The formation of resonance lines in multidimensional media. III Interpolation functions, accuracy, and stability.
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Jones, H. P.↗
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Multidimensional heat conduction
Computer program computes transient temperature history or steady state solution for complex body geometries in three geometries. Program allows option of four methods of solution: forward difference method, midpoint difference (Crank-Nicholson) method, backward difference method, and alternating direction technique.
Connors, T. C., Jr.↗
Computational aspects of the prediction of multidimensional transonic flows in turbomachinery
The analytical prediction and description of transonic flow in turbomachinery is complicated by three fundamental effects: (1) the fluid equations describing the transonic regime are inherently nonlinear, (2) shock waves may be present in the flow, and (3) turbomachine blading is geometrically complex, possessing large amounts of curvature, stagger, and twist. A three-dimensional computation procedure for the study of transonic turbomachine fluid mechanics is described. The fluid differential equations and corresponding difference operators are presented, the boundary conditions for complex blade shapes are described, and the computational implementation and mapping procedures are developed. Illustrative results of a typical unthrottled transonic rotor are also presented.
Oliver, D. A.↗
Multidimensional histograms
Program computes four dimensional histogram of Landsat multispectral image data. System enhances image handling and significantly reduces reprocessing costs.
Jayroe, R. R., Jr.↗
On the clustering of multidimensional pictorial data
Obvious approaches to reducing the cost (in computer resources) of applying current clustering techniques to the problem of remote sensing are discussed. The use of spatial information in finding fields and in classifying mixture pixels is examined, and the AMOEBA clustering program is described. Internally, a pattern recognition program, from without, AMOEBA appears to be an unsupervised clustering program. It is fast and automatic. No choices (such as arbitrary thresholds to set split/combine sequences) need be made. The problem of finding the number of clusters is solved automatically. At the conclusion of the program, all points in the scene are classified; however, a provision is included for a reject classification of some points which, within the theoretical framework, cannot rationally be assigned to any cluster.
Bryant, J. D.↗
A hill-sliding strategy for initialization of Gaussian clusters in the multidimensional space
A hill sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimate of sample data for the first step of iterative unsupervised classification. Each cluster was assumed to posses a unimodal normal distribution. A clustering function proposed distinguished elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with LANDSAT multispectral scanner data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill sliding clustering technique developed herein has the potential applicability to decomposition any multivariate mixture distribution into a number of unimodal distributions when an appropriate distribution function to the data set is employed.
Park, J. K.↗
Analytical prediction and experimental verification of TWT and depressed collector performance using multidimensional computer programs
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Dayton, J. A., Jr.↗
Analytical investigation of efficiency and performance limits in klystron amplifiers using multidimensional computer programs; multi-stage depressed collectors; and thermionic cathode life studies
An extensive parametric investigation was performed of the extraction of energy in output gaps of klystron amplifiers, using 3-D computer programs. Due to complexity of the program which used a hydrodynamic, axially and radially deformable disk ring model and the resulting long computing time, the investigation was limited to the output gap, by far the most important and difficult part of the klystron interaction. Results show that, for a confined flow focused beam throughout the penultimate cavity, radial velocities remain very small and the beam is highly laminar. It was, therefore, concluded that possible errors resulting from treating only the output cavity in 3-D would remain small.
Kosmahl, H. G.↗
Stability theorems for multidimensional linear systems with variable parameters
A Liapunov-type approach is used to derive two equivalent theorems which govern the stability of coupled linear systems with varying multiple parameters. The theorems generalize some of the existing theorems applicable to systems with constant parameters and the Sonin-Polya theorem applicable to a single-degree-of-freedom system with variable coefficients. As an illustration, the proposed theorems are applied to mechanical systems with varying inertia, stiffness, gyroscopic, and damping terms, and velocity and position-dependent forces.
Shrivastava, S. K.↗
Analytic investigation of efficiency and performance limits in klystron amplifiers using multidimensional computer programs; multi-stage depressed collectors; and thermionic cathode life studies
Due to complexity of the program which used a hydrodynamic, axially and radially deformable disk-ring model and the resulting long computing time only the output gap was investigated. Results from independent studies were used to initiate the starting conditions for the electrons and the RF voltage using our program. Although this method of computation is less exact than processing the entire klystron interaction in 3-Dimensions it is shown that, for a confined flow focused throughout the penultimate cavity, radial velocities remain very small and the beam is highly laminar. It is concluded that possible errors resulting from treating only the output cavity in 3-D would remain small.
