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A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter-grid interpolation procedures. It is demonstrated how elliptic problems can be solved in this fashion by using Jacobi smoothers.
The potential benefit of using a smoothing filter to estimate carrier phase over use of phase locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of the deep space network advanced receiver. These are residual carrier PLL, sideband aided residual carrier PLL, and finally sideband aiding with a Kalman smoother. The average symbol signal to noise ratio (SNR) after losses due to carrier phase estimation error is computed for different total power SNRs, symbol rates and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.4 dB over a sideband aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to a residual carrier loop is often in excess of 1 dB.
A 15-meter diameter deployable antenna has been built and is being used as an experimental test system with which to develop interdisciplinary controls, structures, and electromagnetics technology for large space antennas. The program objective is to study interdisciplinary issues important in optimizing large space antenna performance for a variety of potential users. The 15-meter antenna utilizes a hoop column structural concept with a gold-plated molybdenum mesh reflector. One feature of the design is the use of adjustable control cables to improve the paraboloid reflector shape. Manual adjustment of the cords after initial deployment improved surface smoothness relative to the build accuracy from 0.140 in. RMS to 0.070 in. Preliminary structural dynamics tests and near-field electromagnetic tests were made. The antenna is now being modified for further testing. Modifications include addition of a precise motorized control cord adjustment system to make the reflector surface smoother and an adaptive feed for electronic compensation of reflector surface distortions. Although the previous test results show good agreement between calculated and measured values, additional work is needed to study modelling limits for each discipline, evaluate the potential of adaptive feed compensation, and study closed-loop control performance in a dynamic environment.
All beta-SiC films grown using on-axis (001) Si substrates that have been examined with transmission electron microscopy exhibit a high density of interfacial twins, stacking faults, and antiphase disorder. The antiphase boundaries can be decorated by chemical etching, sputter etching, wet oxidation, and beta-SiC growth in the presence of diborane. All traces of antiphase disorder are eliminated when the heteroepitaxial growth is carried out on vicinal (001) Si substrates that are tilted 2 deg about a 110-line axis. In addition, growth on the off-axis Si produces beta-SiC films that are significantly smoother than on-axis films. The density of stacking faults is apparently unaffected by growth on the off-axis substrates.
A status report on the empirical modeling of ionospheric electron and ion temperatures is given with special emphasis on the models used in the International Reference Ionosphere (IRI). Electron temperature models have now reached a state where reliable prediction of the mean altitudinal, latitudinal and diurnal variations is possible. These models are largely based on satellite measurements, but comparisons with incoherent scatter radar measurements have shown excellent agreement. Variations with season and magnetic and solar activity seem to be small and are not yet included consistently in these models. Similar to the electron temperature, the ion temperature shows the largest variations with altitude, latitude and local time. But due to the larger mass, these variations are smoother and more steady in the case of the ions and therefore easier to model. Nevertheless, very few ion temperature models exist. The IRI model takes advantage of the observed concurrence of the ion temperature with the neutral temperature at low altitudes and with the electron temperature at high altitudes.
Simultaneous orbit determination is demonstrated using live range and Doppler data for the NASA/Goddard tracking configuration defined by the White Sands Ground Terminal (WSGT), the Tracking and Data Relay Satellite (TDRS), and the Earth Radiation Budget Satellite (ERBS). A physically connected sequential filter-smoother was developed for this demonstration. Rigorous necessary conditions are used to show that the state error covariance functions are realistic; and this enables the assessment of orbit estimation accuracies for both TDRS and ERBS.
Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates.
Cu/Ti coatings have been applied by sputter deposition to fused quartz housings to serve as the electrodes and lands of electrostatically supported gyroscopes. Niobium-coated fused quartz gyro rotors have been successfully suspended and spun up in those housings. The Cu/Ti bilayer coating and alternative multilayer coatings (Cu/Mo, Mo/Cu/Ti and Mo/Cu/Mo) with 2-micron thickness produced by sputter deposition on flat, fused quartz substrates have been examined with scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and four-point resistivity measurement techniques. The multilayer coatings with a molybdenum bonding layer appear to produce smoother surfaces than those with a titanium bonding layer. All multilayer coatings survived thermal cycling to 77 K without adhesion failure.
