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NASA NTRS1993

Improving the reconstruction of the velocity potential and primordial density fluctuations by choice of smoothing windows

Recently considerable attention has been focused on improving algorithms for restoring primordial density fluctuations in the universe or investigating large-scale velocity fields by going to higher order approximations relating nonlinear states to their initial conditions. An alternative approach is to investigate the use of alternative smoothing windows within the context of first-order approximations. I present evidence that the universally used Gaussian smoothing window is far from optimal. A sharp truncation P(k) = 0 for k greater than k(c) leads to a much more direct connection to initial conditions for either 'Gaussianization' methods or use of the Zel'dovich approximation, as discussed in the text.

Melott, Adrian L.↗

NASA NTRS2004

Chandra Observations of the X-ray Environs of SN 1998bw/GRB 980425

We report X-ray studies of the environs of SN 1998bw and GRB 980425 using the Chandra X-Ray Observatory 1281 days after the GRB. Eight X-ray point sources were localized, three and five each in the original error boxes - S1 and S2 - assigned for variable X-ray counterparts to the GRB by BeppoSAX. The sum of the discrete X-ray sources plus continuous emission in S2 observed by CXO on day 1281 is within a factor of 1.5 of the maximum and the upper limits seen by BeppoSAX. We conclude that S2 is the sum of several variable sources that have not disappeared, and therefore is not associated with the GRB. Within S1, clear evidence is seen for a decline of approximately a factor of 12 between day 200 and day 1281. One of the sources in S1, Sla, is coincident with the well-determined radio location of SN 1998bw, and is certainly the remnant of that explosion. The nature of the other sources is also discussed. Combining our observation of the supernova with others of the GRB afterglow, a smooth X-ray light curve, spanning approximately 1300 days, is obtained by assuming the burst and supernova were coincident at 35.6 Mpc. When this X-ray iight curve is compared with those of the X-ray afterglows of ordinary GRBs, X-ray Flashes, and ordinary supernovae, evidence emerges for at least two classes of lightcurves, perhaps bounding a continuum. By three to ten years, all these phenomena seem to converge on a common X-ray luminosity, possibly indicative of the supernova underlying them all. This convergence strengthens the conclusion that SN 1998bw and GRB 980425 took place in the same object. One possible explanation for the two classes is a (nearly) standard GRB observed at different angles, in which case X-ray afterglows with intermediate luminosities should eventually be discovered. Finally, we comment on the contribution of GRBs to the ULX source population.

Kouveliotou, C.↗

NASA NTRS1992

A comparison of the reduced and approximate systems for the time dependent computation of the polar wind and multiconstituent stellar winds

The paper derives the 'reduced' system of equations commonly used to describe the time evolution of the polar wind and multiconstituent stellar winds from the equations for a multispecies plasma with known temperature profiles by assuming that the electron thermal speed approaches infinity. The reduced system is proved to have unbounded growth near the sonic point of the protons for many of the standard parameter cases. For the same parameter cases, the unmodified system exhibits growth in some of the Fourier modes, but this growth is bounded. An alternate system (the 'approximate' system) in which the electron thermal speed is slowed down is introduced. The approximate system retains the mathematical behavior of the unmodified system and can be shown to accurately describe the smooth solutions of the unmodified system. Other advantages of the approximate system over the reduced system are discussed.

Browning, G. L.↗

NASA NTRS1990

Turbulence measurements using tethered balloon instrumentation during FIRE 1987

As part of the surface-based observations conducted on San Nicolas Island, the U.K. Meteorological Office operated a set of turbulence probes attached to a balloon tether cable. Typically six probes were used, each capable of measuring momentum, heat, and humidity fluxes. Two probes were fitted with net radiometers, one positioned above cloud and the other below; a third probe carried a Lyman-alpha hygrometer fitted with a pre-heater for the measurement of total water content. Some preliminary results are presented from the 14th July describing the variation in structure of the cloudy boundary layer during the daytime. This day was characterized by a complete cloud cover, an inversion height of approximately 600 m. and north-westerly winds of approximately 6 m.s(-1). As an illustration the equivalent potential temperature derived from a profile ascent made between approximately 0830 and 0930 (PDT) is shown. The data has been smoothed to a height resolution of about 4 metres. At this time the cloud base was approximately 200 m. and very light drizzle was reaching the surface. The vertical velocity variance and potential temperature flux for two periods are shown; the first (shown by full lines) immediately follows the profile and the second (shown by dashed lines) is central around 1400 (PDT). The data have been normalized by their maximum values in the first period. Cloud base has now risen to approximately 300 m. There is a marked variation during the morning, particularly in sigma w. The net radiative flux above cloud top has by now reached its maximum value.

