Search NASA⌕ Search

SEARCH · Search NASA

Results for “approximate Newton”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Design of a Minimum Surface-Effect Tendon-Based Microactuator for Micromanipulation

A piezoelectric (PZT) stack-based actuator was developed to provide a means of actuation with dynamic characteristics appropriate for small-scale manipulation. In particular, the design incorporates a highly nonlinear, large-ratio transmission that provides approximately two orders of magnitude motion amplification from the PZT stack. In addition to motion amplification, the nonlinear transmission was designed via optimization methods to distort the highly non-uniform properties of a piezoelectric actuator so that the achievable actuation force is nearly constant throughout the actuator workspace. The package also includes sensors that independently measure actuator output force and displacement, so that a manipulator structure need not incorporate sensors nor the associated wires. Specifically, the actuator was designed to output a maximum force of at least one Newton through a stroke of at least one millimeter. For purposes of small-scale precision position and/or force control, the actuator/sensor package was designed to eliminate stick-slip friction and backlash. The overall dimensions of the actuator/sensor package are approximately 40 x 65 x 25 mm.

Goldfarb, Michael↗

Equations of motion of slung-load systems, including multilift systems

General simulation equations are derived for the rigid body motion of slung-load systems. This work is motivated by an interest in trajectory control for slung loads carried by two or more helicopters. An approximation of these systems consists of several rigid bodies connected by straight-line cables or links. The suspension can be assumed elastic or inelastic. Equations for the general system are obtained from the Newton-Euler rigid-body equations with the introduction of generalized velocity coordinates. Three forms are obtained: two generalize previous case-specific results for single-helicopter systems with elastic and inelastic suspensions, respectively; and the third is a new formulation for inelastic suspensions. The latter is derived from the elastic suspension equations by choosing the generalized coordinates so that motion induced by cable stretching is separated from motion with invariant cable lengths, and by then nulling the stretching coordinates to get a relation for the suspension forces. The result is computationally more efficient than the conventional formulation, is readily integrated with the elastic suspension formulation, and is easily applied to the complex dual-lift and multilift systems. Results are given for two-helicopter systems; three configurations are included and these can be integrated in a single simulation. Equations are also given for some single-helicopter systems, for comparison with the previous literature, and for a multilift system. Equations for degenerate-body approximations (point masses, rigid rods) are also formulated and results are given for dual-lift and multilift systems. Finally, linearlized equations of motion are given for general slung-load systems are presented along with results for the two-helicopter system with a spreader bar.

Cicolani, Luigi S.↗

XMM-Newton Archival Study of the ULX Population in Nearby Galaxies

We present the results of an archival XMM-Newton study of the bright X-ray point sources (L(sub X) greater than 10(exp 38 erg per second)) in 32 nearby galaxies. From our list of approximately 100 point sources, we attempt to determine if there is a low-state counterpart to the Ultraluminous X-ray (ULX) population, searching for a soft-hard state dichotomy similar to that known for Galactic X-ray binaries and testing the specific predictions of the IMBH hypothesis. To this end, we searched for low-state objects, which we defined as objects within our sample which had a spectrum well fit by a simple absorbed power law, and high-state objects, which we defined as objects better fit by a combined blackbody and a power law. Assuming that low-state)) objects accrete at approximately 10% of the Eddington luminosity (Done & Gierlinski 2003) and that high-state objects accrete near the Eddington luminosity we further divided our sample of sources into low and high state ULX sources. We classify 16 sources as low-state ULXs and 26 objects as high-state ULXs. As in Galactic black hole systems, the spectral indices, GAMMA, of the lowstate objects, as well as the luminosities, tend to be lower than those of the high-state objects. The observed range of blackbody temperatures for the high state is 0.1-1 keV, with the most luminous systems tending toward the lowest temperatures. We therefore divide our high-state ULXs into candidate IMBHs (with blackbody temperatures of approximately 0.1 keV) and candidate stellar mass BHs (with blackbody temperatures of approximately 1.0 keV). A subset of the candidate stellar mass BHs have spectra that are well-fit by a Comptonization model, a property similar of Galactic BHs radiating in the very-high state near the Eddington limit.

