Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Function approximation”

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 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Equilibrium wave spectrum and sea state bias in satellite altimetry

For a well-developed sea at equilibrium with a constant wind, the energy-containing range of the wavenumber spectrum for wind-generated gravity waves is approximated by a generalized power law involving the angular spread function and mu, interpreted as a fractal codimension of a small surface patch. Dependence of mu on the wave age is estimated, and the 'Phillips constant', beta, along with the low-wavenumber boundary, k0, of the inertial subrange are analyzed on the basis of the wave action and energy conservation principles. The resulting expressions are employed to evaluate various non-Gaussian statistics of a weakly nonlinear sea surface, which determine the sea state bias in satellite altimetry. The locally accelerated decay of the spectral density function in a high-wavenumber dissipation subrange is pointed out as an important factor of wave dynamics and the geometrical optics treatment of the sea state bias. The analysis is carried out in the approximation of a unidirectional wave field and confined to the case of a well-developed sea.

Glazman, Roman E.↗
NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗
NASA NTRS1972

Light scattering by cirrus cloud layers.

The properties of the reflection, transmission, and absorption of the cirrus cloud layers are calculated under the assumption that the ice crystals in cirrus clouds may be approximated long circular cylinders randomly oriented in space. The phase function, the single scattering albedo, and the extinction cross section are obtained on the basis of Liou's (1972) calculations of light scattering by ice clouds in the visible and infrared. A modified two-stream approximation for radiative transfer is developed and is used to evaluate the radiative properties of the cirrus cloud layers.

Liou, K.-N.↗
NASA NTRS2006

The Hard X-ray 20-40 keV AGN Luminosity Function

We have compiled a complete, significance limited extragalactic sample based on approximately 25,000 deg(sup 2) to a limiting flux of 3 x 10(exp -11) ergs per square centimeter per second. (approximately 7,000 deg(sup 2)) to a flux limit of 10(exp -11) ergs per square centimeter per second)) in the 20 - 40 keV band with INTEGRAL. We have constructed a detailed exposure map to compensate for effects of non-uniform exposure. The flux-number relation is best described by a power-law with a slope of alpha = 1.66 plus or minus 0.11. The integration of the cumulative flux per unit area leads to f(sub 20-40 keV) = 2.6 x 10(exp -10) ergs per square centimeter per second per sr(sup -1) which is about 1% of the known 20-40 keV X-ray background. We present the first luminosity function of AGN in the 20-40 keV energy range, based on 68 extragalactic objects detected by the imager IBIS/ISGRI on-board INTEGRAL. The luminosity function shows a smoothly connected two power-law form, with an index of gamma (sub 1) = 0.9 below, and gamma (sub 2) = 2.2 above the turn-over luminosity of L(sub *), = 4.6 x 10(sup 43) ergs per second. The emissivity of all INTEGRAL AGNs per unit volume is W(sub 20-40keV)(greater than 10(sup 41) ergs per second) = 2.8 x 10(sup 38) ergs per second h(sup 3)(sub 70) Mpc(sup -3). These results are consistent with those derived in the 2-20keV energy band and do not show a significant contribution by Compton-thick objects. Because the sample used in this study is truly local (z(raised bar) = 0.022)), only limited conclusions can be drawn for the evolution of AGNs in this energy band. But the objects explaining the peak in the cosmic X-ray background are likely to be either low luminosity AGN (L(sub x) less than 10(sup 41) ergs per second) or of other type, such as intermediate mass black holes, clusters, and star forming regions.

Beckmann, V.↗
NASA NTRS1994

A hydrodynamic approach to cosmology: The mixed dark matter cosmological scenario

We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h equivalent to (sub 0)/100 km/s Mpc(exp -1) = 0.5, OMEGA(sub C) = 0.3, and OMEGA(sub B) = 0.06, with amplitude of the perturbation spectrum fixed by the Cosmic Background Explorer Satellite (COBE) Dark Matter Radiation (DMR) measurements (Smoot et al. 1992) being sigma (sub 8) = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1) h(exp -1) Mpc, respectively, the two small boxes providing good resolution but little valid information due to absence of large-scale power. We use 128(exp 3) approximate 10(exp 6.3) baryonic cells, 128(exp .3) cold dark matter particles, and 2 x 128(exp 3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H(+), He, He(+), He(++), e(-)) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be y Bar = (5.4 + or - 2.7) x 10(exp -7) below currently attainable observations, with a rms fluctuation of approximately delta bar y = (0.6 + or - 3.0) x 10(exp -7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximate 0.3) than in the standard (OMEGA = 1, sigma sub 8 = 0.67) cold dark matter (CDM) model (z approximate 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma sub 8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of M(sub B) = 10(exp 9.5) solar mass with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h(exp - 1) Mpc) containing 3 x 200(exp 3) = 10(exp 7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the (COBE) normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 + or - 8 km/s at 1/h separation, lower than that of the DCM model normalized to COBE, but still significant higher than observations (Davis & Peebles 1983). A plausible velocity bias b(sub v) = 0.8 + or - 0.1 on this scale will reduce but not remove the discrepancy. The velocity auto-correlat ion function has a coherence length of 40/h Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDB). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma(sub B), but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same sigma(sub 8) and is still probably unsatisfactory with regard to several critical tests.

