Search NASA⌕ Search

SEARCH · Search NASA

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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Approximate optimal atmospheric entry trajectories

Reentry glider approximate optimal atmospheric entry trajectories for maximizing function of terminal velocity, altitude, flight path and heading angle under terminal nonlinear constraints

Speyer, J. L.↗
NASA NTRS1971

Analytical methods for performance evaluation of nonlinear filters.

In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.

Bejczy, A. K.↗
NASA NTRS1973

Analysis of low energy electrons

Simultaneous observations of low energy electrons in the plasma sheet and in the auroral zone were analyzed. Data from the MIT plasma experiment on the OGO-3 satellite and from the Lockheed experiment on the OV1-18 satellite were processed and compared. The OV1-18 carried thirteen magnetic electron spectrometers designed to measure the intensity, angular, and energy distributions of the auroral electrons and protons in the energy range below 50 keV. Two computer programs were developed for reduction of the OV1-18 data. One program computed the various plasma properties at one second intervals as a function of Universal Time and pitch angle; the other program produced survey plots showing the outputs of the various detectors on the satellite as a function of time on a scale of approximately 100 seconds per cm. The OV1-18 data exhibit the high degree of variability associated with substorm controlled phenomena.

Sharp, R. D.↗
NASA NTRS1974

Thermal regime and temperature stresses in bodies during thermoradiational heating

An approach is developed to the application of the perturbation method for the solution of problems with essential external nonlinearities, based on identification in the boundary condition of a small nonlinear complex which is considered a perturbing function. The solutions obtained in the first approximation with error of 1 to 2% in calculating the unsteady temperature fields are then used to determine the temperature stresses and deformations in solid bodies of classical form.

Chistopyanova, N. V.↗
NASA NTRS1973

Semiprecision calculations of electron-hydrogen resonances

Results of a calculation of the lowest (1 S) resonance below the first excitation threshold in electron-hydrogen scattering. This calculation is based on a precision Hylleraas calculation of the resonant wave function, combined with various reasonable physically motivated approximations for the nonresonant continuum. These approximations are basically the exchange- and polarized-orbital approximations. The values obtained, together with previous results obtained for the two higher (3 P and 1 D) resonances, are compared with the previous most accurate calculations, and some differences are noted.

Bhatia, A. K.↗
NASA NTRS1973

The muscle spindle as a feedback element in muscle control

The muscle spindle, the feedback element in the myotatic (stretch) reflex, is a major contributor to muscular control. Therefore, an accurate description of behavior of the muscle spindle during active contraction of the muscle, as well as during passive stretch, is essential to the understanding of muscle control. Animal experiments were performed in order to obtain the data necessary to model the muscle spindle. Spectral density functions were used to identify a linear approximation of the two types of nerve endings from the spindle. A model reference adaptive control system was used on a hybrid computer to optimize the anatomically defined lumped parameter estimate of the spindle. The derived nonlinear model accurately predicts the behavior of the muscle spindle both during active discharge and during its silent period. This model is used to determine the mechanism employed to control muscle movement.

Andrews, L. T.↗
NASA NTRS1975

Multiple scattered radiation emerging from continental haze layers. 1: Radiance, polarization, and neutral points

The complete radiation field is calculated for scattering layers of various optical thicknesses. Results obtained for Rayleigh and haze scattering are compared. Calculated radiances show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are approximately 0.1% for a continental haze phase function. The polarization of reflected and transmitted radiation is given for various optical thicknesses, solar zenith angles, and surface albedos. Two types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points arise from zero polarization that occurs at scattering angles of 0 deg and 180 deg. For Rayleigh phase functions, the position of these points varies with the optical thickness of the scattering layer. Non-Rayleigh neutral points are associated with the zeros of polarization which occur between the end points of the single scattering curve, and are found over a wide range of azimuthal angles.

Kattawar, G. W.↗
NASA NTRS1976

Functional polymeric microspheres based on 2-hydroxyethyl methacrylate for immunochemical studies

Co gamma irradiation of 2-hydroxyethyl methacrylate in the presence or in the absence of other acrylic monomers was found to constitute an effective technique for the synthesis of hydrophilic functional microspheres in the size range of approximately 0.3 to 3 microns in diameter. The effect of monomer concentration, steric stabilization, and electrostatic interaction on the particle size was investigated. Experimental conditions were determined to obtain desired particle sizes of relatively narrow distribution. It was shown that particles may be formed without intermediate micelles, i.e., by homogeneous nucleation, and the rate of particle formation is affected primarily by the rate of particle coalescence in the initial stages of the reaction. When covalently bound to antibodies these microspheres were successfully used to label murine and human lymphocytes.