Winter, Lisa M.↗

An efficient algorithm for solution of the unsteady transonic small-disturbance equation

A time accurate approximate factorization (AF) algorithm is formulated for solution of the three dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time linearization procedure coupled with a Newton iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods.

Batina, John T.↗

Flight Test of a 40-Foot Nominal-Diameter Disk-Gap-Band Parachute Deployed at a Mach Number of 1.91 and a Dynamic Pressure of 11.6 Pounds per Square Foot

A 40-foot (12.2 meter) nominal-diameter disk-gap-band parachute was flight tested as part of the NASA Supersonic Planetary Entry Decelerator Program (SPED-I). The test parachute was ejected by a deployment mortar from an instrumented payload at an altitude of 140,000 feet (42.5 kilometers). The payload was at a Mach number of 1.91 and the dynamic pressure was 11.6 pounds per square foot (555 newtons per square meter) at the time the parachute deployment mortar was fired. The parachute reached suspension line stretch in 0.43 second with a resultant snatch force loading of 1990 pounds (8850 newtons). The maximum parachute opening load of 6500 pounds (28,910 newtons) came 0.61 second later at a total elapsed time from mortar firing of 1.04 seconds. The first full inflation occurred at 1.12 seconds and stable inflation was achieved at approximately 1.60 seconds. The parachute had an average axial-force coefficient of 0.53 during the deceleration period. During the steady-state descent portion of the flight test, the average effective drag coefficient was also 0.53 and pitch-yaw oscillations of the canopy averaged less than 10 degrees in the altitude region above 100,000 feet (30.5 meters).

EXPERIMENTS↗

The Remarkable X-ray Spectrum of the Broad-Line Radio Galaxy 3C 445

The nearby (z=0.057) radio-loud source 3C 445, optically classified as a Broad-Line Radio Galaxy, exhibits an X-ray spectrum strongly reminiscent of an obscured AGN, suggesting we are seeing this source at a relatively large angle from the radio jet. Here we present an archival 15 ks XMM-Newton observation of 3C 445 which confirms the remarkable complexity of its X-ray emission. The X-ray emission is described by a power law continuum with GAMMA approximately equal to 1.4, absorbed by several layers of cold gas, plus strong cold reflection. A narrow, unresolved Fe Kalpha emission line is detected, confirming previous findings, with EW approximately equal to 400 eV. A soft excess is present below 2 keV over the extrapolation of the hard X-ray power law, which we model with a power law with the same photon index and absorbed by a column density N(sub H)5 approximately equal to 10(sup 20) cm(sup -2) in excess to Galactic. Remarkably, a host of emission lines are present below 2 keV, confirming previous indications from ASCA, due to H- and He-like O, Mg, and Si. The detection of two features at 0.74 and 0.87 keV, identified with OVII and OVIII Radiative Recombination Continuum features, suggest an origin of the lines from a photoionized gas, with properties very similar to radio-quiet obscured AGN. Two different ionized media, or a single stratified medium, are required to fit the soft X-ray data satisfactorily. The similarity of the X-ray spectrum of 3C 445 to Seyferts underscores that the central engines of radio-loud and radio-quiet AGN similarly host both cold and warm gas.

Sambruna, R. M.↗

An efficient algorithm for solution of the unsteady transonic small-disturbance equation

A time accurate approximation factorization (AF) algorithm is formulated for solution of the three-dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time linearization procedure coupled with a Newton iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods.

