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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1957

Bodies of Revolution Having Minimum Drag at High Supersonic Airspeeds

Approximate shapes of nonlifting bodies having minimum pressure foredrag at high supersonic airspeeds are calculated. With the aid of Newton's law of resistance, the investigation is carried out for various combinations of the conditions of given body length, base diameter, surface area, and volume. In general, it is found that when body length is fixed, the body has a blunt nose; whereas, when the length is not fixed, the body has a sharp nose. The additional effect of curvature of the flow over the surface is investigated to determine its influence on the shapes for minimum drag. The effect is to increase the bluntness of the shapes in the region of the nose and the curvature in the region downstream of the nose. These shape modifications have, according to calculation, only a slight tendency to reduce drag. Several bodies of revolution of fineness ratios 3 and 5, including the calculated shapes of minimum drag for given length and base diameter and for given base diameter and surface area, were tested at Mach numbers from 2.73 to 6.28. A comparison of theoretical and experimental foredrag coefficients indicates that the calculated minimum-drag bodies are reasonable approximations to the correct shape.

Eggers, A J , Jr↗
NASA NTRS2014

The Soft-X-Ray Emission of Ark 120. XMM-Newton, NuSTAR, and the Importance of Taking the Broad View

We present simultaneous XMM-Newton and NuSTAR observations of the 'bare' Seyfert 1 galaxy, Ark 120, a system in which ionized absorption is absent. The NuSTAR hard-X-ray spectral coverage allows us to constrain different models for the excess soft-X-ray emission. Among phenomenological models, a cutoff power law best explains the soft-X-ray emission. This model likely corresponds to Comptonization of the accretion disc seed UV photons by a population of warm electrons: using Comptonization models, a temperature of approximately 0.3 kiloelectronvolts and an optical depth of approximately 13 are found. If the UV-to-X-ray OPTXAGNF model is applied, the UV fluxes from the XMM-Newton Optical Monitor suggest an intermediate black hole spin. Contrary to several other sources observed by NuSTAR, no high-energy cutoff is detected with a lower limit of 190 kiloelectronvolts.

accretion↗
NASA NTRS1988

Advances in dual algorithms and convex approximation methods

A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.

Smaoui, H.↗
NASA NTRS1979

A general algorithm for the solution of Kepler's equation for elliptic orbits

An efficient algorithm is presented for the solution of Kepler's equation f(E)=E-M-e sin E=0, where e is the eccentricity, M the mean anomaly and E the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics in M, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20,000 pairs of values of e and M show that for single precision, 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision one additional iteration is required.

Ng, E. W.↗
NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗
NASA NTRS1995

Krylov methods for compressible flows

We investigate the application of Krylov methods to compressible flows, and the effect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, approximate factorization (AF) for structured grids and ILU/GMRES for general grids, are considered. Also considered here are Newton-Krylov matrix-free methods that we combined with the use of mixed discretization schemes in the implicitly defined Jacobian and its preconditioner. Numerical experiments that show the performance of our approaches are then presented.

Tidriri, M. D.↗
NASA NTRS2005

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

We have conducted an archival XMM-Newton study of the bright X-ray point sources 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. Indeed, 16 sources in our sample match the criteria we set for a low-state ULX, namely, L(sub X) greater than 10(exp 38 ergs per second) and a spectrum best fit with an absorbed power law. Further, we find evidence for 26 high-state ULXs which are best fit by a combined blackbody and a power law. As in Galactic black hole systems, the spectral indices, GAMMA, of the low-state objects, as well a s the luminosities, tend to be lower than those of the high-state objects. The observed range of blackbody temperatures is 0.1-1 keV with the most luminous systems tending toward the lowest temperatures. We also find a class of object whose properties (luminosity, blackbody temperature, and power law slopes) are very similar to those of galactic stellar mass black holes. In addition, we find a subset of these objects that can be best fit by a Comptonized spectrum similar to that used for Galactic black holes in the very high state, when they are radiating near the Eddington limit.

