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Theoretical and numerical results are presented for inverse problems involving estimation of spatially varying parameters such as stiffness and damping in distributed models for elastic structures such as Euler-Bernoulli beams. An outline of algorithms used and a summary of computational experiences are presented.
The present study has the objective to investigate some iterative parallel-processor linear equation solving algorithms with respect to efficiency for analyses of typical linear engineering systems. Attention is given to a set of n linear equations, Ku = p, where K = an n x n positive definite, sparsely populated, symmetric matrix, u = an n x 1 vector of unknown responses, and p = an n x 1 vector of prescribed constants. This study is concerned with a hybrid method in which iteration is used to solve the problem, while a direct method is used on the local processor level. Variations in the efficiency of parallel algorithms are explored. Measures of the efficiency are based on computer experiments regarding the algorithms. For all the algorithms, the wall clock time is found to decrease as the number of processors increases.
Data displayed on television image of experiment. Video images of experiment sent with digital data on experiment to remote station. Digital data raw and unformatted or in form of characters. For minimal power consumption, interface circuit built of CMOS and HMOS integrated-circuit chips. Buffer/decoder circuit enables experiment computer to communicate with board without excessive loading of computer bus by board. Memory multiplexer/memory array implements buffer-swapping scheme as one buffer is read, other filled with new data.
The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.
The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.
Topics addressed include: wind tunnel and flight experiments; computational fluid dynamics (CFD) applications, industry overviews; and inviscid methods and grid generations.
In order to assess the state of the art in transonic flow disciplines and to glimpse at future directions, NASA-Langley held a Transonic Symposium. Emphasis was placed on steady, three dimensional external, transonic flow and its simulation, both numerically and experimentally. The symposium included technical sessions on wind tunnel and flight experiments; computational fluid dynamic applications; inviscid methods and grid generation; viscous methods and boundary layer stability; and wind tunnel techniques and wall interference. This, being volume 1, is unclassified.
A stable and accurate finite element CFD algorithm for hyperbolic/incompletely parabolic conservation law systems is described and verified. It combines a Taylor weak statement FEM, an optimal implicit Runge-Kutta time integration algorithm, and a matrix tensor product approximate factorization linear algebra procedure. The results of computational experiments show that the developed algorithm is robust.
Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.
The M51 system (NGC 5194/5195) provides an excellent problem both in spiral structure and in galaxy interactions. The authors present an analytic study of a computer experiment on the excitation mechanisms for M51's spiral arms and whether or not a halo is important for these mechanisms. This work extends previous numerical studies of the M51 system by including self-gravitation in a two component disk: gas and stars, and a dark halo. The analytic study provides two new observational constraints: the time (approx. 70 to 84 million years ago) and position angle of perigalacticon (300 degrees). By using these constraints and a simple conic approximation, the search for the companion's possible orbit is greatly simplified. This requires fewer N-body simulations than a fully self-gravitating orbit search.
The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.
The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.
Modulation of a rain wave pattern by longer waves has been studied. An analytical model taking into account capillarity effects and obliquity of short waves has been developed. Modulation rates in wave number and amplitude have been computed. Experiments were carried out in a wave tank. First results agree with theoretical models, but higher values of modulation rates are measured. These results could be taken into account for understanding the radar response from the sea surface during rain.