Batina, John T.↗

Multigrid approaches to non-linear diffusion problems on unstructured meshes

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Mavriplis, Dimitri J.↗

Temperature Structure in the Perseus Cluster Core Observed with Hitomi

The present paper investigates the temperature structure of the X-ray emitting plasma in the core of the Perseus cluster using the 1.8-20.0 keV data obtained with the Soft X-ray Spectrometer (SXS) onboard the Hitomi Observatory. A series of four observations were carried out, with a total effective exposure time of 338 ks and covering a central region _ 7′ in diameter. The SXS was operated with an energy resolution of _5 eV (full width at half maximum) at 5.9 keV. Not only fine structures of K-shell lines in He-like ions but also transitions from higher principal quantum numbers are clearly resolved from Si through Fe. This enables us to perform temperature diagnostics using the line ratios of Si, S, Ar, Ca, and Fe, and to provide the first direct measurement of the excitation temperature and ionization temperature in the Perseus cluster. The observed spectrum is roughly reproduced by a single temperature thermal plasma model in collisional ionization equilibrium, but detailed line ratio diagnostics reveal slight deviations from this approximation. In particular, the data exhibit an apparent trend of increasing ionization temperature with increasing atomic mass, as well as small differences between the ionization and excitation temperatures for Fe, the only element for which both temperatures can be measured. The best-fit two-temperature models suggest a combination of 3 and 5 keV gas, which is consistent with the idea that the observed small deviations from a single temperature approximation are due to the effects of projection of the known radial temperature gradient in the cluster core along the line of sight. Comparison with the Chandra/ACIS and the XMM-Newton/RGS results on the other hand suggests that additional lower-temperature components

Aharonian, Felix↗

Finite-element methods for steady solidification problems

Four Galerkin finite-element methods are tested for solving the free-boundary problem that describes steady solidification. The formulations differ in the solution method used to account for the unknown shape of the melt/solid interface, in the interphase condition (either balance of heat flux or equilibrium of temperature) distinguished for locating the interface, and in the technique used for solving the systems of algebraic equations that result from the finite-element approximations. Methods that use the melting point isotherm to locate the melt/solid interface are found more accurate and efficient than formulations based on the interfacial energy balance. Solution by a Galerkin-Newton algorithm of the free-boundary problem transformed to a fixed domain is most efficient when the field problem in each phase is made nonlinear by including radiation from the melt and solid to the surroundings.

Ettouney, H. M.↗

X-Ray Timing Measurements of NGC 5408 X-1 With XMM-Newton and Swift/XRT: Implications for the Mass of a ULX

I present new X-ray timing measurements of the ULX NGC 5408 X-1 with XMM-Newton, and long term monitoring with the XRT onboard SWIFT. This object is one of only two ULXs in which quasi-periodic oscillations (QPO) have been detected. Recent observations with XMM-Newton confirm the presence of QPOs in this object. Most interestingly, two QPOs are again detected, as in an earlier observation, however, the QPO frequencies are different, now appearing at 10 and approximately 14 mHz. We discuss the implications of the QPO frequencies and spectra at these two different epochs for the mass of the black hole in NGC 5408 X-1. We also present strong evidence for long term flux variations based on the SWIFT monitoring campaign.

Strohmayer, Tod E.↗

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗

Blue lobes in the Hydra A cluster central galaxy

We present new U- and I-band images of the centrally dominant galaxy in the Hydra A cluster, obtained with the 2.5 m Isaac Newton Telescope at La Palma. The galaxy is centered in a poor, X-ray-luminous cluster whose gaseous intracluster medium is apparently cooling at a rate of m-dot(sub CF) approximately 3000 solar masses/yr. The galaxy's structure is that of a normal giant elliptical galaxy, apart from the central approximately 8 x 6 arcsec (approximately 12 x 9 kpc) region which contains an unusually blue, lobelike structure that is spatially coincident with a luminous emission-line nebula in rotation about the nucleus. Based on near spatial coincidence of the central continuum structure and the emission-line nebula, we suggest that the blue continuum is due to a warm stellar population in a central disk. In order to isolate and study the structure of the disk, we have subtracted a smooth galactic background model from the U-band image. The disk's surface brightness profiles along its major and minor axes decline roughly exponentially with radius. The disk's axial ratio is consistent with a nearly edge-on thick disk or a thin disk that is inclined with respect to the line of sight. The bluest regions, located a few arcsec on either side of the nucleus (giving the lobelike appearance), may be due to locally enhanced star formation or a seeing-blurred ring of young stars embedded in the disk observed nearly edge-on. If star-formation is occurring with the local initial mass function, the central color, surface brightness, and dynamical mass would be consistent with models for star formation at a rate of less than and approximately 1 solar masses/yr which has persisted for the past approximately 10(exp 9) yr, a short burst (10(exp 7) yr) of star formation at a rate of approximately 30 solar masses/yr which occurred less than and approximately 10(exp 8) yr ago, or an instantaneous burst of star formation which occurred approximately 5 x 10(exp 7) yr ago. While the young population contributes approximately 30%-40% of the central U-band luminosity, its mass would be less than and approximately 1% to less than and approximately 10% (10(exp 8) solar masses - 2 x 10(exp 9) solar masses of the galaxy's central dynamical mass. We consider a number of possible origins for the disk material.