Cen, Renyue↗
NASA NTRS1984

Analytical characterization of AOTV perigee aerothermodynamic regime

In preliminary design studies of AOTV (Aeroassisted Orbital Transfer Vehicle) configurations, it is desirable to have a simple analytical method for characterizing the aerothermodynamic regime at skip trajectory perigee as a function of vehicle L/D and m/CDA (ballistic coefficient). The present study derives an approximate perigee solution from the generalized equations of motion. For a prescribed entry velocity vector, the solution determines a Zeta function (proportional to density divided by m/CDA) at perigee as a parametric function of the exit velocity vector and (constant) L/D. The perigee Zeta function then determines perigee density (or altitude) as a parametric function of m/CDA. The solution allows the following classic aerothermodynamic parameters to be determined at perigee as parametric functions of m/CDA, L/D, and the exit velocity vector: Reynolds Number (viscous effects), Mach Number (compressibility effects), Knudsen Number (rarefaction effects), sphere and disk bow shock standoff distance, Damkohler Number (relaxation effects), viscous correlation parameter (viscid-inviscid interactions), and Stanton Number (convective heat transfer). Results of the analysis are given for low L/D and mid L/D AOTV configurations on return from geosynchronous and L5 orbits. It is concluded the method successfully provides preliminary estimates of the aerothermodynamic parameters through the use of simple algebraic equations and plots.

Desautel, D.↗
NASA NTRS1985

A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

Rodriguez, G.↗
NASA NTRS1979

Modal propagation angles in a cylindrical duct with flow and their relation to sound radiation

The angles of propagation for the wave front making up a duct mode are presented with the Mach number in the duct. Approximate equations are derived to provide simple utilitarian expressions. These expressions are valid only near the outer wall which is the most important region since the bulk of the acoustic intensity is located there. Exact solutions using Hankel functions are given in an appendix. These data corroborate the approximate solution accuracy near the outer wall. The axial propagation angle is used to infer information about the far-field radiation pattern. The resultant axial angle of propagation in the duct is shown to agree exactly with the peak of the principal lobe to far-field radiation obtained from formal radiation calculations when the Mach number is uniform everywhere. The obtained solution is extended to cover the case of different Mach numbers inside and outside the duct for which exact calculations have not been available for engine inlet configurations.

Rice, E. J.↗
NASA NTRS1992

A hydrodynamic treatment of the cold dark matter cosmological scenario

The evolution of structure in a postrecombination Friedmann-Robertson-Walker universe containing both gaseous baryons and cold dark matter (CDM) is studied by means of an Eulerian code coupled with a standard particle-mesh code. Ionization state and radiative opacity are calculated in detail, and the hydrodynamic simulations make it possible to compute properties of gas distribution on scales larger than three cell sizes. The model yields a soft X-ray background consistent with the latest cosmic nucleosynthesis values, and can accurately reproduce the galaxy-galaxy two-point correlation. The rate of galaxy formation peaks at a relatively late epoch. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum peaks in the vicinity of m(b) = 10 exp 9.2 solar masses with a reasonable fit to the Schecter luminosity function if the baryon mass to blue light ratio is approximately 4. Overall, the simulations provide strong support for the CMD scenario. Of particular interest is that, while the baryons are not biased on scales greater than 1/h Mpc, the galaxies are, and that the 'galaxies' have a correlation function of the required slope and the correct amplitude.

Cen, Renyue↗
NASA NTRS1985

Electron impact excitation of H2 - Rydberg band systems and the benchmark dissociative cross section for H Lyman-alpha

The cross sections sigma R 1 (2p) for excitation of H Ly-alpha emission produced by electron impact on H2 is reexamined. A more accurate estimate for sigma R 1 (2p) is obtained based on Born approximation estimates of the H2 Rydberg system cross sections using measured relative excitation functions. The obtained value is (8.18 + or -1.2) x 10 to the -18th sq cm at 100 eV, a factor of 0.69 below the value universally applied to cross section measurements over the past decade. Cross sections for the H2 Rydberg systems fixed in magnitude by the Born approximation have also been obtained using experimentally determined excitation functions. Accurate analytic expressions for these cross sections allow the direct calculation of rate coefficients.

