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At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Residual Gas Analyzer Calibration

A technique which employs known gas mixtures to calibrate the residual gas analyzer (RGA) is described. The mass spectra from the RGA are recorded for each gas mixture. This mass spectra data and the mixture composition data each form a matrix. From the two matrices the calibration matrix may be computed. The matrix mathematics requires the number of calibration gas mixtures be equal to or greater than the number of gases included in the calibration. This technique was evaluated using a mathematical model of an RGA to generate the mass spectra. This model included shot noise errors in the mass spectra. Errors in the gas concentrations were also included in the valuation. The effects of these errors was studied by varying their magnitudes and comparing the resulting calibrations. Several methods of evaluating an actual calibration are presented. The effects of the number of gases in then, the composition of the calibration mixture, and the number of mixtures used are discussed.

R H Lilienkamp↗
NASA NTRS1971

RF multicoupler design techniques to minimize problems of corona, multipaction, and stability

A mathematical expression was derived describing multipacting and corona effects in a coaxial cavity. Both mechanical and electrical design techniques were investigated to minimize the susceptibility of coaxial cavity to corona and multipacting-type breakdown. To assist in the design of a multicoupler free from corona and multipactor breakdown, a flow chart obtained from the derived mathematical expression is included.

Hurley, H. S.↗
NASA NTRS1972

An innovative approach to compensator design

The primary goal is to present for a control system a computer-aided-compensator design technique from a frequency domain point of view. The thesis for developing this technique is to describe the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. In order to do this several definitions in regard to measuring the performance of a system in the frequency domain are given. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. Then for applying the constraint improvement algorithm generalized gradients for the constraints are derived. Finally, the necessary theory is incorporated in a computer program called CIP (compensator improvement program).

Mitchell, J. R.↗
NASA NTRS1972

Comparison of two gas chromatograph models and analysis of binary data

The overall objective of the gas chromatograph system studies is to generate fundamental design criteria and techniques to be used in the optimum design of the system. The particular tasks currently being undertaken are the comparison of two mathematical models of the chromatograph and the analysis of binary system data. The predictions of two mathematical models, an equilibrium absorption model and a non-equilibrium absorption model exhibit the same weaknesses in their inability to predict chromatogram spreading for certain systems. The analysis of binary data using the equilibrium absorption model confirms that, for the systems considered, superposition of predicted single component behaviors is a first order representation of actual binary data. Composition effects produce non-idealities which limit the rigorous validity of superposition.

Keba, P. S.↗
NASA NTRS1972

Comparison of genetic algorithms with conjugate gradient methods

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Bosworth, J. L.↗
NASA NTRS1972

Spin stability of dual-spin spacecrafts.

The spin-axis attitude stability in torque-free environment of dual-spin spacecrafts with energy losses in both bodies is studied by analytical means. A new mathematical model, which assumes the high speed rotor to be symmetrical, is introduced and analyzed. The linearized variational system of equations for the model with periodic coefficients is transformed to a kinematically similar autonomous system (according to Floquet and Liapunov) which can be analyzed routinely using established procedure. As an example, this technique is used on a recent mathematical model of the SAS-A spacecraft to establish steady state stability over a wide range of speeds.

Guha, A. K.↗
NASA NTRS1971

Analysis of transonic airfoils.

A finite difference scheme for the analysis of transonic airfoils at off-design conditions is described. It is the ultimate goal of the investigations to avoid expensive wind tunnel tests by combining the mathematical techniques in a procedure for designing supercritical airfoils so that they will be effective over a wider range of angles of attack and Mach numbers. A mathematical method is considered for computing two-dimensional transonic flows past a prescribed profile. The method can provide accurate results for a comparison with a known shockless regime. The approach gives also data of engineering reliability concerning the location and the strength of shocks at off-design conditions.

Garabedian, P. R.↗
NASA NTRS1972

Numerical stability in problems of linear algebra.

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Babuska, I.↗
NASA NTRS1972

STOL ride quality criteria - Passenger acceptance.

