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At least 811 records · Page 45

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NASA NTRS1972

Charge-impact excitation of the highly excited hydrogen atoms in the dipole form of the semiclassical impact-parameter and Born approximations.

Derivation of expressions for the excitation cross section in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula given by Menzel (1968, 1969) for the asymptotic expansion of the oscillator strength of the hydrogen-like atoms. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical with the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards (1970). Comparisons are made between the Bethe coefficients obtained by the author and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, where n is the principal quantum number of the excited state.

Omidvar, K.↗

NASA NTRS1972

Current to a moving cylindrical electrostatic probe

The current collection characteristics of a moving cylindrical Langmuir probe are evaluated for a range of probe speeds and potentials which are applicable to earth and planetary measurements. The current expressions derived include the cases of the general accelerated current, sheath area limited current, orbital motion limited current, and retarded current. For the orbital motion limited current, a simple algebraic expression is obtained which includes and generalizes the Mott-Smith and Langmuir expressions for both a stationary probe and a rapidly moving probe. For a rapidly moving probe a single formula adequately represents both the accelerated and the retarded current.

Hoegy, W. R.↗

NASA NTRS1972

Advanced study of video signal processing in low signal to noise environments

A nonlinear analysis of a multifilter phase-lockloop (MPLL) by using the method of harmonic balance is presented. The particular MPLL considered has a low-pass filter and a band-pass filter in parallel. An analytic expression for the relationship between the input signal phase deviation and the phase error is determined for sinusoidal FM in the absence of noise. The expression is used to determine bounds on the proper operating region for the MPLL and to investigate the jump phenomenon previously observed. From these results the proper modulation index, modulating frequency, etc. used for the design of a MPLL are determined. Data for the loop unlock boundary obtained from the theoretical expression are compared to data obtained from analog computer simulations of the MPLL.

Carden, F.↗

NASA NTRS1973

Degenerate R-S perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

Hirschfelder, J. O.↗

NASA NTRS1972

Thermodynamic considerations for the design of a sonic-boom reducing powerplant.

Third-order analytical expressions are obtained for the lift and wave-drag coefficients of a two-dimensional wing. The expressions are used to demonstrate the possibility of boomless lifting configuration designs when the cross-section area of the stream tube is reduced. The reduction is obtained by processing the captured airstream in such a manner that the stream tube area is smaller at the exit than at the entrance. Calculations by these expressions are shown to be in good agreement with exact results obtained from compressive flow tables. It is also shown that three-dimensional wing configurations of this design give the maximum thermodynamic effect when a propulsive power plant is employed for the reduction of the captured-stream area. Thermodynamic guidelines are given for power plant designs to be used for this purpose.

Galanis, N.↗

NASA NTRS1973

Structure in the nonlinear saturation spectrum of parametric instabilities.

The nonlinear saturation spectrum of the decay instability is obtained in the limit of small spontaneous emission, for comparable ion and electron temperatures, from numerical solutions of a kinetic equation based on an accurate expression for the nonlinearity. The spectral energy occupies several pairs of isolated saucer-shaped regions in wave-vector space. The regions increase in thickness, angular diameter, and number as the pump power is increased. The theory thus predicts the generation of waves propagating in directions which can differ substantially from the direction of the pump field. Ionospheric observations confirm this prediction; they were difficult to reconcile with the predictions of previous theories based on an approximated expression for the nonlinearity. The present work also corrects the results of previous one-dimensional theories that used an accurate expression for the nonlinearity and predicted 'spectral lines' in the limit of vanishing spontaneous emission.

Fejer, J. A.↗

NASA NTRS1974

An improved exceedance theory for combined random stresses

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Lester, H. C.↗

NASA NTRS1974

The diffusive idealization of charged particle transport in random magnetic fields

The transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is presented. The same coefficient of diffusion is obtained by three methods. Two corrections must be added to the expression in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections. The well known divergence of the coefficient of diffusion, which is implied by the quasilinear analysis of pitch angle scattering, does not occur if the scattering rate is finite at 90 deg pitch angle. This effect is illustrated by formulas which give the coefficient of diffusion when the quasilinear expression is perturbed by a variable amount of isotropic scattering.

Earl, J. A.↗

NASA NTRS1973

Radial thickness variation in impact crater ejecta - Implications for lunar basin deposits

An expression is proposed for radial thickness variations in lunar impact crater ejecta. The expression was inferred from available cratering data and semi-empirical calculations for approximate modeling of variations in ejecta thickness with the increasing range of lunar craters. A table of predicted stratigraphic sections for the Apollo Landing sites is included. The predictions were made by using this expression. The results suggest that the pre-Nubium crustal material at upland Apollo sites lies at depths of above 280 up to 1940 m.

Mcgetchin, T. R.↗

NASA NTRS1973

Current to a moving cylindrical electrostatic probe

The current collection characteristics of a moving cylindrical Langmuir probe are evaluated for a range of probe speeds and potentials which are applicable to earth and planetary measurements. The current expressions derived include the cases of the general accelerated current, sheath area limited current, orbital motion limited current, and retarded current. For the orbital motion limited current, a simple algebric expression is obtained which includes and generalizes the Mott-Smith and Langmuir expressions for both a stationary probe and a rapidly moving probe. For a rapidly moving probe, a single formula adequately represents both the accelerated and the retarded current.

