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NASA NTRS1974

Modified Brans-Dicke gravitational theory with nonzero divergence of the energy-momentum tensor

The Brans-Dicke theory of gravitation is modified by assuming that the divergence of the energy-momentum tensor is proportional to the covariant derivative of the scalar curvature. No ad hoc additions to the usual Brans-Dicke field equations are required as in Rastall's modification of the Einstein theory or as in the steady-state theories, of which this is a natural possibility. Three parameters emerge from the theory - namely, the unnormalized gravitational constant, the usual Brans-Dicke parameter, and the proportionality constant. In the post-Newtonian approximation, these parameters can be fixed by experiment. However, there exists a certain choice of the parameters for which the theory reduces to an Einstein theory with constant scalar curvature.

Smalley, L. L.↗

NASA NTRS1974

Do massive Brans-Dicke theories of gravitation imitate Brans-Dicke theories with nonzero divergence of energy-momentum tensor

Acharya and Hogan (1973) have introduced a massive scalar field into the usual Brans-Dicke (1961) theory of gravitation. Formally they obtain certain field equations. The assumption of a nonzero divergence for T mu nu (or equivalently the introduction of sources) formally imitates a massive Brans-Dicke and satisfies the condition of Acharya and Hogan that the theory be indistinguishable with the classical test of the Einstein theory. Although it was shown elsewhere that the modified Brans-Dicke theory agrees with the classical test under certain conditions, there were no specified limits on omega, a similar circumstance discovered by Acharya and Hogan for the massive scalar field.

Smalley, L. L.↗

NASA NTRS1975

Quantitative models of magnetic and electric fields in the magnetosphere

In order to represent the magnetic field B in the magnetosphere various auxiliary functions can be used: the current density, the scalar potential, toroidal and poloidal potentials, and Euler potentials -- or else, the components of B may be expanded directly. The most versatile among the linear representations is the one based on toroidal and poloidal potentials; it has seen relatively little use in the past but appears to be the most promising one for future work. Other classifications of models include simple testbed models vs. comprehensive ones and analytical vs. numerical representations. The electric field E in the magnetosphere is generally assumed to vary only slowly and to be orthogonal to B, allowing the use of a scalar potential which may be deduced from observations in the ionosphere, from the shape of the plasmapause, or from particle observations in synchronous orbits.

Stern, D. P.↗

NASA NTRS1976

A parametric investigation of ride quality rating scales

The relative merits of various category scales for the prediction of human discomfort response to vibration and the mathematical relationships that allow for transformations of subjective data from one scale to another scale were determined. A total of 16 category scales were studied and these represented various parametric combinations of polarity, scale type, and number of scalar points. Sixteen subject groups were used and each subject group evaluated its comfort/discomfort to vertical sinusoidal vibration using one of the rating scales. The passenger ride quality apparatus which can expose six subjects simultaneously to predetermined vibrations was utilized. The vibration stimuli were composed of repeats of selected sinusoidal frequencies applied at each of nine peak floor acceleration levels. A higher degree of reliability and discriminability was generally obtained from unipolar continuous type scales containing either seven or nine scalar points as opposed to the other scales investigated.

Dempsey, T. K.↗

NASA NTRS1976

Representation of magnetic fields in space

Several mathematical methods which are available for the description of magnetic fields in space are reviewed. Examples of the application of such methods are given, with particular emphasis on work related to the geomagnetic field, and their individual properties and associated problems are described. The methods are grouped in five main classes: (1) methods based on the current density, (2) methods using the scalar magnetic potential, (3) toroidal and poloidal components of the field and spherical vector harmonics, (4) Euler potentials, and (5) local expansions of the field near a given reference point. Special attention is devoted to models of the magnetosphere, to the uniqueness of the scalar potential as derived from observed data, and to the L parameter.

