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At least 217 records · Page 12

Modeling substorm current systems using conductivity distributions inferred from DE auroral images

The first attempt to systematically use DE 1 auroral images to infer ionospheric conductivities is presented. These conductivities are then used to compute the distributions of ionospheric and field-aligned current patterns during auroral substorms. It is concluded that the western electrojet is, in general, collocated with the region of high auroral luminosity, while the region of relatively low luminosity in the evening sector is collocated with the eastward electrojet. The upward field-aligned currents exist in the brightest auroral region on the poleward side of the evening auroral oval and on the equatorward side of the morning oval. A significant amount of ionospheric currents can flow in regions where there are no bright auroral emissions.

Kamide, Y.↗

A spectral element method for the simulation of unsteady incompressible flows with heat transfer

The spectral element method is a high-order finite element technique for solution of the Navier-Stokes and energy equations. In the isoparametric spectral element discretization, the domain is broken up into general brick elements, and the dependent and independent variables represented as high-order tensor-product Lagrangian interpolants through Chebyshev collocation points. The nonlinear and convective terms in the governing equations are treated with explicit collocation, while the pressure and diffusive contributions are handled implicitly using variational projection operators. The method is applied to flow past a cylinder, flow in grooved channels, and natural convection in an enclosure.

Karniadakis, George E.↗

Vibration and Control of Flexible Rotor Supported by Magnetic Bearings

Active vibration control of flexible rotors supported by magnetic bearings is discussed. Using a finite-element method for a mathematical model of the flexible rotor, the eigenvalue problem is formulated taking into account the interaction between a mechanical system of the flexible rotor and an electrical system of the magnetic bearings and the controller. However, for the sake of simplicity, gyroscopic effects are disregarded. It is possible to adapt this formulation to a general flexible rotor-magnetic bearing system. Controllability with and without collocation sensors and actuators located at the same distance along the rotor axis is discussed for the higher order flexible modes of the test rig. In conclusion, it is proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then it is possible to stabilize for the case of uncollocation by means of this method.

Nonami, Kenzou↗

Shear buckling of specially orthotropic plates with centrally located cutouts

The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.

Klang, Eric C.↗

Temporal stability of multiple-cell vortices

The temporal stability of multiple cell vortices is studied with a staggered Chebyshev spectral collocation technique. It is shown that cell multiplicity in the vortex core has a drastic effect on the stability characteristics. While validating the spectral collocation algorithm, two new viscous modes of instability for Batchelor's (1964) vortex were found. These modes are discussed in detail.

Khorrami, M. R.↗

Global properties of pseudospectral methods

The present application of polynomial interpolation methods to function-approximation and numerical solutions for hyperbolic and elliptic PDEs allows the explicit construction of the derivative matrix for a general sequence of collocation points. An evaluation of the effect of several factors on the performance of these methods indicates an inability to interpret global methods in terms of local ones; the accuracy of the approximation will differ when the function's large gradients occur near the center of the region or near the boundary, irrespective of the boundary vicinity's collocation-point density.

Solomonoff, A.↗

Performance of FFT methods in local gravity field modelling

Fast Fourier transform (FFT) methods provide a fast and efficient means of processing large amounts of gravity or geoid data in local gravity field modelling. The FFT methods, however, has a number of theoretical and practical limitations, especially the use of flat-earth approximation, and the requirements for gridded data. In spite of this the method often yields excellent results in practice when compared to other more rigorous (and computationally expensive) methods, such as least-squares collocation. The good performance of the FFT methods illustrate that the theoretical approximations are offset by the capability of taking into account more data in larger areas, especially important for geoid predictions. For best results good data gridding algorithms are essential. In practice truncated collocation approaches may be used. For large areas at high latitudes the gridding must be done using suitable map projections such as UTM, to avoid trivial errors caused by the meridian convergence. The FFT methods are compared to ground truth data in New Mexico (xi, eta from delta g), Scandinavia (N from delta g, the geoid fits to 15 cm over 2000 km), and areas of the Atlantic (delta g from satellite altimetry using Wiener filtering). In all cases the FFT methods yields results comparable or superior to other methods.

