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NASA NTRS1989

Cosmic ray gradients in the heliosphere

Early estimates of the radial gradient made in the inner heliosphere are presented. In a discussion of discoveries in the outer heliosphere, consideration is given to low radial gradients and nonradial transport, the identification of different components, the large-scale organization of the heliospheric magnetic field, propagating modulation features, and latitude gradients. Current estimates of the spatial distribution of the cosmic ray intensity are presented as well.

Fillius, Walker↗

NASA NTRS1989

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Carter, Richard G.↗

NASA NTRS1990

Spatial gradients in the heliospheric magnetic field - Pioneer 11 observations between 1 AU and 24 AU, and over solar cycle 21

The large-scale temporal behavior and spatial gradients in the heliospheric magnetic field were investigated using magnetic field observations by Pioneer 11 and ISEE 3/ICE satellites, including observations out to a radial distance of 24 AU and over a time interval that includes the recent solar minimum. It was found that, to first order, the gradients in the magnetic field magnitude and in the azimutal component agree well with the Parker (1958) model. The analysis of the Pioneer data confirms previous reports of a magnetic field flux deficit of about 1 percent/AU, so that at 20 AU the relative deficit is of the order of 20 percent. It is argued that most of the magnetic field deficit is in the radial gradient.

Winterhalter, Daniel↗

NASA NTRS1990

A color gradient in the soft X-ray diffuse background

It is shown that the deviations of the soft X-ray diffuse background B band to C band intensity ratio from a constant value can be described as a simple dipole-like variation across the sky. In terms of the observed Wisconsin B/C band intensity ratio, the mean value is 0.355, the dipole magnitude is 0.106, and the positive dipole axis points toward l = 168.7 deg, b = 11.2 deg, almost in the galactic anticenter direction. This gradient in the spectral hardness can be due to several causes; the simplest is a temperature gradient in the X-ray emitting plasma of the local cavity from about 10 exp 6.2 K toward the galactic center to about 10 exp 5.9 K in the anticenter direction. While the physical origin of such a temperature gradient is uncertain, the alignment of the dipole with the higher temperature (and absorbed) Loop I region may be significant.

Snowden, S. L.↗

NASA NTRS1991

Internally mounted thin-liquid-film skin-friction meter - Comparison with floating element method with and without pressure gradient

A new, robust oil film skin friction meter was designed and constructed. This enables skin friction measurements remotely and from within the model, as well as avoiding the need to know the location of the leading edge of the film. The instrument was tested by comparing measurements with those given by a floating element gage in a zero pressure gradient flat plate turbulent boundary layer. Both instruments agreed satisfactorily with the well-known curve for this case. Significant discrepancies between the two instruments were observed in the case of adverse and favorable pressure gradients. The discrepancies were of opposite sign for opposite-sign pressure gradients as is consistent with the error expected from floating-element gages. Additional confidence in the oil film technique is supplied by the good agreement of the behavior of the film profile with predictions from lubrication theory.

Hornung, Hans↗

NASA NTRS1991

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗

NASA NTRS1989

Three-dimensional boundary layer flow with streamwise adverse pressure gradient

The present study examines the effects of a strong adverse pressure gradient on a 3D turbulent boundary layer in an axisymmetric spinning cylinder geometry. Velocity measurements made with a three-component laser Doppler velocimeter include all three mean flow components, all six Reynolds stress components, and all ten triple-product correlations. Total Reynolds shear stress diminishes as the flow becomes 3D. Lower levels of shear stress were found to persist under adverse pressure gradient conditions. This low stress level was observed to roughly correlate with the magnitude of the crossflow. Variations in the pressure gradient do not alter this correlation. It is inferred that a 3D boundary layer is more prone to separate than a 2D boundary layer.

Driver, David M.↗

NASA NTRS1991

Magnetic field gradients and their uses in the study of the earth's magnetic field

Magnetic field gradients are discussed from the standpoint of their usefulness in modeling crustal magnetizations. The fact that gradients enhance shorter wavelength features helps reduce both the core signal and the signal from external fields in comparison with the crustal signal. If the gradient device can be oriented, then directions of lineation can be determined from single profiles, and anomalies caused by unlineated sources can be identified.

Harrison, C. G. A.↗

NASA NTRS1992

Three-Dimensional Turbulent Boundary Layer With Adverse Pressure Gradient

Report describes experiment to measure effects of adverse pressure gradient on three-dimensional turbulent boundary-layer flow; effect of streamwise gradient of pressure on crossflow of particular interest. Production of turbulent kinetic energy grows rapidly in vicinity of step as result of steep mean-flow velocity gradients. Dissipation grows less quickly than production; leading to net growth with distance along streamline.

Driver, David M.↗

NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS1991

Space charge enhanced plasma gradient effects on satellite electric field measurements

It has been recognized that plasma gradients can cause error in magnetospheric electric field measurements made by double probes. Space charge enhanced Plasma Gradient Induced Error (PGIE) is discussed in general terms, presenting the results of a laboratory experiment designed to demonstrate this error, and deriving a simple expression that quantifies this error. Experimental conditions were not identical to magnetospheric conditions, although efforts were made to insure the relevant physics applied to both cases. The experimental data demonstrate some of the possible errors in electric field measurements made by strongly emitting probes due to space charge effects in the presence of plasma gradients. Probe errors in space and laboratory conditions are discussed, as well as experimental error. In the final section, theoretical aspects are examined and an expression is derived for the maximum steady state space charge enhanced PGIE taken by two identical current biased probes.

