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At least 127 records · Page 7
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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 NTRS1991

Near-wall turbine closure for curved flows

At present, turbulence closures for curved flows only account for curvature effects in the fully turbulent region where the Reynolds number is large. The justification is that, near a wall, viscous effects dominate and curvature effects are only of secondary importance. Recent direct simulation data show that this assumption is not valid, even for simple two-dimensional fully developed turbulent curved channel flows. This paper presents an approach to develop a near-wall turbulence closure for wall-bounded curved flows. The curved channel direct simulation data is used as a guide to held develop such a closure. The proposed closure has the unique property of approaching conventional high-Reynolds-number Reynolds-stress closures far away from the wall. Hence, curvature effects in both the near-wall and the fully turbulent parts of the flow are accounted for properly. Validations of the closure are carried out with a set of low-Reynolds-number simulation data and with experimental measurements at high Reynolds number. Good agreement is obtained in both cases; in particular, the anisotropic behavior of the normal stresses and the shear stress behavior near the convex and concave walls.

So, R. M. C.↗
NASA NTRS1991

The wavelength dependence of Triton's light curve

Using Voyager observations, it is demonstrated that Triton's orbital light curve is strongly wavelength-dependent, a characteristic which readily explains some of the apparent discrepancies among pre-Voyager telescopic measurements. Specifically, a light curve amplitude (peak to peak) is found that decreases systematically with increasing wavelength from about 0.08 magnitude (peak to peak) near 200 nm to less than 0.02 magnitude near 1000 nm. Peak brightness occurs near 90 deg orbital longitude (leading hemisphere). The brightness variation across this hemisphere is close to sinusoidal; the variation across the darker hemisphere is more complex. The decrease in light curve amplitude with increasing wavelength appears to be due to a decrease in contrast among surface markings, rather than to atmospheric obscuration. The model also explains the observed decrease in the amplitude of Triton's light curve at visible wavelengths over the past decade, a decrease related to the current migration of the subsolar latitude toward the south pole; it is predicted that this trend will continue into the 1990s.

Hillier, J.↗
NASA NTRS1991

Note on unit tangent vector computation for homotopy curve tracking on a hypercube

Probability-one homotopy methods are a class of methods for solving nonlinear systems of equations that are globally convergent from an arbitrary starting point. The essence of all such algorithms is the construction of an appropriate homotopy map and subsequent tracking of some smooth curve in the zero set of the homotopy map. Tracking a homotopy curve involves finding the unit tangent vector at different points along the zero curve, which amounts to calculating the kernel of the n x (n + 1) Jacobian matrix. While computing the tangent vector is just one part of the curve tracking algorithm, it can require a significant percentage of the total tracking time. This note presents computational results showing the performance of several different parallel orthogonal factorization/triangular system solving algorithms for the tangent vector computation on a hypercube.

Chakraborty, A.↗
NASA NTRS1993

Light-curve solutions for S Cancri and TT Hydrae with rapid rotation

Physical model light- and velocity-curve solutions for S Cancri and TT Hydrae are obtained, and analyses with incorporation of asynchronous rotation are carried out. A photometric rotation rate for the primary star of TT Hya is determined, and excellent agreement with results from spectral line profiles is found. Both separate light- and velocity-curve solutions and simultaneous light-velocity solutions are listed. The photometric rotation for S Cnc from existing light curves is indeterminate, but is compatible with line profile measures. Evidence for third light from the light curves of S Cnc is found. An explanation for the apparent conflict between the rotational states and mass-transfer activities of the two binaries is suggested.

Van Hamme, W.↗
NASA NTRS1993

Global expression for representing cohesive-energy curves. II

Schlosser et al. (1991) showed that the R dependence of the cohesive energy of partially ionic solids may be characterized by a two-term energy relationship consisting of a Coulomb term arising from the charge transfer, delta-Z, and a scaled universal energy function, E*(a *), which accounts for the partially covalent character of the bond and for repulsion between the atomic cores for small R; a* is a scaled length. In the paper by Schlosser et al., the normalized cohesive-energy curves of NaCl-structure alkali-halide crystals were generated with this expression. In this paper we generate the cohesive-energy curves of several families of partially ionic solids with different crystal structures and differing degrees of ionicity. These include the CsCl-structure Cs halides, and the Tl and Ag halides, which have weaker ionic bonding than the alkali halides, and which have the CsCl and NaCl structures, respectively. The cohesive-energy-curve parameters are then used to generate theoretical isothermal compression curves for the Li, Na, K, Cs, and Ag halides. We find good agreement with the available experimental compression data.

