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NASA NTRS1983

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

Ito, K.↗

NASA NTRS1983

Partial and robust linearization by feedback

It is argued that if the nonlinearities in a system are mild, and the controller is sufficiently stabilizing, the inaccuracies of a linear model, which is often taken to be sufficient for a controller design, can be safely neglected. For systems with severe nonlinearity a linearizing technique is described, based on the change of state coordinates and nonlinear feedback; in the total context of a stable feedback design the linearization technique is considered robust. Furthermore, attention is paid to partial linearization using the same transformations. It is found that there always exist maximally linearizing transformations which are not necessarily unique.

Krener, A. J.↗

NASA NTRS1985

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

Weatherford, C. A.↗

NASA NTRS1985

Performance of a normalized energy metric without jammer state information for an FH/MFSK system in worst case partial band jamming

For a frequency-hopped noncoherent MFSK communication system without jammer state information (JSI) in a worst case partial band jamming environment, it is well known that the use of a conventional unquantized metric results in very poor performance. In this paper, a 'normalized' unquantized energy metric is suggested for such a system. It is shown that with this metric, one can save 2-3 dB in required signal energy over the system with hard decision metric without JSI for the same desired performance. When this very robust metric is compared to the conventional unquantized energy metric with JSI, the loss in required signal energy is shown to be small. Thus, the use of this normalized metric provides performance comparable to systems for which JSI is known. Cutoff rate and bit error rate with dual-k coding are used for the performance measures.

Lee, P. J.↗

NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗

NASA NTRS1986

Measurement of partial pressures in vacuum technology and vacuum physics

It is pointed out that the measurement of gaseous pressures of less than 0.0001 torr is based on the ionization of gas atoms and molecules due to collisions with electrons. The particle density is determined in place of the pressure. The ionization cross sections for molecules of various gases are discussed. It is found that the true pressure in a vacuum system cannot be determined with certainty if it is unknown which gas is present. Effects of partial pressure determination on the condition of the vacuum system are discussed together with ion sources, systems of separation, and ion detection.

Huber, W. K.↗

NASA NTRS1986

Determination of solid mass fraction in partially frozen hydrocarbon fuels

Filtration procedures alone are insufficient to determine the amounts of crystalline solid in a partially frozen hydrocarbon distillate fraction. This is due to the nature of the solidification process by which a large amount of liquid becomes entrapped within an interconnected crystalline structure. A technique has been developed to supplement filtration methods with an independent determination of the amount of liquid in the precipitate thereby revealing the actual value of mass percent crystalline solid, %S. A non-crystallizing dye is injected into the fuel and used as a tracer during the filtration. The relative concentrations of the dye in the filtrate and precipitate fractions is subsequently detected by a spectrophotometric comparison. The filtration apparatus was assembled so that the temperature of the sample is recorded immediately above the filter. Also, a second method of calculation has been established which allows significant reduction in test time while retaining acceptable accuracy of results. Data have been obtained for eight different kerosene range hydrocarbon fuels.

Cotterell, E. M.↗

NASA NTRS1986

Partial melting of amphibolite to trondhjemite near Ykutat, Alaska

At Nunatak Fiord, 55 km NE of Yakutat, Alaska, a uniform layer of Cretaceous metabasalt approximately 3 km thick was metamorphosed to amphibolite facies and locally partially melted to trondhjemite pegmatite. Results of the rare earth element analysis performed on the amphibolite and the trondhjemite pegmatite are discussed.

Barker, F.↗

NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Chang, S. C.↗

NASA NTRS1985

On the evaluation of expected performance cost for partially observed closed-loop stochastic systems

New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.

Bayard, D. S.↗

NASA NTRS1985

Partially confined configuration for the growth of semiconductor crystals from the melt in zero-gravity environment

A novel partially confined configuration is proposed for the crystal growth of semiconductors from the melt, including those with volatile constituents. A triangular prism is employed to contain the growth melt. Due to surface tension, the melt will acquire a cylindrical-like shape and thus contact the prism along three parallel lines. The three empty spaces between the cylindrical melt and the edges of the prism will accommodate the expansion of the solidifying semiconductor, and in the case of semiconductor compounds with a volatile constituent, will permit the presence of the desired vapor phase in contact with the melt for controlling the melt stoichiometry. Theoretical and experimental evidence in support of this new type of confinement is presented.

Lagowski, J.↗

NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗

NASA NTRS1986

Tribological properties of graphite-fiber-reinforced, partially fluorinated polyimide composites

Graphite-fiber-reinforced polyimide (GFRPI) composites were formulated from three new partially fluorinated polyimides and three types of graphite fiber. Nine composites were molded into pins and evaluated in a pin-on-disk tribometer. Friction coefficients, wear rates, pin wear surface morphology, and transfer film formation were assessed at 25 and 300 C. Also assessed was the effect of sliding speed on friction. Wear was up to two orders of magnitude lower at 25 C and up to one order of magnitude lower at 300 C than with previously formulated NASA GFRPI composites.