Mcnamara, Brian R.↗

A technique for dynamically calibrating pressure transducers at cryogenic temperatures

A technique was developed for the calibration of dynamic pressure transducers at cryogenic temperatures. The calibration system utilizes an 8.9 Newton peak thrust shaker which oscillates a helium-filled bellows to generate a sinusoidal dynamic pressure to calibrate transducers immersed in a cryogenic environment. The system has a dynamic pressure measurement uncertainty of approximately 11% and is capable of producing peak-to-peak dynamic pressure amplitudes of 1.4 kPa over a frequency range of 40 to 100 hertz and a temperature range of 100 to 300 K. It provides an unprecedented capability of both static and dynamic calibration of pressure transducers from ambient to cryogenic temperature.

Gibbens, B. V.↗

Steady viscous flow past a circular cylinder

Viscous flow past a circular cylinder becomes unstable around Reynolds number Re = 40. With a numerical technique based on Newton's method and made possible by the use of a supercomputer, steady (but unstable) solutions have been calculated up to Re = 400. It is found that the wake continues to grow in length approximately linearly with Re. However, in conflict with available asymptotic predictions, the width starts to increase very rapidly around Re = 300. All numerical calculations have been performed on the CDC CYBER 205 at the CDC Service Center in Arden Hills, Minnesota.

Fornberg, B.↗

Solution algorithms for non-linear singularly perturbed optimal control problems

The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.

Ardema, M. D.↗

A Multi-Epoch Timing and Spectral Study of the Ultraluminous X-Ray NGC 5408 X-1 with XMM-Newton

We present results of new XMM-Newton observations of the ultraluminous X-ray source (ULX) NGC 5408 X-1, one of the few ULXs to show quasi-periodic oscillations (QPOs). We detect QPOs in each of four new (approximately equal to 100 ks) pointings, expanding the range of frequencies observed from 10 to 40 mHz. We compare our results with the timing and spectral correlations seen in stellar-mass black hole systems, and find that the qualitative nature of the timing and spectral behavior of NGC 5408 X-1 is similar to systems in the steep power-law state exhibiting Type-C QPOs. However, in order for this analogy to quantitatively hold we must only be seeing the so-called saturated portion of the QPO frequency-photon index (or disk flux) relation. Assuming this to be the case, we place a lower limit on the mass of NGC 5408 X-1 of greater than or equal to 800 solar mass. Alternatively, the QPO frequency is largely independent of the spectral parameters, in which case a close analogy with the Type-C QPOs in stellar system is problematic. Measurement of the source's timing properties over a wider range of energy spectral index is needed to definitively resolve this ambiguity. We searched all the available data for both a broad Fe emission line as well as high-frequency QPO analogs (0.1- 1 Hz), but detected neither. We place upper limits on the equivalent width of any Fe emission feature in the 6-7 keV band and of the amplitude (rms) of a high-frequency QPO analog of approximately equal to 10 eV and approximately equal to 4%, respectively.

Dheeraj, Pasham↗