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Measured ranges of 600-MeV/amu Fe-56 ions in a variety of substances are shorter than predicted by the standard Bethe stopping-power theory. The ranges are consistent with values computed using high-order corrections to the Mott cross section.
The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.
The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.
On-board computers for control and sequencing from Apollo to Voyager are described along with future trends and recent design examples. Consideration is given to a high-order language for the Space Shuttle program. Emphasis is placed on the usage of modern LSI and new distributed architectural approaches. The distributed computer of the Galileo spacecraft and the data processing system for the Shuttle Orbiter are outlined.
Granular HMX of three degrees of fineness was packed into heavy-walled steel tubes closed at both ends. Ignition was obtained at one end using an intimate mixture of finely divided titanium and boron as an igniter that produced heat with little gas. The distance to detonation was determined by examination of the resulting tube fragments. By inserting tightly-fitted neoprene diaphragms periodically into the HMX column, it was shown that the role of convective combustion was limited to the initial stage of the deflagration to detonation (DDT) process. Experiments in which various combinations of two of the three types of HMX were loaded into the same tube showed that heating by adiabatic shear of explosive grains was an essential factor in the final buildup to detonation. A description of the DDT process is developed in which conductive burning is followed in turn by convective burning, bed collapse with plug formation, onset of accelerated burning at the front of the plug through heating by intercrystalline friction and adiabatic shear, and intense shock formation resulting in high-order detonation.
Satellite-to-satellite Doppler tracking between the ATS 6 and the GEOS 3 spacecraft was used to measure the high-degree and high-order gravity field over an 80-deg region in the central Pacific Ocean. Forty passes of GEOS 3/ATS 6 Doppler data have been analyzed. The precision of these range rate data is about 0.3 mm/s, and the line-of-sight gravity anomalies recovered from these data have a precision of about 0.2 mGal at the GEOS 3 altitude of about 840 km. In general, the agreement between the SST-derived map and the conventional GEM method and an altimeter-derived geoid is good. Eight significant positive gravity anomalies were exposed in the central Pacific. Generally speaking, the anomalies form a roughly east-west pattern of alternating sign in the central region, and near the East Pacific they strike about north and south.
PANAIR uses high-order panel method to predict inviscid subsonic or supersonic flows about arbitrary configuration. Panel method solves linear partial differential equation numerically by approximating configuration surface with panels on which unknown "singularity strengths" are defined. PANAIR includes advanced software technology as well as advanced aerodynamic technology.
A simplified theory of aircraft vertical acceleration gust response based on a model including pitch, vertical displacement and control motions due to autopilot operation is presented. High-order autopilot transfer functions are utilized for improved accuracy in the determination of the overall response characteristics. Four representative commercial jet aircraft were studied over a wide range of operating conditions and comparisons of individual responses are given. It is shown that autopilot operation relative to the controls fixed case causes response attenuation of from 10 percent to approximately 25 percent depending on flight condition and increases in crossing number up to 30 percent, with variations between aircraft of from 5 percent to 10 percent, in general, reflecting the differences in autopilot design. A detailed computer program description and listing of the calculation procedure suitable for the general application of the theory to any airplane autopilot combination is also included.
High-order solar oscillations with degrees l=3, 4, and 5 could be detected. The observations were made by measuring the difference between the shifts in the Fe 5,124 spectrum line from light integrated from a central circular portion of the solar disk and from an annular portion exterior to it. The frequencies of the octupole modes agree well with the values obtained from whole-disk measurements at the South Pole. A least-squares fit of the observed frequencies to values interpolated between and extrapolated from the predictions of a sequence of solar models with different chemical compositions selects two models. One, a helium-rich solution, agrees with that of similar analyses of whole-disk data. The extrapolated solution has a relatively deep convection zone, and is thus consistent with analyses of 5-min oscillations of high degree.
Modal cost analysis furnishes a promising methodology for developing dynamical models of space structures for use in control systems analysis. Economy and accuracy can be attained by only retaining vibration modes that contribute significantly to an appropriately defined cost function. Expressions for modal costs (especially simple for 'lightly damped' structures) are derived for attitude control, vibration suppression, and shape control. These techniques are illustrated through application to a high-order finite element model of a large platform-type structure.
A new terraced lateral wave confining structure is obtained by liquid phase epitaxy over channeled substrates misoriented perpendicular to the channels' direction. Single spatial and longitudinal mode CW operation is achieved to 50 mW from one facet, in large spot sizes (2 x 7.5 micron, 1/e squared points in intensity) and narrow beams (6 deg x 23 deg), full width half-power). At 70 C ambient temperature CW lasing is obtained to 15 mW from one facet. Weak mode confinement in an asymmetric lateral waveguides provides discrimination against high-order mode oscillation.
The application of the self-tuning regulator concept to adaptively control aircraft wing/store flutter instability is described. A simple design based on a reduced-order aircraft model has been successfully tested on a high-order simulation of an advanced aircraft, and performance was found to be comparable to another design using on-line maximum likelihood identification of plant parameters. The main advantage of the self-tuning regulator is its simplicity, while the main disadvantage is the inadequacy of prior performance guarantees.
The issue addressed in the appropriate modeling technique for pilot vehicle analysis of large flexible aircraft, when the frequency separation between the rigid-body mode and the dynamic aeroelastic modes is reduced. This situation was shown to have significant effects on pitch-tracking performance and subjective rating of the task, obtained via fixed base simulation. Further, the dynamics in these cases are not well modeled with a rigid-body-like model obtained by including only 'static elastic' effects, for example. It is shown that pilot/vehicle analysis of this data supports the hypothesis that an appropriate pilot-model structure is an optimal-control pilot model of full order. This is in contrast to the contention that a representative model is of reduced order when the subject is controlling high-order dynamics as in a flexible vehicle. The key appears to be in the correct assessment of the pilot's objective of attempting to control 'rigid-body' vehicle response, a response that must be estimated by the pilot from observations contaminated by aeroelastic dynamics. Finally, a model-based metric is shown to correlate well with the pilot's subjective ratings.
The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.
The selection of a high-order programming language for a real-time distributed network simulation is described. The additional problem of implementing a language on a possibly changing network is addressed. The recently designed language ADA (trademarked by DoD) was chosen since it provides the best model of the underlying application to be simulated.
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
The mineralogy of relatively unweathered rocks on Mars place important constraints on models of planetary oxidation state, volcanism and associated outgassing, accretion and associated volatile inventory, and geochemical changes over time. Reflectance spectra (300 to 2500 nm) provide direct mineralogic information about the surface materials. Spectra measured using Earth-based telescopes were analyzed by a multiple high-order derivative spectroscopy technique. Nine areas, measured during the 1978 opposition, were analyzed by the technique. Each contained suites of well-defined absorption bands. These bands can be interpreted in terms of constituent mineralogy by the technique of Adams. Among the features extracted from the spectra were bands attributed to iron oxides. Other bands can be attributed to silicates within chemically unweathered rocks/fines. Absorption features suggest the presence of Mg-olivine and plagioclase feldspar.
A real-time multiprocessor programming language (RTMPL) has been developed to provide for high-order programming of real-time simulations on systems of distributed computers. RTMPL is a structured, engineering-oriented language. The RTMPL utility supports a variety of multiprocessor configurations and types by generating assembly language programs according to user-specified targeting information. Many programming functions are assumed by the utility (e.g., data transfer and scaling) to reduce the programming chore. This manual describes RTMPL from a user's viewpoint. Source generation, applications, utility operation, and utility output are detailed. An example simulation is generated to illustrate many RTMPL features.