Rational approximations to the incomplete elliptic integrals of the first and second kinds.
Rational approximations to incomplete elliptic integral of first and second kinds derived by main diagonal Pade approximations
APPROXIMATION METHOD↗
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Approximations of distant retrograde orbits for mission design
Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.
Distant Retrograde Orbits (DRO)↗
An optimal guidance approximation theory.
Optimal guidance approximation synthesis via perturbation theory including linear, quadratic and higher order feedback approximation method
GUIDANCE AND CONTROL↗
Charge transfer in the classical binary- encounter approximation.
Charge transfer prediction by classical binary- encounter theory approximation and quantum mechanical approximation
CHARGE TRANSFER↗
Peaking approximations in atomic scattering problems
Born approximation and wave functions, and peaking approximation for Coulomb Born matrix shown to misrepresent excitation and ionization cross sections in atomic scattering problems
Kyle, H. L.↗
Application of Rosseland approximation and solution based on series expansion of the emission power to radiation problems.
Emission-power series expansion solution and Rosseland approximation applied to radiation problems, discussing errors introduced by approximate methods
Hartnett, J. P.↗
On a peaking approximation in scattering theory.
Cross sections computed for excitation and ionization of atoms and ions by electrons, using peaking approximation to evaluate Coulomb-Born matrix approximation
Kyle, H. L.↗
Validity of approximations used in mesonic atom calculations.
The Deser-Goldberger-Baumann-Thirring (DGBT) formula [a = 1/4B(ΔE 1S /|E 1S |)] and other various approximations commonly used to extract meson-nucleus scattering lengths from energy-level measurements on mesonic atoms are studied by means of a model calculation and are shown to be inadequate for most of the π − -mesonic atoms commonly considered. A simple empirical formula is obtained in place of the DGBT formula for the π − -mesonic atoms of the light nuclei. The DGBT formula is also examined for the case of the K − −He 4 atom and is found to be a good approximation.
Ryoichi Seki↗
Evaluation of Jacobian determinants by Monte Carlo methods: Application to the quasiclassical approximation in molecular scattering
A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.
Labudde, R. A.↗
Comparison of exact and approximate evaluations of the single-scattering integral in nucleon-deuteron elastic scattering
The exact nucleon-deuteron elastic single scattering integral was calculated numerically in order to evaluate errors in sticking factor approximations. A similar analysis made by using S wave separable potentials concluded that errors for these approximations were negligible except near backward angles where they were found to be about 10 percent.
Wilson, J. W.↗
New half-range differential approximation for spherically-symmetric radiative transfer.
A new half-range differential approximation for radiative transfer with spherical symmetry is presented. The development is motivated by the various failures of existing differential approximations in determining emissive-power distributions and heat transfer for concentric-spheres problems. The new approach represents a modification of the four-moment double spherical-harmonics method, to which it reduces in the planar limit. The difference is effected by relocating the discontinuity of the assumed directional distribution of radiation intensity. The shift takes the discontinuity from precisely on the division between radially inward and radially outward, to just within the radially-outward directional half range. The method is tested on a variety of concentric spheres problems with and without internal heat sources, reproducing all the important features of the exact results.
Moreno, J. B.↗
The closure approximation in the hierarchy equations.
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.
Adomian, G.↗
Approximate estimation for systems with quantized data.
Estimation of the state of a nonlinear discrete-time system using quantized data is considered. An exact solution for the maximum likelihood estimate is expressed as the solution of a nonlinear two-point boundary-value problem. Approximate recursive solutions for both the maximum likelihood and the conditional-mean estimates are obtained. The results of Monte-Carlo simulations are presented in which the performance of these two algorithms is compared with that of a Kalman filter in which the quantization error is approximated by white noise.-
Clements, K. A.↗
Evaluation of Jacobian determinants by Monte Carlo methods - Application to the quasiclassical approximation in molecular scattering.
Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.
La Budde, R. A.↗
Methods and approximations for the computation of transmission profiles in the v4 band of methane in the atmosphere of Jupiter.
This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.
Taylor, F. W.↗
Approximate thermochemical tables for some C-H and C-H-O species
Approximate thermochemical tables are presented for some C-H and C-H-O species and for some ionized species, supplementing the JANAF Thermochemical Tables for application to finite-chemical-kinetics calculations. The approximate tables were prepared by interpolation and extrapolation of limited available data, especially by interpolations over chemical families of species. Original estimations have been smoothed by use of a modification for the CDC-6600 computer of the Lewis Research Center PACl Program which was originally prepared for the IBM-7094 computer Summary graphs for various families show reasonably consistent curvefit values, anchored by properties of existing species in the JANAF tables.
Bahn, G. S.↗
A high frequency correction to the Kirchhoff approximation, with application to rough surface EM wave scattering
A high frequency correction to the Kirchhoff approximation is developed for application to rough surface scattering. An approximate solution to the magnetic field integral equation for perfect conductivity and plane wave excitation yields a perturbed surface current expressed as a linear function of the second derivatives of surface height. The corrected surface current vector is substituted into the far field Stratton-Chu integral and average backscattered powers for the four polarization combinations are computed on the assumption that the surface is describable as a stationary Gaussian random process. The strength of this scattering solution is that it can account for height curvature correlation without requiring small height and slope.
Jackson, F. C.↗
Use of the Glauber approximation in atomic collisions - A progress report.
Recent progress in the use of the Glauber (1970) theory for estimating atomic collision cross sections is reviewed. It appears that the Glauber approximation is reliable for electron-hydrogen elastic scattering and excitation at incident energies exceeding 30 eV. For more complicated atomic collisions, the usefulness of the Glauber approximation has not yet been significantly tested.
Gerjuoy, E.↗