The ability to mathematically model human reaction to variables involved in transportation systems offers a very desirable tool both for the prediction of passenger acceptance of proposed systems, and for establishing acceptance criteria for the system designer. As a first step in the development of a general model for STOL systems, a mathematical formulation is presented which accepts as inputs nine variables felt to be important in flight under STOL-type conditions and presents an index of human response as the output. The variables used are three linear motions, three angular motions, pressure, temperature and noise level. The results are used to establish specifications for stability augmentation systems to improve the ride quality of existing STOL aircraft.

Jacobson, I. D.↗
NASA NTRS1972

A theory of supercritical wing sections, with computer programs and examples.

Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.

Bauer, F.↗
NASA NTRS1972

The P prime(f) to N(h) inversion problem in ionospheric soundings

A general review is given of the inversion techniques used to derive the ionospheric electron density N as a function of altitude h from group path P versus frequency f measurements obtained by vertical incidence ionospheric sounders. The paper discusses the medium under investigation, the experimental techniques used to obtain the P(f) data, the theoretical considerations leading to the integral equation relating P(f) to N(h), and the assumptions made in the inversion process. The lamination inversion technique is then presented, with special attention given to mathematical difficulties arising from discontinuities in the P(f) function, infinities in the integrand, and in some cases unknown integration limits. Methods outlined for minimizing the uncertainties due to discontinuities include the use of redundant information - that is the two distinct P(f) functions available for a given N(h) profile - and the use of models based on statistical data. Mathematical procedures are discussed that increase significantly the efficiency and accuracy of the required numerical integrations. The accuracy of the inversion technique is deduced by comparing the resulting N(h) profile with N(h) data obtained by simultaneous but independent observations.

Jackson, J. E.↗
NASA NTRS1972

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Sabatier, P. C.↗
NASA NTRS1972

Thermal modeling of phase change solidification in thermal control devices including natural convection effects

Natural convection effects in phase change thermal control devices were studied. A mathematical model was developed to evaluate natural convection effects in a phase change test cell undergoing solidification. Although natural convection effects are minimized in flight spacecraft, all phase change devices are ground tested. The mathematical approach to the problem was to first develop a transient two-dimensional conduction heat transfer model for the solidification of a normal paraffin of finite geometry. Next, a transient two-dimensional model was developed for the solidification of the same paraffin by a combined conduction-natural-convection heat transfer model. Throughout the study, n-hexadecane (n-C16H34) was used as the phase-change material in both the theoretical and the experimental work. The models were based on the transient two-dimensional finite difference solutions of the energy, continuity, and momentum equations.

Ukanwa, A. O.↗
NASA NTRS1972

Use of altimetry data in a sampling-function approach to the geoid

Problems associated with using an altimetry sampling function approach to the geoid are examined. They include: (1) conventent mathematical representation of short-wavelength (eventually approximately 1 deg) features of the geoid or geopotential, (2) utilization of detailed data from only part of the globe (i.e., the oceans) (3) application of appropriate formalism to relate the sea-level equipotential below the atmospheric mass to the external potential above the atmosphere, (4) mathematical applicability of an adopted geopotential representation on the surface of the physical geoid.

Lundquist, C. A.↗
NASA NTRS1972

Near-earth orbital guidance and remote sensing

The curriculum of a short course in remote sensing and parameter optimization is presented. The subjects discussed are: (1) basics of remote sensing and the user community, (2) multivariant spectral analysis, (3) advanced mathematics and physics of remote sensing, (4) the atmospheric environment, (5) imaging sensing, and (6)nonimaging sensing. Mathematical models of optimization techniques are developed.

Powers, W. F.↗
NASA NTRS1973

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

Austin, F.↗
NASA NTRS1973

An innovative approach to compensator design

The design is considered of a computer-aided-compensator for a control system from a frequency domain point of view. The design technique developed is based on describing the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. To do this, several definitions in regard to measuring the performance of a system in the frequency domain are given, e.g., relative stability, relative attenuation, proper phasing, etc. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. This tool is called the constraint improvement algorithm. Then for applying the constraint improvement algorithm generalized, gradients for the constraints are derived. Finally, the necessary theory is incorporated in a Computer program called CIP (compensator Improvement Program). The practical usefulness of CIP is demonstrated by two large system examples.

Mitchell, J. R.↗
NASA NTRS1973

The correlation structure of several popular pseudorandom number generators

One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.

Neuman, F.↗