Winter, Lisa M.↗
NASA NTRS2013

The Suzaku View of Highly Ionized Outflows in AGN: Statistical Detection and Global Absorber Properties - 1

We present the results of a new spectroscopic study of Fe K-band absorption in active galactic nuclei (AGN). Using data obtained from the Suzaku public archive we have performed a statistically driven blind search for Fe XXV Healpha and/or Fe XXVI Lyalpha absorption lines in a large sample of 51 Type 1.0−1.9 AGN. Through extensive Monte Carlo simulations we find that statistically significant absorption is detected at E greater than or approximately equal to 6.7 keV in 20/51 sources at the P(sub MC) greater than or equal tov 95 per cent level, which corresponds to approximately 40 per cent of the total sample. In all cases, individual absorption lines are detected independently and simultaneously amongst the two (or three) available X-ray imaging spectrometer detectors, which confirms the robustness of the line detections. The most frequently observed outflow phenomenology consists of two discrete absorption troughs corresponding to Fe XXV Healpha and Fe XXVI Lyalpha at a common velocity shift. From xstar fitting the mean column density and ionization parameter for the Fe K absorption components are log (N(sub H) per square centimeter)) is approximately equal to 23 and log (Xi/erg centimeter per second) is approximately equal to 4.5, respectively. Measured outflow velocities span a continuous range from less than1500 kilometers per second up to approximately100 000 kilometers per second, with mean and median values of approximately 0.1 c and approximately 0.056 c, respectively. The results of this work are consistent with those recently obtained using XMM-Newton and independently provides strong evidence for the existence of very highly ionized circumnuclear material in a significant fraction of both radio-quiet and radio-loud AGN in the local universe.

Gofford, Jason↗
NASA NTRS2004

Aurora and Non-Auroral X-ray Emissions from Jupiter: A Comparative View

Jovian X-rays can be broadly classified into two categories: (1) auroral emission, which is confined to high-latitudes (approximately greater than 60 deg.) at both polar regions, and (2) dayglow emission, which originates from the sunlit low-latitude (approximately less than 50 deg.) regions of the disk (hereafter called disk emissions). Recent X-ray observations of Jupiter by chandra and XMM-Newton have shown that these two types of X-ray emission from Jupiter have different morphological, temporal, and spectral characteristics. In particular: 1) contrary to the auroral X-rays, which are concentrated in a spot in the north and in a band that runs half-way across the planet in the south, the low-latitude X-ray disk is almost uniform; 2) unlike the approximately 40 plus or minus 20-min periodic oscillations seen in the auroral X-ray emissions, the disk emissions do not show any periodic oscillations; 3) the disk emission is harder and extends to higher energies than the auroral spectrum; and 4) the disk X-ray emission show time variability similar to that seen in solar X-rays. These differences and features imply that the processes producing X-rays are different at these two latitude regions on Jupiter. We will present the details of these and other features that suggest the differences between these two classes of X-ray emissions from Jupiter, and discuss the current scenario of the production mechanism of them.

Bhardwal, Anil↗
NASA NTRS1984

Second-order p-iterative solution of the Lambert/Gauss problem

An algorithm is presented for efficient p-iterative solution of the Lambert/Gauss orbit-determination problem using second-order Newton iteration. The algorithm is based on a universal transformation of Kepler's time-of-flight equation and approximate inverse solutions of this equation for short-way and long-way flight paths. The approximate solutions provide both good starting values for iteration and simplified computation of the second-order term in the iteration formula. Numerical results are presented which indicate that in many cases of practical significance (except those having collinear position vectors) the algorithm produces at least eight significant digits of accuracy with just two or three steps of iteration.

Boltz, F. W.↗
NASA NTRS2000

A High Resolution Spectroscopic Observation of CAL 83 with XMM-Newton/RGS

We present the first high resolution photospheric X-ray spectrum of a Supersoft X-ray Source, the famous CAL 83 in the Large Magellanic Cloud. The spectrum was obtained with the Reflection Grating Spectrometer on XMM-Newton during the Calibration/Performance Verification phase of the observatory. The spectrum covers the range 20-40 A at an approximately constant resolution of 0.05 A, and shows very significant, intricate detail, that is very sensitive to the physical properties of the object. We present the results of an initial investigation of the spectrum, from which we draw the conclusion that the spectral structure is probably dominated by numerous absorption features due to transitions in the Gshells of the mid-2 elements and the M-shell of Fe, in addition to a few strong K-shell features due to CNO.