Diebold, Dan↗

NASA NTRS1992

Implementation of Vigneron's streamwise pressure gradient approximation in the PNS equations

For single sweep parabolized Navier-Stokes solvers, the streamwise pressure gradient must be modified in the subsonic region to eliminate numerical instabilities. The accuracy of this modification on the solution of the parabolized Navier-Stokes equations with Vigneron's technique is shown to depend on how the numerical approximation of the pressure gradient is formed. A simple test case of supersonic laminar flow over a flat plate is computed with two different numerical methods for solving the PNS equations. Significant errors in the temperature profile and skin friction coefficient are demonstrated using a fully conservative differencing treatment of Vigneron's splitting for the pressure gradient typically used in parabolized Navier-Stokes solvers. The physical reason for this error is discussed. An alternate formulation is demonstrated which minimizes these errors.

Morrison, Joseph H.↗

NASA NTRS1993

Moving-Gradient Furnace With Constant-Temperature Cold Zone

Outer heat pipe helps in controlling temperature of cold zone of furnace. Part of heat-pipe furnace that includes cold zone surrounded by another heat pipe equipped with heater at one end and water cooling coil at other end. Temperature of heat pipe maintained at desired constant value by controlling water cooling. Serves as constant-temperature heat source or heat sink, as needed, for gradient of temperature as gradient region moved along furnace. Proposed moving-gradient heat-pipe furnace used in terrestrial or spaceborne experiments on directional solidification in growth of crystals.

Gernert, Nelson J.↗

NASA NTRS1992

One-dimensional transient finite difference model of an operational salinity gradient solar pond

This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.

Hicks, Michael C.↗

NASA NTRS1990

Experimental Study of a Three-Dimensional Shear-Driven Turbulent Boundary Layer with Streamwise Adverse Pressure Gradient

The effects of a strong adverse pressure gradient on a three-dimensional turbulent boundary layer are studied in an axisymmetric spinning cylinder geometry. Velocity measurements made with a three-component laser Doppler velocimeter include all three mean flow components, all six Reynolds stress components, and all ten triple-product correlations. Reynolds stress diminishes as the flow becomes three-dimensional. Lower levels of shear stress were seen to persist under adverse pressure gradient conditions. This low level of stress was seen to roughly correlate with the magnitude of cross-flow (relative to free stream flow) for this experiment as well as most of the other experiments in the literature. Variations in pressure gradient do not appear to alter this correlation. For this reason, it is hypothesized that a three-dimensional boundary layer is more prone to separate than a two-dimensional boundary layer, although it could not be directly shown here. None of the computations performed with either a Prandtl mixing length, k-epsilon, or a Launder-Reece-Rodi full Reynolds-stress model were able to predict the reduction in Reynolds stress.

Driver, David M.↗

NASA NTRS1992

Large infrared and optical color gradients in the Cartwheel ring galaxy - Evidence for the first epoch of star formation in the wake of an expanding ring

Substantial near-infrared and optical color gradients have been observed within the disk of the classical ring galaxy A0035-324 (the 'Cartwheel'). The slope of the radial B-V, V-K color gradient coincides with starburst color evolution predictions, indicating that the age of the disk population is a function of radius. Observations indicate that the youngest stars are on the leading edge of the outer ring, and the stellar population grows increasingly older toward the nucleus. The radial color gradient, taken together with other evidence, strongly support the collisional picture for the formation of ring galaxies. Strong IR emission observed in the outer ring appears to be directly associated with the young star-forming regions rather than an evolved stellar population. We conclude that star formation is occurring in a mainly gaseous expanding density wave and that the Cartwheel is undergoing its first epoch of star formation since its formation.

Marcum, P. M.↗

NASA NTRS1992

The ultraviolet color gradient in the late-type spiral galaxy M33

The ultraviolet surface brightness and color distributions for the late-type spiral galaxy M33 are derived from images at 1520 and 2490 A that were obtained by the Ultraviolet Imaging Telescope (UIT) on the Astro Spacelab mission. Although the surface brightness shows a general decline with radius, the dominant spiral arms cause significant deviations from an exponential fit. Colors in elliptical annuli become 0.2-0.3 mag bluer with increasing radius. Our measures of individual H II regions and sections of spiral arms follow this same trend. Interarm regions are redder than the arms. A metallicity gradient affecting only the colors of stars is inadequate in accounting for the observed color gradient. A plausible explanation invokes a combination of an LMC-type reddening curve and a radial gradient in the internal reddening in M33.

Landsman, Wayne B.↗

NASA NTRS1993

The gradient of galactic cosmic rays at the solar-wind termination shock

We report on a study of the expected spatial variation of the galactic cosmic-ray intensity in the outer heliosphere, in the vicinity of the solar-wind termination shock. Model simulations which contain all of the transport effects, including drifts, predict that the radial gradients change abruptly at the shock, and that the nature of the effect varies significantly with particle energy. At low energies, the radial gradient changes abruptly from a lower value inside the shock to a higher value outside, whereas at high energies, the higher value of the gradient is inside the shock. This effect, which is a consequence of the matching conditions at the shock and is closely related to diffusive shock acceleration, is qualitatively the same for both helisopheric magnetic polarity states and remains much the same in one-dimensional, two-dimensional, and three-dimensional models. Hence drifts do not change the nature of this phenomenon, although they change it quantitatively. The effect is, of course, not present in the absence of a terminal shock and may prove to be an important diagnostic tool for the study of the termination of the solar wind.

Jokipii, J. R.↗