Hignett, Phillip↗

NASA NTRS1972

Computer programs for plotting curves with various dashed-line sequences

Two FORTRAN-callable subprograms have been written to draw a smooth curve through a set of input points as a solid line or as a general sequence of long and short dashes. Subroutine LINSEQ draws conventional curves whereas subroutine CONSEQ draws smooth closed curves (contours). The subprograms are based on an approximate calculation of the arc length along the curve and spline interpolation along the arc length. Options are provided for smoothing of the input data and for offsetting the plotted curve from the input data points. The method of calculation of the arc length and the generation of the line sequence are described.Usage descriptions of the main subprograms, sample calling programs illustrating the various features of the subprograms, and sample plots are given. The subroutines should be readily adaptable to almost any computer-driven incremental plotter.

Desmarais, R. N.↗

NASA NTRS1971

Corkscrews and singularities in fruitflies - Resetting behavior of the circadian eclosion rhythm.

Description of experiments undertaken to define the phase-resetting behavior of the circadian rhythm of pupal eclosion in populations of fruitflies. An attempt is made to determine how and why the resetting response depends on the duration of a standard perturbation as well as on the time at which it is given. Plotting a three-dimensional graph of the measured emergence centroids vs the stimulus variables, the data are found to spiral up around a vertical rotation axis. Using a computer, a smooth surface, called the resetting surface, which approximately fits the helicoidal cloud of data points, is obtained and is shown to be best described as a vertical corkscrew linking together tilted planes. This corkscrew feature of the resetting surface is taken to indicate that there is an isolated perturbation following which there is either no circadian rhythm of emergence in the steady state, or one of unpredictable phase. A hypothesis concerning the clock dynamics underlying the eclosion rhythm is briefly sketched which encompasses the main features of known resetting data using single discrete pulses of any perturbing agent.

Winfree, A. T.↗

NASA NTRS1972

Spline smoothing of histograms by linear programming

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Bennett, J. O.↗

NASA NTRS1984

Multigrid applications to three-dimensional elliptic coordinate generation

The multigrid algorithm was applied to solve the coupled set of elliptic quasilinear partial differential equations associated with three-dimensional coordinate generation. The results indicate that the multigrid scheme is more than twice as fast as conventional relaxation schemes on moderate-size grids. Convergence factors of order 0.90 per work unit were achieved on 36,000-point grids. The paper covers the form of transformation, develops the set of generation equations, and gives details on the multigrid approach used. Included are a development of the full-approximation storage scheme, details of the smoothing-rate analysis, and a section devoted to rational programming techniques applicable to the multigrid algorithm.

Thames, F. C.↗

NASA NTRS1985

Development of seeding techniques for small supersonic wind tunnel

The NASA Lewis 1x1 foot supersonic wind tunnel is used to experimentally verify computational methods. This tunnel, which is continuous running, operates from laboratory-wide high pressure air and vacuum systems. As such, the air does not recirculate but makes a single pass through the tunnel. The Mach number is varied with interchangeable nozzle blocks and has a range from Mach 1.6 to 4.0. Dry and filtered air is available up to pressures of 3 atmospheres. The air enters the tunnel system through a plenum having flow straighteners and 6 fine mesh screens. The exit of the plenum provides smooth contraction with an area ratio of approximately 20 that, along with the screens, provides a uniform flow for the nozzle.

Hingst, W. R.↗

NASA NTRS1991

Calculating Scattering At Circular-Waveguide Junctions

Computer program calculates scattering matrices for circular waveguides including step discontinuities between collinear sections of different radii. Radius and length of each section specified arbitrarily. Examples of devices analyzed with program include waveguides with single step discontinuities, matching sections, corrugated straight sections, and corrugated horns. Sections with smooth tapers and horns with arbitrary profiles approximated by series of small steps.

Hoppe, D. J.↗

NASA NTRS1993

Simulations of particle acceleration in parallel shocks: Direct comparison between Monte Carlo and one-dimensional hybrid codes

We have made a direct comparison between two different computer simulations of a plane, parallel, collisionless shock including particle acceleration to energies typical of those of diffuse ions observed at the earth bow shock. Despite the fact that the one-dimensional hybrid and Monte Carlo techniques employ entirely different algorithms, they give surprisingly close agreement in the overall shapes of the complete distribution functions for protons as well as heavier ions. Both methods show that energetic ions emerge smoothly from the background thermal plasma with approximately the same relative injection rate and that the fraction of the incoming plasma's energy flux that is converted into downstream enthalpy flux of the accelerated population (i.e., the acceleration efficiency) is similar in the two cases. The fraction of the downstream proton distribution made up of superthermal particles is quite large, with at least 10% of the energy flux going into protons with energies above 10 keV. In addition, an upstream precursor, produced by backstreaming energetic particles, is present in both shocks, although the Monte Carlo precursor is considerably longer than that produced in the hybrid shock. These results offer convincing evidence that, at least in these ways, the two simulations are consistent in their description of parallel shock structure and particle acceleration, and they lay the groundwork for development of shock models employing a combination of both methods.

