Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear 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 235 records · Page 13

Ignition characteristics of the nickel-based alloy UNS N07001 in pressurized oxygen

The development of ignition and combustion in pressurized oxygen atmospheres was studied for the nickel-based alloy UNS N07001. Ignition of the alloy was achieved by heating the top surface of a cylindrical specimen with a continuous-wave CO2 laser. Two heating procedures were used. In the first, laser power was adjusted to maintain an approximately linear increase in surface temperature. In the second, laser power was periodically increased until autoheating (self-heating) was established. It was found that the alloy would autoheat to combustion from temperatures below the solidus temperature. In addition, the alloy had a tendency to develop combustion zones (hot spots) at high oxygen pressures when the incremental (step) heating test mode was used. Unique points on the temperature-time curves that describe certain events are defined and the temperatures at which these events occur are given for the oxygen pressure range of 1.72 to 13.8 MPa (250 to 2000 psia).

Bransford, J. W.↗

Prediction of the He distribution at the lunar surface

Data on the contents of He and TiO2 and the maturity index, Is/FeO have been compiled, for all lunar soils for which measurements have been reported, in order to quantitatively asses the relationship between these parameters. The He content in lunar soils correlates approximately linearly with the product (Is/FeO)(TiO2 wt pct) over the range of measured values. The advantage of such a trend is the assistance it may provide in mapping the lunar surface for He and other solar-wind volatiles in a quantitative manner. A remote means of assessing Is/FeO in addition to TiO2 will be required.

Jordan, J. L.↗

Cloud area determination from AVIRIS data using water vapor channels near 1 micron

Fractional cloud area is derived from spectral images collected by the Airborne Visible-IR Imaging Spectrometer (AVIRIS). The derivation is made by ratioing radiances near the 0.94- and the 1.14-microns water vapor band centers against those in the intermediate atmospheric window regions. The derivation makes use of the facts that (1) the reflectances of most ground targets vary approximately linearly with wavelength in the 0.94- and the 1.14-micron water vapor band absorption regions, and (2) the peak absorptions of the water vapor band over cloudy areas are smaller than those over nearby clear surface areas because of the rapidly decreasing atmospheric water vapor concentration with height. The band ratioing technique effectively discriminates among clouds and surface areas having similar reflectance values.

Gao, Bo-Gai↗

Short wavelength striations on expanding plasma clouds

The present evaluation of current understanding of the growth and evolution of less-than-1 ion gyroradius 'flute modes' on a plasma as it expands across and ambient magnetic field notes that the mechanism by which the instability is generated, and its approximate linear theory (encompassing nonlocal, finite-beta, and collisional effects), have reached a satisfactory degree of development. AMPTE Ba releases have been the bases of most of the observational studies. Substantial progress is also noted in the development of a nonlinear mode-coupling theory which can resolve remaining differences between theory and observation.

Winske, D.↗

Calculation of turbulent flow in complex geometries with a second-moment closure model

A full Reynolds stress turbulence model is applied to calculate the flow in various channels with complex cross-section. The model is shown to be more robust and to produce more consistent results than algebraic stress models. The relationship between various versions of the latter is provided. It is shown that differential or algebraic stress models derived from a direct application of a popular linear approximation for the pressure-strain terms in the Reynolds stress equations will always underpredict the secondary motion, and hence the accompanying distortion of other flow properties. A simple approximation which leads to better predictions is presented and related to previous practice.

Demuren, A. O.↗

Shuffling foot points and magnetohydrodynamic discontinuities in the solar wind

ISEE three-field and plasma data are used to investigate the frequency of occurrence of isolated, large-amplitude rotational (RD) and tangential (TD) discontinuities in different types of solar wind flow. It is found that there are relatively more TDs in solar wind that originates in closed field regions and is ejected into interplanetary space by coronal transients than in the solar wind that originates in open field regions. The speed of the wind from open field regions is approximately linearly related to the number of RDs per hour; such a relation does not exist for the wind associated with coronal mass ejections. These results are consistent with the hypothesis that the convection-driven shuffling of magnetic foot points at the solar surface leads to TDs, magnetic reconnection, and heating of the corona on closed field lines, while in the open field regions the disturbances created by the shuffling are carried off by waves which contribute to the acceleration of the solar wind.

Neugebauer, M.↗

A model of regional primary production for use with coarse resolution satellite data

A model of crop primary production, which was originally developed to relate the amount of absorbed photosynthetically active radiation (APAR) to net production in field studies, is discussed in the context of coarse resolution regional remote sensing of primary production. The model depends on an approximately linear relationship between APAR and the normalized difference vegetation index. A more comprehensive form of the conventional model is shown to be necessary when different physiological types of plants or heterogeneous vegetation types occur within the study area. The predicted variable in the new model is total assimilation (net production plus respiration) rather than net production alone or harvest yield.