One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.
A high power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented.
The results of timing and spectral analyses of the X-ray sources Aql X-1 (X1908+005) and 4U1820-30 (NGC6624) are reported using data obtained with the Einstein SSS (Solid State Spectrometer) and MPC (Monitor Proportional Counter) instruments. A classic type I burst was observed from Aql X-1 in both detectors and a coherent modulation with a period of 131.66 + or - 0.02 ms and a pulsed fraction of 10 percent was detected in the SSS data. There is no evidence for a loss of coherance during the approximately 80 sec when the burst is observable. The 2 sigma upper limit on the rate of change of the pulse period is 0.00005s/s. It is argued that an asymmetrical burst occurring on a neutron star rotating at 7.6 Hz offers a plausible explanation for the oscillation. The data from 4U1820-30 show that the amplitude of the 685 sec modulation, identified as the orbital period, is independent of energy down to 0.6 keV. The SSS data show that the light curve in the 0.6 to 4.5 keV band is smoother than at higher energies.
The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section.
A new method is presented for the solution of incompressible flow in generalized coordinates. This method is based on the substitution of the pressure weighted form of the momentum equations into the continuity equation. The algorithm is rigorously derived and a Fourier analysis is used to assess its suitability to act as an error smoother. Linear stability analysis results indicate that the performance of the new pressure substitution method (PSM) and the pressure correction method (PCM) is about the same at low Reynolds numbers, with no significant pressure gradient. At high Reynolds numbers the PSM shows much faster convergence. Likewise prediction of various flows indicate that the PSM has better accuracy for high Reynolds number flows with significant pressure gradients. Since most practical aerodynamic flows have significant pressure gradients, the PSM seems to be attractive for such flows. Solutions for both laminar and turbulent flow are compared with the experimental data. A two-equation low Reynolds number turbulence model is used to resolve the turbulent flowfield.
The new IRAS Faint Source Survey data base is used to confirm the conclusion of Hacking et al. (1987) that the 60 micron source counts fainter than about 0.5 Jy lie in excess of predictions based on nonevolving model populations. The existence of an anisotropy between the northern and southern Galactic caps discovered by Rowan-Robinson et al. (1986) and Needham and Rowan-Robinson (1988) is confirmed, and it is found to extend below their sensitivity limit to about 0.3 Jy in 60 micron flux density. The count anisotropy at f(60) greater than 0.3 can be interpreted reasonably as due to the Local Supercluster; however, no one structure accounting for the fainter anisotropy can be easily identified in either optical or far-IR two-dimensional sky distributions. The far-IR galaxy sky distributions are considerably smoother than distributions from the published optical galaxy catalogs. It is likely that structure of the large size discussed here have been discriminated against in earlier studies due to insufficient volume sampling.
Simple modification yields welds of better quality. Reed valve halves fluctuations in pressure in back-purge chamber attached to workpiece undergoing keyhole plasma arc welding. Identical to one used in fuel system of two-cycle gasoline engine. Backbead smoother, and weld penetrates more uniformly.
The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.
Because of the complexity of helicopter flow field, a zonal method of analysis of computational aerodynamics is required. Here, a new procedure for coupling potential and viscous flow is proposed. An overlapping, velocity coupling technique is to be developed with the unique feature that the potential flow surface singularity strengths are obtained directly from the Navier-Stokes at a smoother inner fluid boundary. The closed-loop iteration method proceeds until the velocity field is converged. This coupling should provide the means of more accurate viscous computations of the near-body and rotor flow fields with resultant improved analysis of such important performance parameters as helicopter fuselage drag and rotor airloads.
A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.