Forsberg, Rene↗

Regional quasigeoid determination in Northern Germany and comparison with GPS

For the northern part of the Federal Republic of Germany, new quasigeoid solutions were computed by least squares collocation and fast Fourier transformation (FFT) techniques using point and mean gravity data, a digital terrain model, and a global geopotential model. As severe accuracy limitations for precise regional quasigeoid determination come from global model uncertainties, different geopotential models were investigated by combining them with gravimetric data and comparing the quasigeoid heights with GPS and leveling. Optimum results were obtained by a global model tailored to gravity data in Europe. Collocation and FFT results based on this model agree well. The comparison with GPS and leveling yields rms discrepancies of + or - 2 cm over approximately 400 km range.

Denker, Heiner↗

Analysis of altimetry over inland seas

Satellite-based altimetric data taken by GEOS-3 and SEASAT over the Black Sea and Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulation on a .25-degree by .25-degree grid and to transform these geoid undulations to free air gravity anomalies. This project entailed processing satellite altimeter data over inland seas for recovery of area mean gravity information. Gravity information in this area of the world is not readily available, so the possibility of obtaining it from the processing of altimeter observations is attractive. The principal objective was to complete and extend analyses done in a previous study, verify those results, and document the results and techniques. A secondary objective was to improve the algorithms and results, if possible. The approach used involved editing geoid height data to remove overland data; evaluating geoid height differences at crossover points; removing orbit errors from geoid heights using crossover differences; gridding geoid height data at .25-degree by .25-degree intervals; and estimating the gravity anomalies from gridded geoid heights using the collocation technique.

Au, A. Y.↗

Multispectral retrieval of rainfall rates using the Special Sensor Microwave/Imager (SSM/I)

Collocated SSM/I and radar measurements are compared to model simulated radiances upwelling from precipitating clouds. A methodology maximizing the correlation between the radar rain rate estimates and surface rainfall amounts is presented, along with data sources and samples. Geolocation of both the satellite and radar data is assessed, and statistical rainfall-rate retrieval algorithms are analyzed. Regression analysis of collocated SSM/I brightness-temperature measurements and radar-derived rainfall rates show the potential of the SSM/I to provide 25-km resolution rain-rate estimates over land and ocean surfaces.

Olson, William S.↗

Limitations of vibration suppression in flexible space structures

The uncertainties inherent in the dynamics of flexible spacecraft make robustness questions very important when designing vibration suppression systems for these vehicles. This often leads to the use of sensors and actuators which are collocated on the structure, so as to avoid the potentially destabilizing problem of unknown modal phase differences between noncollocated sensors and actuators. The closed-loop performance attainable is, of course, reduced if only collocated pairs are considered. The object of the present study is to investigate whether the special properties of the transmission zeros of such structures can be used to quantify these performance limitations. The approach is based on recent results concerning the transmission zeros of flexible structures.

Williams, T. W. C.↗

Statistical prediction of satellite magnetic anomalies

Computationally rapid statistical procedures are presented for satellite altitude normalizations and the gridding of magnetic anomaly data, as an alternative to the more commonly used but computationally expensive equivalent-source inversion procedures. The statistical predictions of Magsat observations over South America have demonstrated the great computational advantages of collocation over equivalent source inversion in gridding magnetic anomally data; in general, three-dimensional collocation is an efficient and cost-effective approach for obtaining altitude-normalized anomally grids from orbital or arbitrarily distributed data.

Goyal, H. K.↗

Discrete approximations to optimal trajectories using direct transcription and nonlinear programming

A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.

