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At least 1,099 records · Page 61

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NASA NTRS1972

Finite amplitude instability of second-order fluids in plane Poiseuille flow.

The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.

Mcintire, L. V.↗

NASA NTRS1972

Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems.

Most of the known results concerning convergence of iterative methods for solving linear systems involve either positive definiteness or monotonicity. In this paper a new concept, called K-semipositivity, is introduced, which provides a link between convergence theory, monotonicity, and positive definiteness. By using this concept, together with partial orderings in Euclidean n-space, several new convergence theorems are proved. Application to Jacobi's methods and the theory of regular splittings shows the usefulness of these new results.

Vandergraft, J. S.↗

NASA NTRS1972

An approach for generation of second order RC-active filters.

It is shown that node (or loop) matrix equations can be written which yield second order low-pass, band-pass, and high-pass network functions. Networks corresponding to the equations can in turn be formulated by inspection of the equations. The networks employ ideal VCT or CVT sources which can be physically realized using transistors and/or operational amplifiers. The technique yields several structures which are believed to be new.

Dunn, W. R., Jr.↗

NASA NTRS1971

Order, topology and preference

Some standard order-related and topological notions, facts, and methods are brought to bear on central topics in the theory of preference and the theory of optimization. Consequences of connectivity are considered, especially from the viewpoint of normally preordered spaces. Examples are given showing how the theory of preference, or utility theory, can be applied to social analysis.

Sertel, M. R.↗

NASA NTRS1973

A solution of the geodetic boundary value problem to order e3

A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.

Mather, R. S.↗

NASA NTRS1973

Analysis of noise produced by an orderly structure of turbulent jets

The orderly structure which has been observed recently by numerous researchers within the transition region of subsonic turbulent jets is analyzed to reveal its noise-producing potential. For a circular jet, this structure is molded as a train of toroidal vortex rings which are formed near the jet exit and propagate downstream. The noise produced by the model is evaluated from a reformulation of Lighthill's expression for the far-field acoustic density, which emphasizes the importance of the vorticity within the turbulent flow field. It is shown that the noise production occurs mainly close to the jet exit and depends primarily upon temporal changes in the toroidal radii. The analysis suggests that the process of formation of this regular structure may also be an important contribution of the high-frequency jet noise. These results may be helpful in the understanding of jet-noise generation and in new approaches to jet-noise suppression.

Hardin, J. C.↗

NASA NTRS1973

Eleventh order resonance terms in the geopotential from the orbit of Vanguard 3

The orbit of Vanguard 3 (1959-7A) is strongly resonant with 11th order and odd degree terms in the geopotential. It affords an excellent opportunity to determine a significant linear constraint between these terms. Tracking data on this satellite (in the form of mean Kepler elements) are analyzed over a 3 1/2 year period in the early 1960's, which ends with the orbit having just passed through perfect commensurability. The eccentricity and inclination show the deep resonance variations (up to 0.0002 in e and .02 deg in i) with great clarity. Previous and current geopotential solutions fail to explain these perturbations.

Wagner, C. A.↗

NASA NTRS1973

Filter for third order phase locked loops

Filters for third-order phase-locked loops are used in receivers to acquire and track carrier signals, particularly signals subject to high doppler-rate changes in frequency. A loop filter with an open-loop transfer function and set of loop constants, setting the damping factor equal to unity are provided.

Crow, R. B.↗

NASA NTRS1973

Modeling of linear time-varying systems by linear time-invariant systems of lower order.

A method for modeling linear time-varying differential systems by linear time-invariant systems of lower order is proposed, extending the results obtained by Bierman (1972) by resolving such qualities as the model stability, various possible models of differing dimensions, and the uniqueness or nonuniqueness of the model coefficient matrix. In addition to the advantages cited by Heffes and Sarachik (1969) and Bierman, often by modeling a subsystem of a larger system it is possible to analyze the overall system behavior more easily, with resulting savings in computation time.

