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At least 937 records · Page 52

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NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗

NASA NTRS1976

Evaluation of the 'mean frequency' technique

The 'mean frequency' technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the 'mean frequency' lies near certain integers.

Gaddy, E. M.↗

NASA NTRS1976

Rotating stratified flow over finite isolated topography

Inviscid, steady, stratified rotating flow over a finite, isolated topographic feature is critically analyzed. The formulation is based on approximating the horizontal momentum by the geostrophic momentum. A boundary value problem governs the perturbation pressure field. The solution is an anticyclonic, topographically-bound vortex whose characteristics are independent of the upstream velocity but do depend on stratification, rotation, and the nature of the topography. The vortex is baroclinic in the vicinity of the mountain but barotropic in the far field. The velocity field is a combination of the bound vortex and an upstream velocity interacting with the perturbation pressure field. The effects of stratification, upstream velocity and the nature of the topography are investigated, and fluid trajectories are plotted.

Merkine, L.-O.↗

NASA NTRS1976

On optimal soft-decision demodulation

A necessary condition is derived for optimal J-ary coherent demodulation of M-ary (M greater than 2) signals. Optimality is defined as maximality of the symmetric cutoff rate of the resulting discrete memoryless channel. Using a counterexample, it is shown that the condition derived is generally not sufficient for optimality. This condition is employed as the basis for an iterative optimization method to find the optimal demodulator decision regions from an initial 'good guess'. In general, these regions are found to be bounded by hyperplanes in likelihood space; the corresponding regions in signal space are found to have hyperplane asymptotes for the important case of additive white Gaussian noise. Some examples are presented, showing that the regions in signal space bounded by these asymptotic hyperplanes define demodulator decision regions that are virtually optimal.

Lee, L.-N.↗

NASA NTRS1976

Optimal strategies in the neighborhood of a collision course

We consider a simple differential game between pursuer P and evader E in the neighborhood of a nominal collision course. The payoff is the terminal lateral miss-distance. The control of each player is his acceleration normal to his velocity vector, and both players' controls are bounded. Saddlepoint strategies are deduced for three combinations of the acceleration bounds and are shown to be related to the sign of the derivative of the orientation of the line of sight (L.O.S.).

Gutman, S.↗

NASA NTRS1976

Feature combinations and the Bhattacharyya criterion

A procedure for calculating a kxn rank k matrix B for data compression using the Bhattacharyya bound on the probability of error and an iterative construction using Householder transformation was developed. Two sets of remotely sensed agricultural data are used to demonstrate the application of the procedure. The results of the applications gave some indication of the extent to which the Bhattacharyya bound on the probability of error is affected by such transformations for multivariate normal populations.

Decell, H. P., Jr.↗

NASA NTRS1976

Preentry communications study. Outer planets atmospheric entry probe

A pre-entry communications study is presented for a relay link between a Jupiter entry probe and a spacecraft in hyperbolic orbit. Two generic communications links of interest are described: a pre-entry link to a spun spacecraft antenna, and a pre-entry link to a despun spacecraft antenna. The propagation environment of Jupiter is defined. Although this is one of the least well known features of Jupiter, enough information exists to reasonably establish bounds on the performance of a communications link. Within these bounds, optimal carrier frequencies are defined. The next step is to identify optimal relative geometries between the probe and the spacecraft. Optimal trajectories are established for both spun and despun spacecraft antennas. Given the optimal carrier frequencies, and the optimal trajectories, the data carrying capacities of the pre-entry links are defined. The impact of incorporating pre-entry communications into a basic post entry probe is then assessed. This assessment covers the disciplines of thermal control, power source, mass properties and design layout. A conceptual design is developed of an electronically despun antenna for use on a Pioneer class of spacecraft.

Hinrichs, C. A.↗

NASA NTRS1977

Modeling error analysis of stationary linear discrete-time filters

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

Patel, R.↗

NASA NTRS1977

Two photon excitation of atomic oxygen

A standard perturbation expansion in the atom-radiation field interaction is used to calculate the two photon excitation cross section for 1s(2) 2s(2) 2p(4) p3 to 1s(2) 2s(2) 2p(3) (s4) 3p p3 transition in atomic oxygen. The summation over bound and continuum intermediate states is handled by solving the equivalent inhomogeneous differential equation. Exact summation results differ by a factor of 2 from a rough estimate obtained by limiting the intermediate state summation to one bound state. Higher order electron correlation effects are also examined.

Pindzola, M. S.↗

NASA NTRS1977

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above.