Paerels, Frits↗
NASA NTRS2014

NuSTAR Observations of Heavily Obscured Quasars at z Is Approximately 0.5

We present NuSTAR hard X-ray observations of three Type 2 quasars at z approx. = 0.4-0.5, optically selected from the Sloan Digital Sky Survey. Although the quasars show evidence for being heavily obscured, Compton-thick systems on the basis of the 2-10 keV to [O(sub III)] luminosity ratio and multiwavelength diagnostics, their X-ray absorbing column densities (N(sub H)) are poorly known. In this analysis, (1) we study X-ray emission at greater than 10 keV, where X-rays from the central black hole are relatively unabsorbed, in order to better constrain N(sub H). (2) We further characterize the physical properties of the sources through broad-band near-UV to mid-IR spectral energy distribution analyses. One of the quasars is detected with NuSTAR at greater than 8 keV with a no-source probability of less than 0.1%, and its X-ray band ratio suggests near Compton-thick absorption with N(sub H) is approximately greater than 5 × 10(exp 23) cm(exp -2). The other two quasars are undetected, and have low X-ray to mid-IR luminosity ratios in both the low-energy (2-10 keV) and high-energy (10-40 keV) X-ray regimes that are consistent with extreme, Compton-thick absorption (N(sub H) is approximately greater than 10(exp 24) cm(exp −2)). We find that for quasars at z is approximately 0.5, NuSTAR provides a significant improvement compared to lower energy (less than 10 keV) Chandra and XMM-Newton observations alone, as higher column densities can now be directly constrained.

quasars↗
NASA NTRS2017

The NuSTAR Serendipitous Survey: The 40-month Catalog and the Properties of the Distant High-Energy X-Ray Source Population

We present the first full catalog and science results for the Nuclear Spectroscopic Telescope Array (NuSTAR) serendipitous survey. The catalog incorporates data taken during the first 40 months of NuSTAR operation, which provide approx. 20 Ms of effective exposure time over 331 fields, with an areal coverage of 13 deg2, and 497 sources detected in total over the 324 keV energy range. There are 276 sources with spectroscopic redshifts and classifications, largely resulting from our extensive campaign of ground-based spectroscopic follow-up. We characterize the overall sample in terms of the X-ray, optical, and infrared source properties. The sample is primarily composed of active galactic nuclei (AGNs), detected over a large range in redshift from z = 0.002 to 3.4 (median of [z] = 0.56), but also includes 16 spectroscopically confirmed Galactic sources. There is a large range in X-ray flux, from log(f_3-24 keV/erg/s/sq cm) approx. -14 to -11, and in rest-frame 10-40 keV luminosity, from log(L10-40 keV/erg/s) approx. 39 to 46, with a median of 44.1. Approximately 79% of the NuSTAR sources have lower-energy (<10 keV) X-ray counterparts from XMM-Newton, Chandra, and Swift XRT. The mid-infrared (MIR) analysis, using WISE all-sky survey data, shows that MIR AGN color selections miss a large fraction of the NuSTAR-selected AGN population, from approx. 15% at the highest luminosities (LX> 10(exp 44) erg/s) to 80 at the lowest luminosities (LX > 10(exp 43) erg/s).

catalogs-galaxies: active ; nuclei↗
NASA NTRS1991

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.↗
NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗
NASA NTRS2015

A Numerical and Experimental Study of Coflow Laminar Diffusion Flames: Effects of Gravity and Inlet Velocity

In this work, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting behavior of laminar coflow methane-air diffusion flames was investigated both computationally and experimentally. A series of flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) was assessed numerically under microgravity and normal gravity conditions with the fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the MC-Smooth vorticity-velocity formulation of the governing equations was employed to describe the reactive gaseous mixture; the soot evolution process was considered as a classical aerosol dynamics problem and was represented by the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computational domain was employed, where the grid on the axisymmetric domain was a nonuniform tensor product mesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind scheme and all other derivatives approximated by centered differences. The resulting set of fully coupled, strongly nonlinear equations was solved simultaneously using a damped, modified Newton's method and a nested Bi-CGSTAB linear algebra solver. Experimentally, the flame shape, size, lift-off height, and soot temperature were determined by flame emission images recorded by a digital camera, and the soot volume fraction was quantified through an absolute light calibration using a thermocouple. For a broad spectrum of flames in microgravity and normal gravity, the computed and measured flame quantities (e.g., temperature profile, flame shape, lift-off height, and soot volume fraction) were first compared to assess the accuracy of the numerical model. After its validity was established, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusion flames was explored further by examining quantities derived from the computational results.

microgravity↗
NASA NTRS1980

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗
NASA NTRS1989

Iterative procedures for space shuttle main engine performance models

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented.

Santi, L. Michael↗