Hoegy, W. R.↗

NASA NTRS1974

Degenerate RS perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Hirschfelder, J. O.↗

NASA NTRS1974

Derivatives of eigenvalues and eigenvectors for a general matrix

Expressions are obtained for the derivatives of the eigenvalues and eigenvectors which are expressions of only one left-hand and one right-hand eigenvector. The approach described makes use of a Choleski decomposition or some other decomposition method. The method may be extended to find any order of derivative of the eigenvalue and eigenvector. The expressions obtained for finding the derivatives of eigenvalues and eigenvectors for nonself-adjoint systems may be applied to self-adjoint systems.

Rudisill, C. S.↗

NASA NTRS1973

Reentry guidance for Space Shuttle

An explicit guidance scheme is outlined which provides the appropriate energy management in order for the shuttle orbiter to reach any location within the required footprint. Considering the orbiter as entering the earth's atmosphere, expressions for the downrange, crossrange, and the time of the termination of the entry phase as functions of the control variables are developed. Performing an order-of-magnitude analysis of the terms in these expressions, only dominant terms are retained. Analytical expressions for the elements of the sensitivity matrix which represents the partial derivatives of the desired range with respect to control variables are formulated. Using the Gauss-Jordan inversion technique, the required change in guidance commands as a function of the deviations in the downrange and crossrange are explicitly computed.

Causey, W.↗

NASA NTRS1974

Evaluation of approximate relations for Delta /Q/ using a numerical solution of the Boltzmann equation

Data obtained from a numerical solution of the Boltzmann equation for shock-wave structure are used to test the accuracy of accepted approximate expressions for the two moments of the collision integral Delta (Q) for general intermolecular potentials in systems with a large translational nonequilibrium. The accuracy of the numerical scheme is established by comparison of the numerical results with exact expressions in the case of Maxwell molecules. They are then used in the case of hard-sphere molecules, which are the furthest-removed inverse power potential from the Maxwell molecule; and the accuracy of the approximate expressions in this domain is gauged. A number of approximate solutions are judged in this manner, and the general advantages of the numerical approach in itself are considered.

Nathenson, M.↗

NASA NTRS1973

Pitch paper pilot revisited

Two methods are described for predicting the handling qualities of an aircraft in pitch. Both methods are based on minimizing a pilot rating expression with respect to free pilot parameters. In one case the pilot rating expression was developed from a set of moving base simulation data. In the other case, the pilot rating expression was developed from a set of fixed base simulation data. In both cases pilot rating is primarily a function of pitch attitude and pitch rate; however, in the moving base case, the pilot rating is more sensitive to pitch rate than in the fixed base case. For each method, predicted pilot ratings and performance measures agree well with the measured data corresponding to that case. Both methods are used to predict pilot ratings for a set of flight test configurations and the results of the two methods agree to within one half a rating unit. The predicted ratings in both cases correlate well with the actual pilot ratings from the flight tests.

Arnold, J. D.↗

NASA NTRS1975

Growth of surface and corner cracks in beta-processed and mill-annealed Ti-6Al-4V

Empirical stress-intensity expressions were developed to relate the growth of cracks from corner flaws to the growth of cracks from surface flaws. An experimental program using beta-processed Ti-6Al-4V verified these expressions for stress ratios, R greater than or equal to 0. An empirical crack growth-rate expression which included stress-ratio and stress-level effects was also developed. Cracks grew approximately 10 percent faster in transverse-grain material than in longitudinal-grain material and at approximately the same rate in longitudinal-grain mill-annealed Ti-6Al-4V. Specimens having surface and corner cracks and made of longitudinal-grain, beta-processed material were tested with block loads, and increasing the stresses in a block did not significantly change the crack growth rates. Truncation of the basic ascending stress sequence within a block caused more rapid crack growth, whereas both the descending and low-to-high stress sequences slowed crack growth.

Bell, P. D.↗

NASA NTRS1975

Mutual impedance of nonplanar-skew sinusoidal dipoles

The mutual impedance expressions for parallel dipoles in terms of sine-integrals and cosine-integrals have been published by King (1957). The investigation reported provides analogous expressions for nonparallel dipoles. The expressions presented are most useful when the monopoles are close together. The theory of moment methods shows an approach for employing the mutual impedance of filamentary sinusoidal dipoles to calculate the impedance and scattering properties of straight and bent wires with small but finite diameter.

Richmond, J. H.↗

NASA NTRS1975

Two-electron bond-orbital model, 1

Harrison's one-electron bond-orbital model of tetrahedrally coordinated solids was generalized to a two-electron model, using an extension of the method of Falicov and Harris for treating the hydrogen molecule. The six eigenvalues and eigenstates of the two-electron anion-cation Hamiltonian entering this theory can be found exactly general. The two-electron formalism is shown to provide a useful basis for calculating both non-magnetic and magnetic properties of semiconductors in perturbation theory. As an example of the former, expressions for the electric susceptibility and the dielectric constant were calculated. As an example of the latter, new expressions for the nuclear exchanges and pseudo-dipolar coefficients were calculated. A simple theoretical relationship between the dielectric constant and the exchange coefficient was also found in the limit of no correlation. These expressions were quantitatively evaluated in the limit of no correlation for twenty semiconductors.

Huang, C.↗