Photo-ionization of the hydrogen molecule.
H molecule photoionization, using one center wave function with polarized orbital approximation to obtain oscillator strengths in 700 to 300 angstrom range
Khare, S. P.↗
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.
Rocket sonde measurements of ozone in the upper atmosphere
Rocket sonde measurement of ozone content in the mesosphere and stratosphere is accomplished by an in situ determination of the ozone mixing rates as a function of altitude from approximately 65 km to 20 km. A chemiluminescent detector is used as an ozone sensor.
Hilsenrath, E.↗
Approximate calculation of cumulative probability from a moment-generating function
Numerical method for calculating cumulative distribution of positive random variable
Helstrom, C. W.↗
Approximate calculation of cumulative probability from a moment-generating function.
Cumulative probability distribution of positive random variable from moment generating function, exemplifying exponential and Poisson functions
Helstrom, C. W.↗
On dimensional line radiative transfer
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.
Harstad, K. G.↗
One-dimensional line radiative transfer.
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.
Harstad, K. G.↗
Synthesis of oscillating adaptive feedback systems
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.
Smay, J. W.↗
The applicability of special subject groups for assessing passenger reaction to flight environments
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.
Jacobson, I. D.↗
Systematics of heavy ion enhancements in solar flares
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.
Price, P. B.↗
Application of the comparison principle to analysis of nonlinear systems
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.
Gunderson, R. W.↗
A characterization of transionospheric fading communication channel
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.
Liu, C. H.↗
Digital processing of satellite imagery application to jungle areas of Peru
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.
Pomalaza, J. C.↗
Measurement of the turbulence in a gaseous rocket combustion chamber
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.
Tou, P. P.↗
A study of the geographic coverage properties of a satellite borne Doppler lidar wind velocity measuring system
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.
Pate, T. H.↗
Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three dimension
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.
Anderson, B. H.↗
Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three-dimension
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.
Anderson, B. H.↗
Space radiation interaction mechanisms in materials
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.
Wilson, J. W.↗
Parameter estimation for the Euler-Bernoulli-beam
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.
Graif, E.↗