Schlosser, Herbert↗
NASA NTRS1943

A method for determining the column curve from tests of columns with equal restraints against rotation on the ends

The results are presented of a theoretical study for the determination of the column curve from tests of column specimens having ends equally restrained against rotation. The theory of this problem is studied and a curve is shown relating the fixity coefficient c to the critical load, the length of the column, and the magnitude of the elastic restraint. A method of using this curve for the determination of the column curve for columns with pin ends from tests of columns with elastically restrained ends is presented. The results of the method as applied to a series of tests on thin-strip columns of stainless steel are also given.

Lundquist, Eugene E↗
NASA NTRS1924

The general efficiency curve for air propellers

This report presents a formula which may be used to obtain a "general efficiency curve" in addition to the well-known maximum efficiency curve. These two curves, when modified somewhat by experimental data, enable performance calculations to be made without detailed knowledge of the propeller. The curves may also be used to estimate the improvement in efficiency due to reduction gearing, or to judge the performance of a new propeller design.

Diehl, Walter S↗
NASA NTRS1993

On curve veering and flutter of rotating blades

The eigenvalues of rotating blades usually change with rotation speed according to the Stodola-Southwell criterion. Under certain circumstances, the loci of eigenvalues belonging to two distinct modes of vibration approach each other very closely, and it may appear as if the loci cross each other. However, our study indicates that the observable frequency loci of an undamped rotating blade do not cross, but must either repel each other (leading to 'curve veering'), or attract each other (leading to 'frequency coalescence'). Our results are reached by using standard arguments from algebraic geometry--the theory of algebraic curves and catastrophe theory. We conclude that it is important to resolve an apparent crossing of eigenvalue loci into either a frequency coalescence or a curve veering, because frequency coalescence is dangerous since it leads to flutter, whereas curve veering does not precipitate flutter and is, therefore, harmless with respect to elastic stability.

Afolabi, Dare↗
NASA NTRS1994

Nonlinear bulging factor based on R-curve data

In this paper, a nonlinear bulging factor is derived using a strain energy approach combined with dimensional analysis. The functional form of the bulging factor contains an empirical constant that is determined using R-curve data from unstiffened flat and curved panel tests. The determination of this empirical constant is based on the assumption that the R-curve is the same for both flat and curved panels.

Jeong, David Y.↗
NASA NTRS1995

Delayed detonation models for normal and subluminous type Ia sueprnovae: Absolute brightness, light curves, and molecule formation

We compute optical and infrared light curves of the pulsating class of delayed detonation models for Type Ia supernovae (SN Ia's) using an elaborate treatment of the Local Thermodynamic Equilbrium (LTE) radiation transport, equation of state and ionization balance, expansion opacity including the cooling by CO, Co(+), and SiO, and a Monte Carlo gamma-ray deposition scheme. The models have an amount of Ni-56 in the range from approximately or equal to 0.1 solar mass up to 0.7 solar mass depending on the density at which the transition from a deflagration to a detonation occurs. Models with a large nickel production give light curves comparable to those of typical Type Ia supernovae. Subluminous supernovae can be explained by models with a low nickel production. Multiband light curves are presented in comparison with the normally bright event SN 1992bc and the subluminous events Sn 1991bg and SN 1992bo to establish the principle that the delayed detonation paradigm in Chandrasekhar mass models may give a common explosion mechanism accounting for both normal and subluminous SN Ia's. Secondary IR-maxima are formed in the models of normal SN Ia's as a photospheric effect if the photospheric radius continues to increase well after maximum light. Secondary maxima appear later and stronger in models with moderate expansion velocities and with radioactive material closer to the surface. Model light curves for subluminous SN Ia's tend to show only one 'late' IR-maximum. In some delayed detonation models shell-like envelopes form, which consist of unburned carbon and oxygen. The formation of molecules in these envelopes is addressed. If the model retains a C/O-envelope and is subluminous, strong vibration bands of CO may appear, typically several weeks past maximum light. CO should be very weak or absent in normal Sn Ia's.