Ellison, Donald C.↗

NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗

NASA NTRS2008

Structural Maps of the V-17 Beta Regio Quadrangle, Venus

These represent slices of the geologic map into 7 time-stratigraphic levels whose descriptions are found in [3-6]. From older to younger they are: 1) Tessera material unit (t), 2) Densely fractured plains material unit (pdf), 3) Fractured and ridged plains material unit (pfr), 4) Tessera transitional terrain structural unit (tt), 5) Fracture belts structural unit (fb), 6) Shield plains (psh) and plains with wrinkle ridges (pwr) material units combined, and 7) Lobate (pl) and smooth (ps) plains material units combined and, approximately contemporaneous with them, the structural unit of rifted terrain (rt). Each slice shows the generalized pattern of structures typical of these units. Figures 1-7 show the seven maps and Figure 8 shows the combined map illustrating what is shown in the seven maps. To visualize the Beta Regio uplift outlines, the major structure of this area, we show the +0.5 km and +2.5 km contour lines, corresponding respectively to the base and the mid-height of the uplift. It is seen in Figures 1-2 and 4 the trends of t, pdf and tt occupy relatively small areas and their structures seen in these small windows appear rather variable and with almost no orientation heritage with time. Figure 3 shows that swarms of ridge belts trend mostly NW and go through the Beta structure with no alignment with it, suggesting that this structure did not yet exist at this time. Figure 5 shows that fracture belts align along the northern base of the Beta uplift suggesting onset of the formation of this structure. Figure 6 shows that wrinkle ridges do not show alignment with the Beta uplift suggesting that this already forming structure was not high enough to exert topographic stress in its vicinity. Figure 7 shows that the Beta uplift has Devana Chasma as an axial rift zone, suggesting a genetic link between the uplift and rifting. Figure 8 shows that structural trends in this area significantly changed with time.

Basilevsky, A. t.↗

NASA NTRS1995

Solar cycle variation of interplanetary shocks, coronal mass ejections, and stream interactions observed at 0.7 AU

A survey of the Pioneer Venus Orbiter (PVO) magnetometer and plasma data from 1979-1980, shows that the occurrence frequency of interplanetary shocks, coronal mass ejections (CMEs) and stream interactions observed at 0.7 AU exhibits a solar cycle variation. As previously found at 1 AU, the observed number of both interplanetary shocks and CMEs peaks during solar maximum (approximately 16 and approximately 27 per year, respectively) and reaches a low during solar minimum (approximately 0 and approximately 7 per year, respectively), in phase with the variation in smoothed sunspot number. The number of stream interactions observed varies in the opposite manner, having a minimum during solar maximum (approximately 15 per year) and a maximum during solar minimum (approximately 34 per year). The percentage of CMEs and stream interactions producing interplanetary shocks also varies during the solar-cycle and exhibits interesting behavior during the declining phase. While the number of CMEs observed during this phase is decreasing, the percentage of CMEs producing interplanetary shocks reaches a maximum. Also, while the number of stream interactions observed is increasing, but has not reached maximum during the declining phase, the percentage of stream interactions producing interplanety shocks is at a maximum.

Lindsay, G. M.↗

NASA NTRS1993

Accurate upwind methods for the Euler equations

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Huynh, Hung T.↗

NASA NTRS1986

Analysis of growth patterns during gravitropic curvature in roots of Zea mays by use of a computer-based video digitizer

A computer-based video digitizer system is described which allows automated tracking of markers placed on a plant surface. The system uses customized software to calculate relative growth rates at selected positions along the plant surface and to determine rates of gravitropic curvature based on the changing pattern of distribution of the surface markers. The system was used to study the time course of gravitropic curvature and changes in relative growth rate along the upper and lower surface of horizontally-oriented roots of maize (Zea mays L.). The growing region of the root was found to extend from about 1 mm behind the tip to approximately 6 mm behind the tip. In vertically-oriented roots the relative growth rate was maximal at about 2.5 mm behind the tip and declined smoothly on either side of the maximum. Curvature was initiated approximately 30 min after horizontal orientation with maximal (50 degrees) curvature being attained in 3 h. Analysis of surface extension patterns during the response indicated that curvature results from a reduction in growth rate along both the upper and lower surfaces with stronger reduction along the lower surface.

NASA Discipline Plant Biology↗

NASA NTRS1990

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Stengel, Robert F.↗

NASA NTRS1978

Drag and heat transfer on surfaces with small longitudinal fins

An investigation is conducted regarding the drag characteristics of longitudinally ribbed surfaces using various configurations which attempt to confine the turbulent wall bursts to regions of small transverse extent in the initial birth region. The ratio of heat transfer increase to drag increase for the high area ratio rib configurations is determined and the heat transfer efficiency of the present surfaces is compared with data found in the literature. The drag data obtained indicate local 'wetted area skin friction' reductions but due to the increased surface area the planform drag is increased in most instances. There is no indication of drag reduction with the rectangular ribbed models that had sharp leading and fin tip edges. Heat transfer data indicate that several of the triangular grooved models have efficiencies approximately 10 percent higher than that of a smooth flat plate.

Walsh, M. J.↗