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At least 109 records · Page 6

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NASA NTRS1978

Statistical formulation of one-dimensional electron fluid turbulence

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Nondissipative equilibrium canonical distributions are determined in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to 1/k squared for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Fyfe, D.↗

NASA NTRS1977

Attitude determination techniques for Nimbus 6 and Nimbus G

Techniques for measuring attitude deviations in the Nimbus 6 and Nimbus G 3-axis stabilized, zero-momentum, earth observation satellites are presented. The on-orbit telemetered data include scanner roll and pitch error signals, an illuminated DSAS which can read the azimuth and elevation of the sunline when the spacecraft is not in the umbra, the signal from the single gyro in the RMP, and the momenta of the reaction wheels. Mathematical methods for interpreting the measured data are described with attention to filter equations, especially the Kalman filter because of its ability to eliminate high frequency noise.

Das, A.↗

NASA NTRS1979

Updating the limit efficiency of silicon solar cells

Evaluation of the limit efficiency based on the simplest, most basic mathematical method that is appropriate for the conditions imposed by the cell model is discussed. The methodology, the solar cell structure, and the selection of the material parameters used in the evaluation are described. The results are discussed including a set of design goals derived from the limit efficiency.

Wolf, M.↗

NASA NTRS1979

Solar activity cycle during classical antiquity

Early accounts of phenomena that may be identified as auroral displays have been abstracted from reports of unusual celestial prodigies in the classical literature. An extensive catalog of ancient aurorae and a new mathematical method of analyzing fragmentary time series of observations have been used to demonstrate, provisionally, that an auroral cycle actually existed in antiquity, at least during the 2nd century BC, and that it had an average length and amplitude comparable with those of the modern auroral cycle. On the reasonable supposition that solar activity has always been the factor responsible for aurorae, it can be concluded that the solar cycle two millennia ago was very similar to what it is today.

Stothers, R.↗

NASA NTRS1980

Theoretical interpretation of Traveling Interplanetary Phenomena and their solar origins

A review is made of recent theoretical studies on Traveling Interplanetary Phenomena (TIP) and their possible solar origins in the context of mathematical methods and physical processes. Flare-generated interplanetary shocks are used as examples to illustrate the following set of contrasting approaches to the phenomena: analytical vs numerical, hydrodynamic vs magnetohydrodynamic, dissipative vs non-dissipative, continuum/macroscopic vs kinetic/microscopic. It is suggested in conclusion that future research should emphasize continuum/macroscopic physical processes together with the kinetic approach to deepen understanding of microscopic interactions.

Wu, S. T.↗

NASA NTRS1981

Remote sensing of temperature profiles in vegetation canopies using multiple view angles and inversion techniques

A mathematical method is presented which allows the determination of vertical temperature profiles of vegetation canopies from multiple sensor view angles and some knowledge of the vegetation geometric structure. The technique was evaluated with data from several wheat canopies at different stages of development, and shown to be most useful in the separation of vegetation and substrate temperatures with greater accuracy in the case of intermediate and dense vegetation canopies than in sparse ones. The converse is true for substrate temperatures. Root-mean-square prediction accuracies of temperatures for intermediate-density wheat canopies were 1.8 C and 1.4 C for an exact and an overdeterminate system, respectively. The findings have implication for remote sensing research in agriculture, geology or other earth resources disciplines.

Kimes, D. S.↗

NASA NTRS1982

Application of modal control to wing-flutter suppression

A discrete modal control design approach that is applied to a single control surface, unswept aircraft wing subject to bending torsion flutter is described. The modal approach is a mathematical method to decouple the equations of motion into isolated differential equations. In this paper, a pole-placement approach is then applied to determine stability gains in the discrete plane using only the two complex-conjugate flutter-mode equations. A fixed gain Kalman filter is used to estimate the model amplitudes using three measurements. Results are presented for a full-state estimator (36 states) and two reduced state estimators using two different closed-loop pole locations. The control law is designed for a dynamic pressure that is 50 percent greater than the uncontrolled-flutter dynamic pressure. With constant control-law gains, the closed-loop system remains stable over the dynamic-pressure range from flutter onset to approximately an 80-percent increase in pressure.