Hoflich, P.↗
NASA NTRS1995

Analysis of tipping-curve measurements performed at the DSS-13 beam-waveguide antenna at 32.0 and 8.45 GigaHertz

This article reports on the analysis of the Ka-band Antenna Performance Experiment tipping-curve data acquired at the DSS-13 research and development beam-waveguide (BWG) antenna. By measuring the operating system temperatures as the antenna is moved form zenith to low-elevation angles and fitting a model to the data, one can obtain information on how well the overall temperature model behaves at zenith and approximate the contribution due to the atmosphere. The atmospheric contribution estimated from the data can be expressed in the form of (1) atmospheric noise temperatures that can provide weather statistic information and be compared against those estimated from other methods and (2) the atmospheric loss factor used to refer efficiency measurements to zero atmosphere. This article reports on an analysis performed on a set of 68 8.4-GHz and 67 32-GHz tipping-curve data sets acquired between December 1993 and May 1995 and compares the results with those inferred from a surface model using input meteorological data and from water vapor radiometer (WVR) data. The general results are that, for a selected subset of tip curves, (1) the BWG tipping-curve atmospheric temperatures are in good agreement with those determined from WVR data (the average difference is 0.06 +/- 0.64 K at 32 GHz) and (2) the surface model average values are biased 3.6 K below those of the BWG and WVR at 32 GHz.

Morabito, D. D.↗
NASA NTRS1994

Dissociative Recombination without a Curve Crossing

Ab initio calculations show that a curve crossing is not always needed for a high dissociative- recombination cross section. For HeH(+), in which no neutral states cross the ion potential curve, dissociative recombination is driven by the nuclear kinetic-energy operator on adiabatic potential curves. The kinetic-energy derivative operator allows for capture into repulsive curves that are outside of the classical turning points for the nuclear motion. The dominant dissociative route is the C (2)Sigma(+) state leading to H(n = 2) atoms. An analogous mechanism is proposed for the dissociative recombination of H3(+).

Guberman, Steven L.↗
NASA NTRS1997

Extending ROSAT Light Curves of Ecliptic Pole AGN Formation and Galaxy Evolution

In collaboration with UCLA graduate student Fred Baganoff, Professor Malkan has obtained the longest continuous light curves ever available for a large sample (# = 60) of active galactic nuclei. This was accomplished by using the ROSATAII-Sky Survey, which covered the ecliptic pole regions once every 9O-minute orbit. Using this Astrophysics Data Processing grant from NASA, we extended these light curves by combining the RASS data with pointed observations over the next several years of operation of the ROSAT PSPC. This lengthens the baselines of about half of the light curves from a few months up to a few years. The proportion of AGN showing variability increases substantially with this improvement. In fact most AGN in this representative sample are now shown to be significantly variable in the X-rays. We are also able to say something about the amplitudes of variability on timescales from days to years, with more detail than previously has been possible. We have also identified some dependence of the X-ray variability properties on a) the luminosity of the AGN; and b) The presence of a "Blazar" nucleus. By extending the ROSAT light curves, we are also able to learn more about the correlation of X-ray and optical emission on longer time-scales. It appears to be very weak, at best.

Malkan, Matthew A.↗
NASA NTRS1999

Open-Mode Debonding Analysis of Curved Sandwich Panels Subjected to Heating and Cryogenic Cooling on Opposite Faces

Increasing use of curved sandwich panels as aerospace structure components makes it vital to fully understand their thermostructural behavior and identify key factors affecting the open-mode debonding failure. Open-mode debonding analysis is performed on a family of curved honeycomb-core sandwich panels with different radii of curvature. The curved sandwich panels are either simply supported or clamped, and are subjected to uniform heating on the convex side and uniform cryogenic cooling on the concave side. The finite-element method was used to study the effects of panel curvature and boundary condition on the open-mode stress (radial tensile stress) and displacement fields in the curved sandwich panels. The critical stress point, where potential debonding failure could initiate, was found to be at the midspan (or outer span) of the inner bonding interface between the sandwich core and face sheet on the concave side, depending on the boundary condition and panel curvature. Open-mode stress increases with increasing panel curvature, reaching a maximum value at certain high curvature, and then decreases slightly as the panel curvature continues to increase and approach that of quarter circle. Changing the boundary condition from simply supported to clamped reduces the magnitudes of open-mode stresses and the associated sandwich core depth stretching.