Rembaum, A.↗
NASA NTRS1976

Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions. Blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, non-rectangular elements and discontinuous approximation of shock waves are also discussed.

Hafez, M. M.↗
NASA NTRS1977

Acoustic performance of inlet multiple-pure-tone suppressors installed on NASA Quiet Engine 'C'

The purpose of the experimental program reported herein was to define the length of multiple pure tone (MPT) treatment required to reasonably suppress the MPT's produced by a supersonic tip speed fan and also determine what other suppression, broadband, and blade passing frequency (BPF), might be accomplished. The experimental results are presented in terms of both far-field and duct acoustic data. Front quadrant sound power level reduction in the far field is shown to agree with duct measurements over the range of treatment lengths. Detailed one-third octave and narrow band spectra at the maximum forward noise angle are presented. Some detailed analyses of one-third-octave band amplitudes are shown as a function of far-field angle. An approximate spinning mode duct propagation analysis is then introduced which predicts the acoustic suppression by the treatment on the multiple pure tones.

Bloomer, H. E.↗
NASA NTRS1977

Hybrid methods are helpful

Multiple scattering problems in a plane layer often permit the convenient use of different methods joined together. Sample numerical results to illustrate this point refer to X- and Y-functions, asymptotic fitting, the small-loss approximations, polarization in high orders, and photon path distribution.

Vandehulst, H. C.↗
NASA NTRS1978

Preliminary design of composite wings for buckling, strength and displacement constraints

An unstiffened panel buckling constraint for balanced, symmetric laminated composites is included on the global design level in a mathematical programming structural optimization procedure for designing wing structures. Constraints are introduced by penalty functions, and Newton's method based on approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. Constraint approximations used during the optimization process contribute to the computational efficiency of the procedure. A criterion is developed that identifies the appropriate conservative form of the constraint approximations that are used with the optimization procedure. Minimum-mass design results are obtained for a multispar high-aspect-ratio wing subjected to material strength, minimum-gage, displacement, panel buckling and twist constraints. The material systems considered for the examples are all graphite-epoxy, graphite-epoxy with boron-epoxy spar caps, and all aluminum. The composite material designs are shown to have an advantage over the aluminum designs since they can often satisfy additional constraints with only small mass increases.

Starnes, J. H., Jr.↗
NASA NTRS1978

Development of sputtering process to deposit stoichiometric zirconia coatings for the inside wall of regeneratively cooled rocket thrust chambers

Thermal barrier coatings of yttria stabilized zirconia and zirconia-ceria mixtures were deposited by RF reactive sputtering. Coatings were 1-2 mils thick, and were deposited on copper cylinders intended to simulate the inner wall of a regeneratively cooled thrust chamber. Coating stoichiometry and adherence were investigated as functions of deposition parameters. Modest deposition rates (approximately 0.15 mil/hr) and subambient sustrate temperatures (-80 C) resulted in nearly stoichiometric coatings which remained adherent through thermal cycles between -196 and 400 C. Coatings deposited at higher rates or substrates temperatures exhibited greater oxygen deficiences, while coatings deposited at lower temperatures were not adherent. Substrate bias resulted in structural changes in the coating and high krypton contents; no clear effect on stoichiometry was observed.

Busch, R.↗
NASA NTRS1978

Lunar crater volumes - Interpretation by models of impact cratering and upper crustal structure

Lunar crater volumes can be divided by size into two general classes with distinctly different functional dependence on diameter. Craters smaller than approximately 12 km in diameter are morphologically simple and increase in volume as the cube of the diameter, while craters larger than about 20 km are complex and increase in volume at a significantly lower rate implying shallowing. Ejecta and interior volumes are not identical and their ratio, Schroeters Ratio (SR), increases from about 0.5 for simple craters to about 1.5 for complex craters. The excess of ejecta volume causing the increase, can be accounted for by a discontinuity in lunar crust porosity at 1.5-2 km depth. The diameter range of significant increase in SR corresponds with the diameter range of transition from simple to complex crater morphology. This observation, combined with theoretical rebound calculation, indicates control of the transition diameter by the porosity structure of the upper crust.

Croft, S. K.↗