The thermal state of the Earth at the time relevant to formation of a magma ocean was dominated by the great impact that created the Moon. As shown in computer experiments, the iron in the impacting bodies quickly sank to the core of the proto-Earth, while a significant fraction of silicates was pushed far enough out beyond the geosynchronous limit to constitute the main material of the Moon. Most of any atmosphere would have been pushed aside, rather than being expelled in the impact. However, the energy remaining in the material not going to the core or expelled was still sufficient to raise its temperature some 1000's of degrees, enough to vaporize silicates and to generate a strong 'planetary wind': a hydrodynamic expansion carrying with it virtually all volatiles plus appreciable silicates. This expansion was violent and uneven in its most energetic stage, but probably the resulting magma ocean was global. The duration, until cooling, was sufficient for silicates to condense to melt and the duration was probably short. Comparison of the Earth and Venus indicates that the great impact was extraordinarily effective in removing volatiles from the proto-Earth; in particular, the enormous differences in primordial inert gases between the planets demand a catastrophic difference in origin circumstances. On the other hand, the comparison limits the amount of silicates lost by the Earth to a rather minor fraction; most of that expelled in the wind must have condensed soon enough for the silicate to fall back to Earth or be swept up by the proto-Moon. So the Earth was left with a magma ocean. The question is whether sufficient water was retained to constitute a steam atmosphere. Probably not, but unknowns affecting this question are the efficiencies of outgassing in great impacts and in subsequent convective churnings deep in the mantle. During the stage when mantle convection is turbulent, an appreciable fraction of volatiles were also retained at depth, perhaps in some mineral phases not yet well-defined. We still have primordial helium being outgassed.
A method for partially correcting the spatial coherence of an array of laser beams is discussed. The method trades far-field intensity for simplistic implementation and array lifetime extension, resulting in a quasi-coherent array with features of adaptive optics. An algorithm for implementing the method is described and feasible options for improvement are presented. A computer experiment used the algorithm and fast Fourier transforms to calculate typical far-field intensity distributions of such arrays. The far-field distributions illustrate beam power concentration, beam steering, and (indirectly) extended lifetime of the array.
The basic physics involving the interaction of a high voltage sphere with a LEO-Plasma was investigated via computer experiments. Two approaches were used: the fluid description and the more general particle pushing method. Both techniques displayed qualitatively similar features. Thus, the initial time-dependent response of the plasma predicted by the fluid model, including the initial current surge and sheath formation, the formation of ion and electron density shells about the sphere with a double layer potential structure, and the subsequent propagation of the density shells away from the sphere. The PIC results also displayed an oscillatory character and slightly different time constants for the growth and decay mechanisms involved.
In this report we describe the research performed at the Naval Research Laboratory in support of the NASA Microgravity Science and Applications Program over the past three years with emphasis on the work performed since February 1992, the beginning of the current project. The focus of our research has been on investigating fundamental combustion questions concerning the propagation and extinction of gas-phase flames in microgravity and earth-gravity environments. Our approach to resolving these fundamental questions has been to use detailed time-dependent, multidimensional numerical models to perform carefully designed computational experiments. The basic questions we have addressed, a general description of the numerical approach, and a summary of the results are described in this report. More detailed discussions are available in the papers published which are referenced herein.
The National Aeronautics and Space Administration (NASA) at Goddard Space Flight Center (GSFC) has developed a laser ranging device (LIDAR) which provides accurate and timely data of earth features. NASA/GSFC recently modified the sensor to include a scanning capability to produce LIDAR swaths. They have also integrated a Global Positioning System (GPS) and an Inertial Navigation System (INS) to accurately determine the absolute aircraft location and aircraft attitude (pitch, yaw, and roll), respectively. The sensor has been flown in research mode by NASA for many years. The LIDAR has been used in different configurations or modes to acquire such data as altimetry (topography), bathymetry (water depth), laser-induced fluorosensing (tracer dye movements, oil spills and oil thickness, chlorophyll and plant stress identification), forestry, and wetland discrimination studies. NASA and HARC are developing a commercial version of the instrument for topographic mapping applications. The next phase of the commercialization project will be to investigate other applications such as wetlands mapping and coastal bathymetry. In this paper we report on preliminary laboratory measurements to determine the feasibility of making accurate depth measurements in relatively shallow water (approximately 2 to 6 feet deep) using a LIDAR system. The LIDAR bathymetry measurements are relatively simple in theory. The water depth is determined by measuring the time interval between the water surface reflection and the bottom surface reflection signals. Depth is then calculated by dividing by the index of refraction of water. However, the measurements are somewhat complicated due to the convolution of the water surface return signal with the bottom surface return signal. Therefore in addition to the laboratory experiments, computer simulations of the data were made to show these convolution effects in the return pulse waveform due to: (1) water depth, and (2) changes in bottom surface reflectivity.