Ko, William L.↗
NASA NTRS2000

Comparison of 1998 and 1999 Leonid Light Curve Morphology and Meteoroid Structure

Photometric low-light level video observations of 1999 Leonid storm meteors have been obtained from airborne platforms during the Leonid multi-instrument aircraft campaign (Leonid MAC). The 1999 Leonid light curves tend to be skewed towards the end point of the trajectory, while the 1998 Leonid light curves were not. The variation in the light curves from 1998 and 1999 can be explained as an overall reduction in the mass distribution index, alpha from approximately 1.95 in 1998 to approximately 1.75 in 1999. We have interpreted this behavior as being either indicative of a gradual loss of the "glue" that keeps the grains together, or the fact that the meteoroids sampled in 1998 had a different morphological structure to those sampled in 1999. The early fragmentation of a dustball meteoroid results in a light curve that peaks sooner than that predicted by classical single body ablation theory.

Murray, Ian S.↗
NASA NTRS2001

Structural and Acoustic Numerical Modeling of a Curved Composite Honeycomb Panel

The finite and boundary element modeling of the curved section of a composite honeycomb aircraft fuselage sidewall was validated for both structural response and acoustic radiation. The curved panel was modeled in the pre-processor MSC/PATRAN. Geometry models of the curved panel were constructed based on the physical dimensions of the test article. Material properties were obtained from the panel manufacturer. Finite element models were developed to predict the modal parameters for free and supported panel boundary conditions up to a frequency of 600 Hz. Free boundary conditions were simulated by providing soft foam support under the four comers of the panel or by suspending the panel from elastic bands. Supported boundary conditions were obtained by clamping the panel between plastic tubing seated in grooves along the perimeter of a stiff and heavy frame. The frame was installed in the transmission loss window of the Structural Acoustic Loads and Transmission (SALT) facility at NASA Langley Research Center. The structural response of the curved panel due to point force excitation was predicted using MSC/NASTRAN and the radiated sound was computed with COMET/Acoustics. The predictions were compared with the results from experimental modal surveys and forced response tests on the fuselage panel. The finite element models were refined and updated to provide optimum comparison with the measured modal data. Excellent agreement was obtained between the numerical and experimental modal data for the free as well as for the supported boundary conditions. Frequency response functions (FRF) were computed relating the input force excitation at one panel location to the surface acceleration response at five panel locations. Frequency response functions were measured at the same locations on the test specimen and were compared with the calculated FRF values. Good agreement was obtained for the real and imaginary parts of the transfer functions when modal participation was allowed up to 3000 Hz. The validated finite element model was used to predict the surface velocities due to the point force excitation. Good agreement was obtained between the spatial characteristics of the predicted and measured surface velocities. The measured velocity data were input into the acoustic boundary element code to compute the sound radiated by the panel. The predicted sound pressure levels in the far-field of the panel agreed well with the sound pressure levels measured at the same location.

Grosveld, Ferdinand W.↗
NASA NTRS1991

A kill curve for Phanerozoic marine species

A kill curve for Phanerozoic species is developed from an analysis of the stratigraphic ranges of 17,621 genera, as compiled by Sepkoski. The kill curve shows that a typical species' risk of extinction varies greatly, with most time intervals being characterized by very low risk. The mean extinction rate of 0.25/m.y. is thus a mixture of long periods of negligible extinction and occasional pulses of much higher rate. Because the kill curve is merely a description of the fossil record, it does not speak directly to the causes of extinction. The kill curve may be useful, however, to li inverted question markmit choices of extinction mechanisms.

NASA Discipline Number 52-40↗