Enright, Paul J.↗

NRL tethered balloon measurements at San Nicolas Island during FIRE IFO 1987

An overview is given of the tethered balloon measurements made during the First ISCCP Regional Experiment (FIRE) marine stratocumulus intensive field observations (IFO) at San Nicolas Island in 1987. The instrument utilized on the balloon flights, the 17 flights over a 10 day period, the state of the data analysis, and some preliminary results are described. A goal of the measurements with the Naval Research Laboratory (NRL) balloon was to give a unique and greatly improved look at the microphysics of the clear and cloud-topped boundary layer. For this goal, collocated measurements were made of turbulence, aerosol, cloud particles, and meteorology. Two new instruments which were expected to make significant contributions to this effort were the saturation hygrometer, capable of measuring 95 percent less than RH 105 percent (with an accuracy of 0.05 percent near 100 percent) and used for the first time in clouds; and the forward scatter meter which gives in situ LWC measurements at more than 10 Hz. The data set, while unfortunately only partially simultaneous with the bulk of the FIRE stratocumulus observations, is unique and worthwhile in its own right. For the first time accurate RH measurements near 100 percent have been made in-cloud; although, the use of the saturation hygrometer reflected a learning experience which will result is substantially better performance the next time. These measurements were made in conjunction with other microphysical measurements such as aerosol and cloud droplet spectra, and perhaps most important of all, they were all collocated with bivane turbulence measurements thus permitting flux calculations. Thus the analysis of this data set, which consisted of about 50 percent stratocumulus cases including increasing and decreasing partial cloud cover, should lead to new insights on the physical mechanisms which drive the boundary-layer/cloud/turbulence system.

Gerber, Hermann↗

A single-axis testbed for slewing control experiments

A simple single-axis testbed is described, and initial experimental results are presented to illustrate collocated and noncollocated control for this structure. The testbed is made up of a pair of single-axis flexible beams attached to a DC servo motor. An optical encoder and strain gauges provide hub and beam position information, respectively. The system is driven by an IBM PC system; with a motor controller, a programmable digital filter processes position error information through user-selected gains and pole-zero configurations. A 25-kHz data acquisition system provides the necessary interface between processor and motor. The control approaches currently being investigated include collocated PD control and noncollocated phase compensation.

Hamilton, Jonathan↗

Stability of compressible Taylor-Couette flow

Compressible stability equations are solved using the spectral collocation method in an attempt to study the effects of temperature difference and compressibility on the stability of Taylor-Couette flow. It is found that the Chebyshev collocation spectral method yields highly accurate results using fewer grid points for solving stability problems. Comparisons are made between the result obtained by assuming small Mach number with a uniform temperature distribution and that based on fully incompressible analysis.

Kao, Kai-Hsiung↗

An equatorial temperature and wind anomaly (ETWA)

Data obtained from the WATS (Wind and Temperature Spectrometer) and LP (Langmuir Probe) experiments on board DE-2 (Dynamic Explorer) during high solar activity show evidence of anomalous latitudinal variations in the zonal winds and temperature at low latitudes. The zonal winds exhibit a broad maximum centered around the dip equator, flanked by minima on either side around 25 degrees; while the temperature exhibits a pronounced bowl-shaped minimum at the dip equator which is flanked by maxima. The two minima in the zonal winds and the corresponding maxima in the temperature are nearly collocated with the crests of the well known Equatorial Ionization Anomaly (EIA). The maximum in the zonal winds and the minimum in the gas temperature are collocated with the trough of the EIA. The differences between the maxima and minima in temperature and zonal winds, on many occasions, are observed to exceed 100 K and 100 m/s, respectively. The characteristics of this new phenomenon have eluded present day empirical models of thermospheric temperature and winds. The connection among these variables can be understood from the ion-neutral drag effect on the motions of the neutrals that in turn affect their energy balance.

Raghavarao, R.↗

On the accurate prediction of the wall-normal velocity in compressible boundary-layer flow

A method for predicting the wall-normal velocity in compressible boundary layer flow is presented which is the extension of the fully implicit, spectral collocation method developed by Pruett and Streett (1991). The spectrally accurate method under consideration is capable of extracting the wall-normal velocity from the transformation from the physical plane to a computational plane, without interpolation, leaving the continuity equation free as a check on the quality of the solution. When used in conjunction with a highly accurate spectral collocation method for the compressible boundary-layer equations, the method gives a discrete solution which satisfies the continuity equation nearly to machine precision.

Pruett, C. D.↗