Fusaro, R. L.↗

NASA NTRS1985

Observed and computed stellar line profiles - The roles played by partial redistribution, geometrical extent and expansion

Partial redistribution (PRD) radiative transfer is reviewed with emphasis on the complex interaction of observations and theoretical predictions of spectral line shapes. Although the physics of PRD was understood and formal solutions to the radiative transfer equation including PRD were published as early as 1962, more than a decade elapsed before the clear inconsistency between observed and theoretical profiles calculated with the restrictive assumption of complete redistribution stimulated the development and use of PRD semiempirical spectral analysis for the solar Lyman alpha, Ca II, and Mg II resonance lines. Work is summarized that led to 'realistic' plane parallel static chromospheric models for the sun and other late type stars, with emphasis on the determination of the temperature minimum at the base of the chromosphere and the physical basis for resonance line limb darkening, the brightness of the line wings, and the width of the emission features. Finally the various roles played by atmospheric extension and expansion (winds) in determining resonance line profile shapes are discussed, and the existing PRD calculations for late type stars are summarized.

Linsky, J. L.↗

NASA NTRS1985

Role of carbonic anhydrase in bone - Partial inhibition of disuse atrophy of bone by parenteral acetazolamide

The effectiveness of orally and subcutaneously administered acetazolamide sodium in preventing denervation-induced bone loss in rats is examined. Male Sprague-Dawley rats were treated with acetazolamide either orally by incorporation of 0.2, 0.5, or 1.5 percent concentrations in their diet for 15 days, or subcutaneously by either injection of 0.5 ml/rat of a solution containing either 20 or 100 mg/ml of the drug twice daily for 15 days or by continuous infusion of 5, 50, 500, or 1000 mg/ml of acetazolamide sodium for 8 days using an osmotic minipump. The effects of acetazolamide on body weight, food consumption, and plasma calcium content are evaluated. It is observed that parenteral administration is equally effective as oral administration in partially preventing denervation-induced bone mass changes. The data reveal that approximately 50 percent protection occurs with daily doses of 1094, 129, and 8 mg/kg body weight for the oral, subcutaneous injection, and subcutaneous infusion methods, respectively.

Kenny, A. D.↗

NASA NTRS1986

Numerical simulation of unsteady, viscous, high-angle-of-attack flows using a partially flux-split algorithm

Viscous separated flow surrounding a hemisphere-cylinder body at angles of attack ranging up to 19 deg in transonic flow has been computed using an implicit, approximately-factored, partially flux-split algorithm. The resulting flowfield structures, including the vortical flow on the leeward side of the body and the three-dimensional separation patterns, have been investigated. The computed results show good qualitative and quantitative agreement with experimental data. Furthermore, visualization of the flowfield patterns has yielded insight into the behavior of the three-dimensional separated flow.

Ying, S. X.↗

NASA NTRS1986

Hardware requirements: A new generation partial reflection radar for studies of the equatorial mesosphere

A new partial reflection (PR) radar is being developed for operation at the proposed Equatorial Observatory. The system is being designed to make maximum use of recent advances in solid-state technology in order to minimize the power requirements. In particular, it is planned to use a solid-state transmitter in place of the tube transmitters previously used in PR systems. Solid-state transmitters have the advantages that they do not need high voltage supplies, they do not require cathode heaters with a corresponding saving in power consumption and parts are readily available and inexpensive. It should be possible to achieve 15 kW peak powers with recently announced fast switching transistors. Since high mean powers are desirable for obtaining good signal-to-noise ratios, it is also planned to phase code the transmitted pulses and decode after coherent integration. All decoding and signal processing will be carried out in dedicated microprocessors before the signals are passed to a microcomputer for on-line analysis. Recent tests have shown that an Olivetti M24 micro (an IBM compatible) running an 8-MHz clock with a 8087 coprocessor can analyze data at least as fast as the minicomputers presently being used with the Adelaide PR rad ar and at a significantly lower cost. The processed winds data will be stored in nonvolatile CMOS RAM modules; about 0.5 to 1 Mbyte is required to store one week's information.

Vincent, R. A.↗

NASA NTRS1986

The Adelaide MF partial-reflection radar and VHF ST radar

The microwave frequency (MF) partial-reflection radar ran continuously since November 1983, with data being analyzed in real time. The spaced antenna technique was used routinely to produce a climatology of the mean circulation, atmospheric tides, and gravity waves. Since the beginning of 1985, the system was also used as a Doppler radar to measure the spectral widths of the mesospheric echoes. This has enabled the turbulence dissipation rates to be determined. The Stratosphere-Troposphere (ST) radar was operated in the spaced antenna mode to measure winds in November 1984, in conjunction with a cooperative campaign to study the propagation of cold fronts across SE Australia. Observations were also performed to study the structure of the more intense and deeper cold fronts, which occur in late winter.

Vincent, R. A.↗