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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Gatewood, B. E.↗
NASA NTRS1971

Mathematical analysis of a Vuilleumier refrigerator.

A comprehensive analysis of the Vuilleumier refrigerator was conducted. This analysis includes the effects of nonisothermal gas heat addition and rejection, hot and cold regenerator inefficiencies, conduction losses, and gas leakage losses. A computer program was written which solves the equations resulting from the analysis. The program calculates internal pressures, temperatures, and gas flow rates as functions of refrigerator crank angle, as well as overall refrigerator cooling load and power input. Comparisons between the program results and available data show good agreement, with a marked improvement over the predictions of the ideal model.

Sherman, A.↗
NASA NTRS1975

Wavefront-error evaluation by mathematical analysis of experimental Foucault-test data

The diffraction theory of the Foucault test provides an integral formula expressing the complex amplitude and irradiance distribution in the Foucault pattern of a test mirror (lens) as a function of wavefront error. Recent literature presents methods of inverting this formula to express wavefront error in terms of irradiance in the Foucault pattern. The present paper describes a study in which the inversion formulation was applied to photometric Foucault-test measurements on a nearly diffraction-limited mirror to determine wavefront errors for direct comparison with ones determined from scatter-plate interferometer measurements. The results affirm the practicability of the Foucault test for quantitative wavefront analysis of very small errors, and they reveal the fallacy of the prevalent belief that the test is limited to qualitative use only. Implications of the results with regard to optical testing and the potential use of the Foucault test for wavefront analysis in orbital space telescopes are discussed.

Wilson, R. G.↗
NASA NTRS1976

A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.

Mitchell, D. G.↗
NASA NTRS1982

Mathematical analysis of the Photovoltage Decay (PVD) method for minority carrier lifetime measurements

When the diffusion length of minority carriers becomes comparable with or larger than the thickness of a p-n junction solar cell, the characteristic decay of the photon-generated voltage results from a mixture of contributions with different time constants. The minority carrier recombination lifetime tau and the time constant l(2)/D, where l is essentially the thickness of the cell and D the minority carrier diffusion length, determine the signal as a function of time. It is shown that for ordinary solar cells (n(+)-p junctions), particularly when the diffusion length L of the minority carriers is larger than the cell thickness l, the excess carrier density decays according to exp (-t/tau-pi(2)Dt/4l(2)), tau being the lifetime. Therefore, tau can be readily determined by the photovoltage decay method once D and L are known.

Vonroos, O. H.↗
NASA NTRS1982

Mathematical analysis for radiometric calorimetry of a radiating sphere

Equations are derived from which the temperature dependence of both the specific heat and the thermal diffusivity of a spherical sample of material can be calculated from observations of the time dependence of the surface temperature and the time-rate of energy loss from the sample as it cools. The derivation takes into account the nonuniformity of the interior temperature field of the sample, and the resulting equations can be applied not only to radiative cooling, but also to any other cooling mechanism that does not violate the assumed spherical symmetry. The analysis excludes change of phase, but it does take thermal expansion into account. To permit the making of estimates necessary for the design of radiative cooling experiments, a universal temperature-time cooling curve is derived for the post-transient cooling regime of a radiating sphere of any size with arbitrary, but constant, thermal parameters.

Schmid, L. A.↗
NASA NTRS1984

Mathematical analysis

Simple continuum models used in the design, analysis, and control of large space structures are examined. Particular emphasis is placed on boundary value problems associated with the Load Correction Method and control problems involving partial differential equations for the large space structure models. Partial differential equations will be used to model a large space structure, base the design of an optimal controller on this model, approximate the resulting optimal control model, and compare the results with data from other methods.

Donaldson, J. A.↗
NASA NTRS1985

Mathematical analysis study for radar data processing and enhancement. Part 1: Radar data analysis

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altiude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This is in two parts. This is part 1, an analysis of radar data.

James, R.↗
NASA NTRS1985

Mathematical analysis study for radar data processing and enchancement. Part 2: Modeling of propagation path errors

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altitude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This report is in two parts. This is part 2, a discussion of the modeling of propagation path errors.

James, R.↗
NASA NTRS1995

Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

Tidriri, M. D.↗