Kosmahl, H. G.↗
Incorporating spatial context into statistical classification of multidimensional image data
Compound decision theory is employed to develop a general statistical model for classifying image data using spatial context. The classification algorithm developed from this model exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. A key input to this contextural classifier is a quantitative characterization of this tendency: the context function. Several methods for estimating the context function are explored, and two complementary methods are recommended. The contextural classifier is shown to produce substantial improvements in classification accuracy compared to the accuracy produced by a non-contextural uniform-priors maximum likelihood classifier when these methods of estimating the context function are used. An approximate algorithm, which cuts computational requirements by over one-half, is presented. The search for an optimal implementation is furthered by an exploration of the relative merits of using spectral classes or information classes for classification and/or context function estimation.
Bauer, M. E.↗
Evaluation of SMART sensor displays for multidimensional precision control of Space Shuttle remote manipulator
An enhanced proximity sensor and display system was developed at the Jet Propulsion Laboratory (JPL) and tested on the full scale Space Shuttle Remote Manipulator at the Johnson Space Center (JSC) Manipulator Development Facility (MDF). The sensor system, integrated with a four-claw end effector, measures range error up to 6 inches, and pitch and yaw alignment errors within + or 15 deg., and displays error data on both graphic and numeric displays. The errors are referenced to the end effector control axes through appropriate data processing by a dedicated microcomputer acting on the sensor data in real time. Both display boxes contain a green lamp which indicates whether the combination of range, pitch and yaw errors will assure a successful grapple. More than 200 test runs were completed in early 1980 by three operators at JSC for grasping static and capturing slowly moving targets. The tests have indicated that the use of graphic/numeric displays of proximity sensor information improves precision control of grasp/capture range by more than a factor of two for both static and dynamic grapple conditions.
Bejczy, A. K.↗
Fitting multidimensional splines using statistical variable selection techniques
This report demonstrates the successful application of statistical variable selection techniques to fit splines. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs using the B-spline basis were developed, and the one for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.
Smith, P. L.↗
Estimation of divergence and vorticity using multidimensional smoothing splines
Laplacian smoothing splines, smoothing splines on the sphere, and smoothing pseudo splines on the sphere are presented. The method of generalized cross validation to choose the smoothing parameter is described. These methods are applied to estimate divergence and vorticity of the atmosphere from wind speed and wind direction.
Wendelberger, J. G.↗
Multidimensional explicit difference schemes for hyperbolic conservation laws
First and second order explicit difference schemes are derived for a three dimensional hyperbolic system of conservation laws, without recourse to dimensional factorization. All schemes are upwind (backward) biased and optimally stable.
Vanleer, B.↗
Multidimensional Modeling of Atmospheric Effects and Surface Heterogeneities on Remote Sensing
A modeling capability that allows a quantitative determination of atmospheric effects on remote sensing including the effects of surface heterogeneities is established. The objectives include: (1) the adaptation of existing radiative transfer codes to remote sensing applications, (2) the implementation of a realistic atmospheric data base, (3) the definition and verification against field measurements of a coupled atmosphere/canopy model, and (4) the quantitative characterization of the effects of some biophysical canopy parameters and soil surface boundary conditions on satellite-sensed Multispectral Scanner System (MSS) data. Substantial progress was also made in quantifying the effects of varying atmospheric turbidity and different non-Lambertian and specular ground reflectances on MSS data and its transforms like greenness and brightness.
Gerstl, S. A.↗
A new method for mapping multidimensional data to lower dimensions
A multispectral mapping method is proposed which is based on the new concept of BEND (Bidimensional Effective Normalised Difference). The method, which involves taking one sample point at a time and finding the interrelationships between its features, is found very economical from the point of view of storage and processing time. It has good dimensionality reduction and clustering properties, and is highly suitable for computer analysis of large amounts of data. The transformed values obtained by this procedure are suitable for either a planar 2-space mapping of geological sample points or for making grayscale and color images of geo-terrains. A few examples are given to justify the efficacy of the proposed procedure.
Gowda, K. C.↗
Method for calculating multidimensional electric fields in photovoltaic modules
A finite element method for evaluating the electrical isolation characteristics of photovoltaic modules was developed; its accuracy was verified by comparison with an exact solution for a geometry similar to that of solar cells. Tests on a square test coupon, employed in electrical isolation tests, and a group of disc-shaped solar cells illustrated the finite element method's usefulness in evaluating module encapsulation designs. Finite element models had to avoid adjacent large and small elements and elements with large aspect ratios, and the NASTRAN output had to be curve fitted to calculate the maximum field. Geometric limits were indicated: cells with very sharp edges, and cells much thinner or thicker than the dielectric pottant layer.
Kallis, J. M.↗