Prince, S. D.↗

An efficient method for estimating neighboring steady-state numerical solutions to the Euler equations

The paper concentrates on a linear approximation method for predicting the changes occurring in steady-state numerical solutions of the Euler equations as a consequence of small changes in the independent variables which control the problem. The importance of proper boundary-condition treatment and other issues concerning the problem are covered along with the importance of proper algorithm selection for a fully supersonic inviscid flow. The method is applied to a subsonic nozzle involving variation of the pressure on the outflow boundary and to a supersonic inlet involving variation of the inflow Mach number. In the subsonic test case, the comparisons between the predicted and conventional numerical solutions are shown to be good, while in the supersonic test case, the agreement between the approximation method and conventional numerical solution starts out well but rapidly degenerates at some point in the flowfield as the perturbation of the boundary conditions is increased.

Taylor, Arthur C., III↗

Procedure for computer-controlled milling of accurate surfaces of revolution for millimeter and far-infrared mirrors

A simple method for milling accurate off-axis parabolic mirrors with a computer-controlled milling machine is discussed. For machines with a built-in circle-cutting routine, an exact paraboloid can be milled with few computer commands and without the use of the spherical or linear approximations. The proposed method can be adapted easily to cut off-axis sections of elliptical or spherical mirrors.

Emmons, Louisa↗

Dynamics And Control Of Flexible Manipulator

Nonlinear equations solved with linear approximations applicable during small increments of time. Report presents theoretical study of selected aspects of dynamics and control of robotic manipulator that includes multiple flexible links. Addresses problem of control primarily from perspective of inverse-dynamics problem.

Gawronski, Wodek K.↗

Orbit-determination performance of Doppler data for interplanetary cruise trajectories. Part 1: Error analysis methodology

An error covariance analysis methodology is used to investigate different weighting schemes for two-way (coherent) Doppler data in the presence of transmission-media and observing-platform calibration errors. The analysis focuses on orbit-determination performance in the interplanetary cruise phase of deep-space missions. Analytical models for the Doppler observable and for transmission-media and observing-platform calibration errors are presented, drawn primarily from previous work. Previously published analytical models were improved upon by the following: (1) considering the effects of errors in the calibration of radio signal propagation through the troposphere and ionosphere as well as station-location errors; (2) modelling the spacecraft state transition matrix using a more accurate piecewise-linear approximation to represent the evolution of the spacecraft trajectory; and (3) incorporating Doppler data weighting functions that are functions of elevation angle, which reduce the sensitivity of the estimated spacecraft trajectory to troposphere and ionosphere calibration errors. The analysis is motivated by the need to develop suitable weighting functions for two-way Doppler data acquired at 8.4 GHz (X-band) and 32 GHz (Ka-band). This weighting is likely to be different from that in the weighting functions currently in use; the current functions were constructed originally for use with 2.3 GHz (S-band) Doppler data, which are affected much more strongly by the ionosphere than are the higher frequency data.

Ulvestad, J. S.↗

Accurate upwind-monotone (nonoscillatory) methods for conservation laws

The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.

Huynh, Hung T.↗

Statistical linearization for multi-input/multi-output nonlinearities

Formulas are derived for the computation of the random input-describing functions for MIMO nonlinearities; these straightforward and rigorous derivations are based on the optimal mean square linear approximation. The computations involve evaluations of multiple integrals. It is shown that, for certain classes of nonlinearities, multiple-integral evaluations are obviated and the computations are significantly simplified.

Lin, Ching-An↗

Linear evolution of current sheets in sheared force-free magnetic fields with discontinuous connectivity

Thin current sheets arising in tenuous, magnetized solar coronal plasmas may constitute an important mechanism for energy buildups and subsequent energy releases; they could arise from the continuous-and-random motion of magnetic footprints associated with photospheric velocity fields. A model is presented for study of the quasi-static evolution of current sheets due to shearing of the footpoints, in a highly idealized geometry that incorporates an abrupt jump in field-line connectivity. The model highlights that formation of thin current layers and allows large shearing motions prior to violation of the linear approximation. Excess energy comparable to that released by solar flares can be stored in a sheared field.

Wolfson, Richard↗

Sea surface mean square slope from Ku-band backscatter data

A surface mean-square-slope parameter analysis is conducted for 14-GHz airborne radar altimeter near-nadir, quasi-specular backscatter data, which in raw form obtained by least-squares fitting of an optical scattering model to the return waveform show an approximately linear dependence over the 7-15 m/sec wind speed range. Slope data are used to draw inferences on the structure of the high-wavenumber portion of the spectrum. A directionally-integrated model height spectrum that encompasses wind speed-dependent k exp -5/2 and classical Phillips k exp -3 power laws subranges in the range of gravity waves is supported by the data.

Jackson, F. C.↗

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

Asteroid orbital error analysis: Theory and application

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Muinonen, K.↗

Incomplete fuzzy data processing systems using artificial neural network

In this paper, the implementation of a fuzzy data processing system using an artificial neural network (ANN) is discussed. The binary representation of fuzzy data is assumed, where the universe of discourse is decartelized into n equal intervals. The value of a membership function is represented by a binary number. It is proposed that incomplete fuzzy data processing be performed in two stages. The first stage performs the 'retrieval' of incomplete fuzzy data, and the second stage performs the desired operation on the retrieval data. The method of incomplete fuzzy data retrieval is proposed based on the linear approximation of missing values of the membership function. The ANN implementation of the proposed system is presented. The system was computationally verified and showed a relatively small total error.

Patyra, Marek J.↗