Stern, D. P.↗

NASA NTRS1976

Remarks on the construction of a second-order closure description of turbulent reacting flows

In this paper an attempt is made to illustrate how second-order closure techniques might be used to make detailed calculations of turbulent diffusion flames. Two of the problems of closure that are peculiar to turbulent chemically reacting flows are discussed in some detail. These are the problem of computing in a consistent way all the correlations of fluctuations in scalar quantities needed for closure and the problem of the generation of turbulence by chemical reactions. Tentative closure models are put forward for both of these problems. Although the closure model for fluctuations in scalar quantities can, to a certain extent, be checked against idealized numerical examples for which exact solutions are known, the validity of both the closure models proposed here must, in the end, be determined by detailed comparison of computed results with experimental data.

DONALDSON C. DUP.↗

NASA NTRS1977

A second-order closure analysis of turbulent diffusion flames

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

Varma, A. K.↗

NASA NTRS1978

A single user efficiency measure for evaluation of parallel or pipeline computer architectures

A precise statement of the relationship between sequential computation at one rate, parallel or pipeline computation at a much higher rate, the data movement rate between levels of memory, the fraction of inherently sequential operations or data that must be processed sequentially, the fraction of data to be moved that cannot be overlapped with computation, and the relative computational complexity of the algorithms for the two processes, scalar and vector, was developed. The relationship should be applied to the multirate processes that obtain in the employment of various new or proposed computer architectures for computational aerodynamics. The relationship, an efficiency measure that the single user of the computer system perceives, argues strongly in favor of separating scalar and vector processes, sometimes referred to as loosely coupled processes, to achieve optimum use of hardware.

Jones, W. P.↗

NASA NTRS1979

A viscous flow analysis of the tip vortex generation process

A viscous primary-secondary flow analysis designed for numerical solution by forward marching integration is applied to the tip vortex generation problem. Equations governing streamwise momentum, streamwise vorticity, and a gas law are solved in conjunction with equations governing scalar and vector surface potentials for the secondary velocities. The numerical method used combines a consistently split linearized block implicit (LBI) scheme for parabolic equations and a scalar iterative ADI scheme for elliptic equations. Computed results are presented for a wing of rectangular planform immersed in a high Reynolds number stream at 6 degrees incidence. The physical mechanism for generation of the tip vortex, as revealed by the analysis and computations, is discussed. Detailed flow results for the case of 6 degree incidence are included.

Shamroth, S. J.↗

NASA NTRS1979

Robustness of multiloop linear feedback systems

This paper presents a new approach to the frequency-domain analysis of multiloop linear feedback systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.

Doyle, J. C.↗

NASA NTRS1981

Investigations of medium wavelength magnetic anomalies in the eastern Pacific using MAGSAT data

The suitability of using magnetic field measurements obtained by MAGSAT is discussed with regard to resolving the medium wavelength anomaly problem. A procedure for removing the external field component from the measured field is outlined. Various methods of determining crustal magnetizations are examined in light of satellite orbital parameters resulting in the selection of the equivalent source technique for evaluating scalar measurements. A matrix inversion of the vector components is suggested as a method for arriving at a scalar potential representation of the field.

Harrison, C. G. A.↗

NASA NTRS1980

Compatibility study of the Magsat data and aeromagnetic data in the eastern Piedmont of US

Data from a 2 day period recorded by Magsat were used to produce world magnetic maps of the scalar total field and three vector component total fields. Subtracting the reference field of Magsat 6/80, a scalar anomalous field and three vector component anomalous fields were also mapped. After removing 718 bad points from the original data, every fifth point was picked for contouring. While the main geomagnetic field of the Earth is surprisingly well mapped considering the short data period, the anomaly maps suffer from data sparseness. The entire Magsat file collected at altitudes of 500-700 m in nonmountainous terrain and at 900-1,000 m in mountainous terrain was averaged to reduce the total data to 6,500 measurements, yielding a 0.1 deg sampling interval along the flight path. A U.S. aeromagnetic anomaly surface map was produced and the field was upward continued to a 300 km altitude. Differences in anomaly structure between the POGO data and the map produced were attributed to insufficient removal of the reference field. Reprocessing of the data using the GSFC reference field (9/80-2) should remove the low harmonic field and improve the anomalous field structure.