Shemansky, D. E.↗
NASA NTRS1963

Application of Dorodnitsyn's Integral Method to Nonequilibrium Flows over Pointed Bodies

Dorodnitsyn's integral method is used to obtain an approximate solution to the supersonic nonequilibrium flow over pointed bodies with attached shock waves. The partial differential equations governing the flow are converted to an approximate set of ordinary equations, which are solved by numerical integration starting at the body tip. Detailed analytical and numerical results for the first approximation are presented, considering the vibrational relaxation of a diatomic gas over a wedge or cone. It is shown that the first approximation yields: (1) The exact flow-variable gradients at the wedge tip (2) Expressions for the flow-variable gradients at the cone tip which are in agreement with extrapolations of characteristics calculations (3) A good approximate algebraic solution for frozen or equilibrium conical flow (4) An approximate expression for the nonequilibrium-flow stream function which affords a means of obtaining variations across the shock layer of the temperature and vibrational energy. Numerical results for both the wedge and cone compare favorably with identical cases computed by the method of characteristics.

NONEQUILIBRIUM FLOW↗
NASA NTRS1972

Reflection and transmission of acoustic waves from a moving layer

The refraction of acoustic waves by a moving medium layer is theoretically treated and the expressions for reflection and transmission coefficients are determined. The moving medium layer velocity is assumed to have a space dependence in one direction. A partitioning of the moving medium layer into constant-velocity sublayers is introduced and the number of sublayers is allowed to increase until the reflection and transmission coefficients converage to their respective values. Numerical results for several sublayer approximations of Poiseuille's flow are presented as functions of the moving layer velocity for several angles of incidence of the acoustic wave. The degenerate case of single constant-velocity layer is also treated, both theoretically and by a numerical analysis.

Steinmetz, G. G.↗
NASA NTRS1972

Lunar soil properties and soil mechanics. Flow in porous media under rarefied gas conditions. Research phase: Fluid conductivity of lunar surface materials

Theoretical and experimental research on fluid conductivity of lunar surface materials is summarized. Theoretical methods were developed for the analysis of transitional and free-molecular flows, and for analysis of lunar permeability probe data in general. Experimental studies of rarefied flows under conditions of a large pressure gradient show flows in the continuum regime to be responsible for the largest portion of the pressure drop between source and sink for one dimensional flow, provided the entrance Knudsen number is sufficiently small. The concept of local similarity leading to a universal nondimensional function of Knudsen number was shown to have approximate validity; flows in all regimes may be described in terms of an area fraction and a single length parameter. Synthetic porous media prepared from glass beads exhibited flow behavior similar in many regards to that of a natural sandstone; studies using artificial stones with known pore configurations may lead to new insight concerning the structure of natural materials. The experimental method involving the use of segmented specimens of large permeability is shown to be fruitful.

Hurlbut, F. C.↗
NASA NTRS1972

Dynamics of stratified liquids in the presence of space charge.

The dispersion characteristics of small signal electrohydrodynamic space charge and polarization waves in continuously and discretely stratified liquids are developed. The liquids, modeled as incompressible, inviscid, and perfectly insulating have distributions of mass density, charge density, permittivity, and electric field. A general set of relations for perturbation field and flow variables defined for a prototype layer are used to describe the dynamics of many superposed planar layers. It is shown that the general relations can be used to represent systems of coupled layers which approximate continuous distributions by a series of step functions. Specific examples of weak gradient and exponential distributions are presented showing that the solution found directly from the distributed theory is approached by the system of coupled layers, if the limit is taken in which the number of layers become large while each layer thickness approaches zero.

Zahn, M.↗
NASA NTRS1972

On propagation of long waves in curved ducts.

A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.

Rostafinski, W.↗
NASA NTRS1974

Long-duration life tests of slip ring capsule assemblies for inertial guidance platforms

Eight slip ring capsules, each having 80 or 100 circuits, were operated for time periods ranging from 14,300 hours to 24,700 hours. The test mode simulated the motion of gimbal axes of the Saturn inertial guidance the platform in an organic free nitrogen environment. Computer-compiled noise data (approximately 45,000 recordings) were graphed as a function of test time and position within the capsules and as extreme probability distributions. Greater than ninety-nine percent of the noise measurements for the capsules with sufficient lubrication were less than 10 milliohms. Capsules with glass dielectrics did not perform significantly differently than those with filled epoxy dielectrics. The initial wear mode of prow formation was followed by rider wear. After 10 to the 8th power wipes, ring wear depth did not exceed the surface finish and the radial rider wear depth was less than 13 microns.

Cole, S. R.↗
NASA NTRS1973

Doppler broadening effect on collision cross section functions - Deconvolution of the thermal averaging

The surprising feature of the Doppler problem in threshold determination is the 'amplification effect' of the target's thermal energy spread. The small thermal energy spread of the target molecules results in a large dispersion in relative kinetic energy. The Doppler broadening effect in connection with thermal energy beam experiments is discussed, and a procedure is recommended for the deconvolution of molecular scattering cross-section functions whose dominant dependence upon relative velocity is approximately that of the standard low-energy form.

Bernstein, R. B.↗