Ostroff, A. J.↗

NASA NTRS1981

Laser electro-optic system for rapid three-dimensional /3-D/ topographic mapping of surfaces

It is pointed out that the generic utility of a robot in a factory/assembly environment could be substantially enhanced by providing a vision capability to the robot. A standard videocamera for robot vision provides a two-dimensional image which contains insufficient information for a detailed three-dimensional reconstruction of an object. Approaches which supply the additional information needed for the three-dimensional mapping of objects with complex surface shapes are briefly considered and a description is presented of a laser-based system which can provide three-dimensional vision to a robot. The system consists of a laser beam array generator, an optical image recorder, and software for controlling the required operations. The projection of a laser beam array onto a surface produces a dot pattern image which is viewed from one or more suitable perspectives. Attention is given to the mathematical method employed, the space coding technique, the approaches used for obtaining the transformation parameters, the optics for laser beam array generation, the hardware for beam array coding, and aspects of image acquisition.

Altschuler, M. D.↗

NASA NTRS1982

Phenomenological and mechanics aspects of nondestructive evaluation and characterization by sound and ultrasound of material and fracture properties

Developments in fracture mechanics and elastic wave theory enhance the understanding of many physical phenomena in a mathematical context. Available literature in the material, and fracture characterization by NDT, and the related mathematical methods in mechanics that provide fundamental underlying principles for its interpretation and evaluation are reviewed. Information on the energy release mechanism of defects and the interaction of microstructures within the material is basic in the formulation of the mechanics problems that supply guidance for nondestructive evaluation (NDE).

Fu, L. S. W.↗

NASA NTRS1988

Calculation of non-stationary aerodynamic forces in the near sonic range

The development of a mathematical method for calculating nonstationary supersonic flow in the near-sonic range is described. A perturbation formula is derived based on the exact stationary values; it is applicable to the equation for potential. The problem can thus be divided into stationary and nonstationary fields. The pressure distribution in an oscillating profile is determined, based on hyperbolic differential equations. It is shown that there are important corollaries concerning the application of linear theory. With suitable extrapolations, linear theory can be used up to about Mach 0.8. Linear theory is not applicable, however, when determining the moment coefficients; for this case, a special technique is described.

Teipel, I.↗

NASA NTRS1988

Minimal Joule dissipation models of magnetospheric convection

This paper gives a topical review of theoretical models of magnetospheric convection based on the concept of minimal Joule dissipation. A two-dimensional slab model of the ionosphere featuring an enhanced conductivity auroral oval is used to compute high-latitude electric fields and currents. Mathematical methods used in the modeling include Fourier analysis, fast Fourier transforms, and variational calculus. Also, conformal transformations are introduced in the analysis, which enable the auroral oval to be represented as a nonconcentric, crescent-shaped figure. Convection patterns appropriate to geomagnetic quiet and disturbed conditions are computed, the differentiating variable being the relative amount of power dissipated in the magnetospheric ring current. When ring current dissipation is small, the convection electric field is restricted to high latitudes (shielding regime), and when it is large, a significant penetration of the field to low latitudes occurs, accompanied by an increase in the ratio of the region I current to the region 2 current.

Barbosa, D. D.↗

NASA NTRS1991

Programs For Modeling Fault-Tolerant Computing Systems

Pade Approximation with Scaling, (PAWS) and Scaling Taylor Exponential Matrix (STEM) computer programs are software tools for design and validation. Provide flexible, user-friendly, language-based interface for input of Markov mathematical methods describing behaviors of fault-tolerant computer systems. Markov models include both recovery from faults via reconfiguration and behaviors of such systems when faults occur. PAWS and STEM produce exact solutions of probability of system failure and provide conservative estimate of number of significant digits in solution. Written in PASCAL and FORTRAN.