Nosrati, H.↗

NASA NTRS1972

A simple second-order digital phase-locked loop.

A simple second-order digital phase-locked loop has been designed for the Viking Orbiter 1975 command system. Excluding analog-to-digital conversion, implementation of the loop requires only an adder/subtractor, two registers, and a correctable counter with control logic. The loop considers only the polarity of phase error and corrects system clocks according to a filtered sequence of this polarity. The loop is insensitive to input gain variation, and therefore offers the advantage of stable performance over long life. Predictable performance is guaranteed by extreme reliability of acquisition, yet in the steady state the loop produces only a slight degradation with respect to analog loop performance.

Tegnelia, C. R.↗

NASA NTRS1973

Higher order Compton-Getting anisotropies.

The Compton-Getting effect relates the distribution function of a particle population in a given frame of reference to that in another frame, moving at constant velocity V relative to the first. A study is made of the effects that arise when, contrary to previous assumptions, second-order terms in (V/v), where v is the particle velocity, are retained, and when the given distribution function is not isotropic. The importance of the extra terms is then examined in the specific case of low-energy solar protons in interplanetary space.

Balogh, A.↗

NASA NTRS1975

Digital second-order phase-locked loop

Actual tests with second-order digital phase-locked loop at simulated relative Doppler shift of 1x0.0001 produced phase lock with timing error of 6.5 deg and no appreciable Doppler bias. Loop thus appears to achieve subcarrier synchronization and to remove bias due to Doppler shift in range of interest.

Holmes, J. K.↗

NASA NTRS1973

Research on the sonic boom problem. Part 2: Flow field measurement in wind tunnel and calculation of second order F-function

An experimental investigation has been carried out in a wind tunnel to test some of the results of Landahl's second order theory. The slender models consisted of a parabolic spindle, tested at M = 3, and a wing body configuration, suggested by Ferri, and tested at M = 2.7. The theory indicates that shock position and strength at an arbitrary distance can be calculated by means of near field measurements. The results show that this method is an appropriate one for simple bodies and for bodies with complicated geometries as well.

Landahl, M.↗

NASA NTRS1973

Digital second-order phase-locked loop

A digital second-order phase-locked loop is disclosed in which a counter driven by a stable clock pulse source is used to generate a reference waveform of the same frequency as an incoming waveform, and to sample the incoming waveform at zero-crossover points. The samples are converted to digital form and accumulated over M cycles, reversing the sign of every second sample. After every M cycles, the accumulated value of samples is hard limited to a value SGN = + or - 1 and multiplied by a value delta sub 1 equal to a number of n sub 1 of fractions of a cycle. An error signal is used to advance or retard the counter according to the sign of the sum by an amount equal to the sum.

Holes, J. K.↗

NASA NTRS1973

Periodicity of high-order neural functions

The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.

Kellaway, P.↗

NASA NTRS1973

The second order gravitational redshift: Tracking analysis study

A first-phase, perturbation analysis is presented for the tracking requirements necessary for the measurement of the second-order redshift in a heliocentric probe experiment. The clock performance required for such an experiment is also investigated.

Jaffe, J.↗

NASA NTRS1973

First-order corrections to approximate solutions to two-point boundary-condition problems

A method, applicable to real time guidance, is developed for accurate solution to exo-atmospheric space flight optimization problems. In principle the method is applicable to many other two-point boundary-condition (TPBC) problems. The first step of the method is the iterative solution (using a shooting method) of a TPBC problem with differential equations simplified so that they may be solved analytically by means of a single closed-form solution over each stage of the flight. The second step is the addition of a closed-form correction to the solution to the TPBC problem obtained in the first step. The correction accounts (to first-order accuracy) for the errors due to the aforementioned simplifications. Numerical results are given for several orbital injection problems.

Andrus, J. F.↗

NASA NTRS1974

A second-order all-digital phase-locked loop

A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.

Holmes, J. K.↗