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Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
A synthesis theory is developed which allows system design to proceed from practical specifications on system command and/or disturbance response to a design which is very nearly optimal in terms of feedback sensor noise effects. The approach taken is to replace the nonlinear element by a mean square error minimizing approximation (dual-input describing function), and then use linear frequency domain synthesis techniques subject to additional constraints imposed by the limit cycle and the approximator. Synthesis techniques are also developed for a similar system using an externally excited oscillating signal with the above approach. The results remove the design of the systems considered from the realm of simulation and experimentation, permitting true synthesis and the optimization that accompanies it.
The following conclusions were reached on passenger responses: (1) Within acceptable limits, the crew/flight attendants do not appear to be able to predict passenger responses. (2) There exists a relationship between passenger and subject overall responses. (3) Finally, a strong relationship exists between a suitably weighted running and overall subjective response. The recommended weighting function W(I) is approximately equal to I to the 0.75 power, indicating that the latter part of a flight is given more importance in a subject's overall comfort evaluation than the beginning of the flight.
Using Lexan and glass detectors, the composition of solar particles with atomic number 2 or greater was determined as a function of energy from approximately 0.2 to 50 MeV/nucleon in four flares of quite different intensity and during a time when the sun was nearly quiet. Fe is nearly completely stripped. The enhancement factor increases with atomic number at a given energy but decreases with energy. Heavy element enhancements are detectable at higher energies in stronger flares. They occurred in ancient as well as in present-day flares. We have observed Li and Be in one flare. Incomplete ionization, preferential leakage of heavy ions, energy loss by ionization, and nuclear reactions appear to be involved in solar particle production.
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Using a multiple-scatter propagation theory, the characteristics of the transionospheric satellite-earth communication links are related to the parameters of the ionosphere. General equations for the frequency correlation functions are derived. Some approximate solutions are obtained and numerical examples are given. Also discussed are the degree of coherence and potential applications of the procedure to characterize the intense fading channel.
The author has identified the following significant results. The use of clustering methods permits the development of relatively fast classification algorithms that could be implemented in an inexpensive computer system with limited amount of memory. Analysis of CCTs using these techniques can provide a great deal of detail permitting the use of the maximum resolution of LANDSAT imagery. Potential cases were detected in which the use of other techniques for classification using a Gaussian approximation for the distribution functions can be used with advantage. For jungle areas, channels 5 and 7 can provide enough information to delineate drainage patterns, swamp and wet areas, and make a reasonable broad classification of forest types.
The intensity of turbulence and the Lagrangian correlation coefficient in a gaseous hydrogen (GH2)-gaseous oxygen (GOX) rocket combustion chamber are studied. A helium tracer gas was injected at an upstream point on the combustion chamber centerline. Samples collected downstream were analyzed for the spreading of the tracer gas concentration. Using Taylor's turbulent diffusion theory and Gosman's numerical method, turbulence parameters were found. In order to evaluate turbulence field inhomogeneity in the axial direction, Taylor's theory was extended. An exponential function was used to approximate the Lagrangian correlation coefficient. It was found that turbulence intensity varies from 15% near the injector to 4% at the nozzle entrance, and that the Lagrangian coefficient rapidly decreases when the dispersion time difference increases.
Geographic coverage frequency and geographic shot density for a satellite borne Doppler lidar wind velocity measuring system are measured. The equations of motion of the light path on the ground were derived and a computer program devised to compute shot density and coverage frequency by latitude-longitude sections. The equations for the coverage boundaries were derived and a computer program developed to plot these boundaries, thus making it possible, after an application of a map coloring algorithm, to actually see the areas of multiple coverage. A theoretical cross-swath shot density function that gives close approximations in certain cases was also derived. This information should aid in the design of an efficient data-processing system for the Doppler lidar.
A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.
A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.
Models of charged-particle impact under conditions typical of the space environment are reported, with a focus on impact excitation and nuclear reactions, especially for heavy ions. Impact excitation is studied by using a global model for electronic excitation based on formal relations through the classical dielectric function to derive an approximation related to the local plasma (electron density distribution) within the atoms and molecules; and corrections to the model resulting from the nonfluid nature of this plasma are discussed. Nuclear reactions are studied by reducing quantum-mechanical treatment of this general N-body problem to an equivalent two-body problem that is solvable, and by comparing the results with experimental data. The equations for heavy-charged-particle transport are derived and solution techniques demonstrated. Finally, these methods of analysis are applied to study the change in the electrical properties of a GaAs semiconductor for photovoltaic applications; proton damage to GaAs crystals is found to arise from stable replacement defects and to be nonannealable, in contrast to electron-induced damage.
An approximation involving cubic spline functions for parameter estimation problems in the Euler-Bernoulli-beam equation (phrased as an optimization problem with respect to the parameters) is described and convergence is proved. The resulting algorithm was implemented and several of the test examples are documented. It is observed that the use of penalty terms in the cost functional can improve the rate of convergence.
This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.
Using a single-scattering approximation, equations for the scattering attenuation coefficients of P-body and S-body waves are derived. The results are discussed in the light of the energy-renormalization approaches of Wu (1980, 1982) and Sato (1982) to seismic wave scattering. Practical methods for calculating the scattering attenuation coefficients for various earth models are emphasized. The conversions of P-waves to S-waves and S-waves to P-waves are included in the theory. The earth models are assumed to be randomly inhomogeneous, with their properties known only through their average-wavenumber power spectra. The power spectra are approximated with piecewise constant functions, each segment of which contributes to the net frequency-dependent scattering attenuation coefficient. The smallest and largest wavenumbers of a segment can be plotted along with the wavevectors of the incident and scattered waves on a wavenumber diagram. This diagram gives a geometric interpretation for the frequency behavior associated with each spectral segment, including a transition peak that is due entirely to the wavenumber limits of the segment. For regions of the earth where the inhomogeneity spectra are concentrated in a band of wavenumbers, it should be possible to observe such a peak in the apparent attenuation of seismic waves. Both the frequency and distance limits on the accuracy of the theoretical results are given.
A scheme to clean cometary digital images from offending background-star trails, and this technique has been applied to a pair of deep Kitt Peak 4-m plates of comet P/Encke, taken in October 1980. Simultaneous and subsequent digital spectra have been obtained at Lick Observatory. The non-polluted coma images show a strong asymmetric sunward-oriented fan/jet, and an extended and rounder (mostly gaseous) main coma, out to approximately 100,000 km radius. The stellar-trail point-spread function has a narrow width (sigma approximately 0.6 arcsec), so that spatial resolution better than approximately 300 km is achieved at the comet. The photometric gradient near the nucleus is very steep, strongly suggesting an icy-grain component which evaporates quickly (at radii equal to or less than 500 km) in the sunlight. Further from the nucleus, the profile becomes shallower, bluer, and more gas dominated. The effect of solar radiation pressure on C2, CN, and other molecules is probably responsible for the rounding of the outer, fainter isophotes. The source of the molecules is likely to be larger than the nucleus itself, and a substantial fraction may originate in the jet. The technique described here may also be applicable in surface photometry of galaxies, in cases where the heavy image pollution by foreground stars is present.
The spectral domain computations for slotline guide wavelength and characteristic impedance provide the basic parameters that are need to calculate the radiation pattern of an Linearly Tapered Slot Antenna (LTSA) by using the half-plane Green's function and a stepped approximation to the LTSA structure. However, the spectral domain computations are somewhat time consuming and not suitable for computer aided design application. Therefore, the results of several computation were fitted by formulas that are readily evaluated on a calculator or computer. Antenna measurements were continued, and an attempt was made to predict the truncation effect by three different methods.