Butler, Ricky W.↗

NASA NTRS1991

A case study for the real-time experimental evaluation of the VIPER microprocessor

An experiment to evaluate the applicability of the Verifiable Integrated Processor for Enhanced Reliability (VIPER) microprocessor to real time control is described. The VIPER microprocessor was invented by the Royal Signals and Radar Establishment (RSRE), U.K., and is an example of the use of formal mathematical methods for developing electronic digital systems with a high degree of assurance on the system design and implementation correctness. The experiment consisted of selecting a control law, writing the control law algorithm for the VIPER processor, and providing real time, dynamic inputs into the processor and monitoring the outputs. The control law selected and coded for the VIPER processor was the yaw damper function of an automatic landing program for a 737 aircraft. The mechanisms for interfacing the VIPER Single Board Computer to the VAX host are described. Results include run time experiences, performance evaluation, and comparison of VIPER and FORTRAN yaw damper algorithm output for accuracy estimation.

Carreno, Victor A.↗

NASA NTRS1992

Testing of FTS fingers and interface using a passive compliant robot manipulator

This report deals with testing of a pair of robot fingers designed for the Flight Telerobotic Servicer (FTS) to grasp a cylinder type of Orbital Replaceable Unit (ORU) interface. The report first describes the objectives of the study and then the testbed consisting of a Stewart Platform-based manipulator equipped with a passive compliant platform which also serves as a force/torque sensor. Kinematic analysis is then performed to provide a closed-form solution for the force inverse kinematics and iterative solution for the force forward kinematics using the Newton's Raphson Method. Mathematical expressions are then derived to compute force/torques applied to the FTS fingers during the mating/demating with the interface. The report then presents the three parts of the experimental study on the feasibility and characteristics of the fingers. The first part obtains data of forces applied by the fingers to the interface under various misalignments, the second part determines the maximum allowable capture angles for mating, and the third part processes and interprets the obtained force/torque data.

Nguyen, Charles C.↗

NASA NTRS1991

On the reflectivity of complex mesh surfaces

Poorer than expected surface reflectivity was observed in an early Tracking and Data Relay Satellite System antenna utilizing a tricot mesh weave. This poor reflectivity was determined to be caused by inadequate electrical contact at wire crossover points. A proper mathematical and numerical approach to assess the impact of wire junctions on reflectivity performance is developed. A mathematical method is presented for computing the surface reflectivity of complex mesh configurations like those on unfurlable-type spacecraft antennas. The method is based on the Floquet mode expansion to establish an integral equation for mesh wire currents. The equation is solved using the method of moments with triangular basis functions. It is observed that it is necessary to give special attention to the junction treatment among different branches of the mesh configurations. A vector junction current approach that resulted in satisfactory solutions for the current is described. The results of numerical simulations are compared against measured data and excellent agreement is observed.

Imbriale, William A.↗

NASA NTRS1991

Atmospheric constituent density profiles from full disk solar occultation experiments

Mathematical methods are described which permit the derivation of the number of density profiles of atmospheric constituents from solar occultation measurements. The algorithm is first applied to measurements corresponding to an arbitrary solar-intensity distribution to calculate the normalized absorption profile. The application of Fourier transform to the integral equation yields a precise expression for the corresponding number density, and the solution is employed with the data given in the form of Laguerre polynomials. The algorithm is employed to calculate the results for the case of uniform distribution of solar intensity, and the results demonstrate the convergence properties of the method. The algorithm can be used to effectively model representative model-density profiles with constant and altitude-dependent scale heights.

Lumpe, J. D.↗

NASA NTRS1993

Feedback control for unsteady flow and its application to the stochastic Burgers equation

The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.

Choi, Haecheon↗

NASA NTRS1925

Elements of the Wing Section Theory and of the Wing Theory

This report contains those results of the theory of wings and of wing sections which are of immediate practical value. They are proved and demonstrated by the use of the simple conceptions of "kinetic energy" and "momentum" only, familiar to every engineer; and not by introducing "isogonal transformations" and "vortices," which latter mathematical methods are not essential to the theory and better are used only in papers intended for mathematicians and special experts.

Munk, Max M↗