometeoroid and orbital debris flux that must be considered in the design process. In order to simplify the calculations, eject and spall mass were assumed to scale directly with the energy of the projectile. Other scaling systems may be closer to reality. The secondary particles considered are only those particles that may impact other structure immediately after the primary impact. The addition to the orbital debris problem from these primary impacts was not addressed. Data from this study should be fed into the orbital debris model to see if Space Station secondaries make a significant contribution to orbital debris. The hazard to a Space Station element from secondary particles above and beyond the micrometeoroid and orbital debris hazard is categorized in terms of two factors: (1) the 'view factor' of the element to other Space Station structure or the geometry of placement of the element, and (2) the sensitivity to damage, stated in terms of energy. Several example cases were chosen, the Space Station module windows, windows of a Shuttle docked to the Space Station, the habitat module walls, and the photovoltaic solar cell arrays. For the examples chosen the secondary flux contributed no more than 10 percent to the total flux (primary and secondary) above a given calculated critical energy. A key assumption in these calculations is that above a certain critical energy, significant damage will be done. This is not true for all structures. Double-walled, bumpered structures are an example for which damage may be reduced as energy goes up. The critical energy assumption is probably conservative, however, in terms of secondary damage. To understand why the secondary impacts seem to, in general, contribute less than 10 percent of the flux above a given critical energy, consider the case of a meteoroid impact of a given energy on a fixed, large surface. This impact results in a variety of secondary particles, all of which have much less energy than the original impact. Conservation of energy prohibits any other situation. Thus if damage is linked to a critical energy of a particle, the primary flux will always deliver particles of much greater energy. Even if all the secondary particles impacted other Space Station structures, none would have a kinetic energy more than a fraction of the primary impact energy.

Source record↗

NASA NTRS1992

AXAF user interfaces for heterogeneous analysis environments

The AXAF Science Center (ASC) will develop software to support all facets of data center activities and user research for the AXAF X-ray Observatory, scheduled for launch in 1999. The goal is to provide astronomers with the ability to utilize heterogeneous data analysis packages, that is, to allow astronomers to pick the best packages for doing their scientific analysis. For example, ASC software will be based on IRAF, but non-IRAF programs will be incorporated into the data system where appropriate. Additionally, it is desired to allow AXAF users to mix ASC software with their own local software. The need to support heterogeneous analysis environments is not special to the AXAF project, and therefore finding mechanisms for coordinating heterogeneous programs is an important problem for astronomical software today. The approach to solving this problem has been to develop two interfaces that allow the scientific user to run heterogeneous programs together. The first is an IRAF-compatible parameter interface that provides non-IRAF programs with IRAF's parameter handling capabilities. Included in the interface is an application programming interface to manipulate parameters from within programs, and also a set of host programs to manipulate parameters at the command line or from within scripts. The parameter interface has been implemented to support parameter storage formats other than IRAF parameter files, allowing one, for example, to access parameters that are stored in data bases. An X Windows graphical user interface called 'agcl' has been developed, layered on top of the IRAF-compatible parameter interface, that provides a standard graphical mechanism for interacting with IRAF and non-IRAF programs. Users can edit parameters and run programs for both non-IRAF programs and IRAF tasks. The agcl interface allows one to communicate with any command line environment in a transparent manner and without any changes to the original environment. For example, the authors routinely layer the GUI on top of IRAF, ksh, SMongo, and IDL. The agcl, based on the facilities of a system called Answer Garden, also has sophisticated support for examining documentation and help files, asking questions of experts, and developing a knowledge base of frequently required information. Thus, the GUI becomes a total environment for running programs, accessing information, examining documents, and finding human assistance. Because the agcl can communicate with any command-line environment, most projects can make use of it easily. New applications are continually being found for these interfaces. It is the authors' intention to evolve the GUI and its underlying parameter interface in response to these needs - from users as well as developers - throughout the astronomy community. This presentation describes the capabilities and technology of the above user interface mechanisms and tools. It also discusses the design philosophies guiding the work, as well as hopes for the future.

Mandel, Eric↗

NASA NTRS1993

On the dynamics of approximating schemes for dissipative nonlinear equations

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Jones, Donald A.↗