Klimas, A. J.↗

NASA NTRS1977

A new algorithm for the integration of exponential and logarithmic functions

An algorithm for symbolic integration of functions built up from the rational functions by repeatedly applying either the exponential or logarithm functions is discussed. This algorithm does not require polynomial factorization nor partial fraction decomposition and requires solutions of linear systems with only a small number of unknowns. It is proven that if this algorithm is applied to rational functions over the integers, a computing time bound for the algorithm can be obtained which is a polynomial in a bound on the integer length of the coefficients, and in the degrees of the numerator and denominator of the rational function involved.

Rothstein, M.↗

NASA NTRS1976

Excitation of He/+/ by electron impact

A five-state close-coupling approximation, in which the exact He(+) bound states 1s, 2s, and 2p are retained along with 3s and 3p pseudostates, is employed to calculate 1s-to-2s and 1s-to-2p excitation of He(+) by electron impact in the energy range 61.2-136 eV. The inclusion of pseudostates is to allow in some average manner for the infinity of bound and continuum states that are neglected in a truncated close-coupling expansion. The pseudostates are constructed orthonormal to lower states of the same symmetry, and they have the same threshold energy of 0.2 Ry. The inclusion of pseudostates reduces considerably the excitation cross section, yielding better agreement with measurements.

Henry, R. J. W.↗

NASA NTRS1976

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

NASA NTRS1977

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.

Johannesson, R.↗

NASA NTRS1977

Diagrammatic perturbation theory - N2 X1 Sigma/plus/g

The diagrammatic many-body perturbation theory is used to calculate the correlation energy of the nitrogen molecule in its electronic ground state. Using the algebraic approximation, the energy is evaluated through third order, including all many-body effects. (2/1) Pade approximants and variational upper bounds are constructed. For one of the perturbation expansions considered, the (2/1) Pade approximant leads to the recovery of 79.5 percent of the empirical correlation energy, while the variational upper bound recovers 72.0 percent. Three-body effects are examined in some detail. The relationships with previous work on N2 are discussed.

Wilson, S.↗

NASA NTRS1977

The stereoisomeric composition of phytanyl chains in lipids of Dead Sea sediments

Lipid extracts from five recent Dead Sea sediments were analyzed for isoprenoid compounds and the following were isolated: free and phospholipid-bound di-O-phytanylglycerol, free phytanol and free and esterified phytanic acid. The phytanyl groups of the diether and the free phytanol were oxidized to the corresponding phytanic acid; the stereoisomeric composition of the derived phytanic acids as well as of the ester-bound phytanic acid was determined by open-tubular gas-liquid chromatography of the corresponding methyl esters on butanediolsuccinate polyester. Only the 3R, 7R, 11R-isomer of phytanic acid was detected in each of the phytanate samples, indicating that these phytanyl chains in the Dead Sea sediments are most likely derived from extremely halophilic bacteria rather than from phytol of chlorophyll origin. These findings also provide further evidence that the mixtures of RRR and SRR-phytanic acids previously isolated from organic-rich shales were most likely derived from the phytyl chain in chlorophyll.

Anderson, R.↗

NASA NTRS1977

Prediction of large negative shaded-side spacecraft potentials

A calculation by Knott, for the floating potential of a spherically symmetric synchronous-altitude satellite in eclipse, was adapted to provide simple calculations of upper bounds on negative potentials which may be achieved by electrically isolated shaded surfaces on spacecraft in sunlight. Large (approximately 60 percent) increases in predicted negative shaded-side potentials are obtained. To investigate effective potential barrier or angular momentum selection effects due to the presence of less negative sunlit-side or adjacent surface potentials, these expressions were replaced by the ion random current, which is a lower bound for convex surfaces when such effects become very severe. Further large increases in predicted negative potentials were obtained, amounting to a doubling in some cases.

Prokopenko, S. M. L.↗

NASA NTRS1977

Performance and emissions of a catalytic reactor with propane, diesel, and Jet A fuels

Tests were made to determine the performance and emissions of a catalytic reactor operated with propane, No. 2 diesel, and Jet A fuels. A 12-cm diameter and 16-cm long catalytic reactor using a proprietary noble metal catalyst was operated at an inlet temperature of 800 K, a pressure of 300,000 Pa and reference velocities of 10 to 15 m/s. No significant differences between the performance of the three fuels were observed when 98.5 percent purity propane was used. The combustion efficiency for 99.8-percent purity propane tested later was significantly lower, however. The diesel fuel contained 135 ppm of bound nitrogen and consequently produced the highest NOx emissions of the three fuels. As much as 85 percent of the bound nitrogen was converted to NOx. Steady-state emissions goals based on half the most stringent proposed automotive standards were met when the reactor was operated at an adiabatic combustion temperature higher than 1350 K with all fuels except the 99.8-percent purity propane. With that fuel, a minimum temperature of 1480 K was required.

Anderson, D. N.↗