Won, I. J.↗

NASA NTRS1981

STAR adaptation of QR algorithm

The QR algorithm used on a serial computer and executed on the Control Data Corporation 6000 Computer was adapted to execute efficiently on the Control Data STAR-100 computer. How the scalar program was adapted for the STAR-100 and why these adaptations yielded an efficient STAR program is described. Program listings of the old scalar version and the vectorized SL/1 version are presented in the appendices. Execution times for the two versions applied to the same system of linear equations, are compared.

Shah, S. N.↗

NASA NTRS1980

Backus effect observed by Magsat

Two harmonic expansions of the geomagnetic potential, obtained from Magsat, are compared, one based on scalar data and one based on vector data. It is found that although the field magnitudes given by the two models are in close agreement, the vector fields are not; the vector difference was highly regular. Analysis of the data showed that the Backus effect (1970) accounted for most of the discrepancy. This result emphasizes the importance of using vector data in deriving global models of the geomagnetic field and suggests that some past models based on scalar data alone may suffer from errors of a similar nature.

Source record↗

NASA NTRS1981

An implicit marching procedure for the treatment of supersonic flow fields using the conservative full potential equation

A new aerodynamic prediction technique based on the conservative full potential equation is developed for the treatment of supersonic flow fields. This new technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar phi. The method produces results that compare well with Euler solvers and requires an order of magnitude less computer time and significantly less computer memory over existing nonlinear codes. The scalar phi formulation can be extended to handle subsonic pockets in the marching direction and also is suitable for developing inverse procedures where the shape corresponding to a prescribed loading is sought.

Shankar, V.↗

NASA NTRS1981

The reduction, verification and interpretation of Magsat magnetic data over Canada

Magnetic anomalies of lithospheric origin are weak at Magsat altitudes (20 to 30 nT at most), and are easily masked by much larger effects caused by field-aligned and other currents at high latitudes. Most of Canada lies under the influence of ionospheric currents in the auroral zone and polar cap. A more refined selection of quiet Magsat data allowed a revised scalar magnetic anomaly map of the whole region north of about 40 deg N latitude. Very preliminary vector anomaly maps and absolute vector component maps were derived. The scalar magnitudes show great promise for mapping the total force and anomaly fields. The Z vector data also appear to be good. The horizontal X and Y vector data are seriously contaminated with external fields and maybe other effects.

Coles, R. L.↗

NASA NTRS1981

Investigation of Antarctic crust and upper mantle using MAGSAT and other geophysical data

Progress in processing and analysis of Investigator B MAGSAT data is reported. Data processing tasks required prior to data analysis, including translation and reformatting of tapes and development of computer routines, were performed. A scalar anomaly map of Antarctica is near completion. Data analysis included a qualitative correlation of NASA's 4/81 scalar map of Antarctica with other geopotential data and correlation of POGO and continental scale gravity data with MAGSAT data. A magnetic high was found to exist over the Ross Embayment.

Bentley, C. R.↗

NASA NTRS1981

The Use of Interactive Raster Graphics in the Display and Manipulation of Multidimensional Data

Techniques for the review, display, and manipulation of multidimensional data are developed and described. Multidimensional data is meant in this context to describe scalar data associated with a three dimensional geometry or otherwise too complex to be well represented by traditional graphs. Raster graphics techniques are used to display a shaded image of a three dimensional geometry. The use of color to represent scalar data associated with the geometries in shaded images is explored. Distinct hues are associated with discrete data ranges, thus emulating the traditional representation of data with isarithms, or lines of constant numerical value. Data ranges are alternatively associated with a continuous spectrum of hues to show subtler data trends. The application of raster graphics techniques to the display of bivariate functions is explored.

Anderson, D. C.↗