The formation of resonance lines in multidimensional media. I - Scaling properties in two dimensions
Resonance line formation in multidimensional media, applying to non-LTE line transfer for two dimensional temperature variations
Jones, H. P.↗
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Multidimensional rotations in feature selection
Mathematical feature selection transformations by multidimensional rotations, considering character recognition experiment
Andrews, H. C.↗
Multidimensional analysis of fast-spectrum material replacement measurements for systematic estimation of cross section uncertainties
A series of central core and core-reflector interface sample replacement experiments for 16 materials performed in the NASA heavy-metal-reflected, fast spectrum critical assembly (NCA) were analyzed in four and 13 groups using the GAM 2 cross-section set. The individual worths obtained by TDSN and DOT multidimensional transport theory calculations showed significant differences from the experimental results. These were attributed to cross-section uncertainties in the GAM 2 cross sections. Simultaneous analysis of the measured and calculated sample worths permitted separation of the worths into capture and scattering components which systematically provided fast spectrum averaged correction factors to the magnitudes of the GAM 2 absorption and scattering cross sections. Several Los Alamos clean critical assemblies containing Oy, Ta, and Mo as well as one of the NCA compositions were reanalyzed using the corrected cross sections. In all cases the eigenvalues were significantly improved and were recomputed to within 1 percent of the experimental eigenvalue. A comparable procedure may be used for ENDF cross sections when these are available.
Klann, P. G.↗
Subjective evaluation with FAA criteria: A multidimensional scaling approach
Perceived orderliness in the ground tracks of five A/C during their simulated flights was studied. Dynamically developing ground tracks for five A/C from 21 separate runs were reproduced from computer storage and displayed on CRTS to professional pilots and controllers for their evaluations and preferences under several criteria. The ground tracks were developed in 20 seconds as opposed to the 5 minutes of simulated flight using speedup techniques for display. Metric and nonmetric multidimensional scaling techniques are being used to analyze the subjective responses in an effort to: (1) determine the meaningfulness of basing decisions on such complex subjective criteria; (2) compare pilot/controller perceptual spaces; (3) determine the dimensionality of the subjects' perceptual spaces; and thereby (4) determine objective measures suitable for comparing alternative traffic management simulations.
Kreifeldt, J. G.↗
Multidimensional stochastic approximation using locally contractive functions
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Lawton, W. M.↗
Joint Classification and Data Compression of multidimensional information sources - Application to ERTS
This paper describes a concept of Joint Classification and Data Compression of multidimensional information sources in the context of applications to Earth Resources Technology Satellites. The concept is used to define an Information Extraction System intended to remove data redundancy early in the sensor to user link in both classification and film interpretation applications. The approach uses cascaded partially supervised clustering to extract spectral intensity features from spatially local sources. Data compression is then used to efficiently represent spatial features within the spectral intensity feature map.
Hilbert, E. E.↗
Multidimensional difference schemes with fourth-order accuracy
An explicit finite-difference algorithm is presented for the solution of quasilinear divergence free multidimensional hyperbolic systems. The method consists of four steps per time level. The resulting scheme is fourth-order accurate in both space and time, though the intermediate steps are only first-order accurate. The family of schemes introduced is dissipative, and hence, suitable for both smooth flows and flows containing shocks. This method is compared, in several numerical examples, with both second-order schemes and others that are fourth order in space, but second order in time.
Turkel, E.↗
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
Mcreynolds, S. R.↗
The effects of context on multidimensional spatial cognitive models
Spatial cognitive models obtained by multidimensional scaling represent cognitive structure by defining alternatives as points in a coordinate space based on relevant dimensions such that interstimulus dissimilarities perceived by the individual correspond to distances between the respective alternatives. The dependence of spatial models on the context of the judgments required of the individual was investigated. Context, which is defined as a perceptual interpretation and cognitive understanding of a judgment situation, was analyzed and classified with respect to five characteristics: physical environment, social environment, task definition, individual perspective, and temporal setting. Four experiments designed to produce changes in the characteristics of context and to test the effects of these changes upon individual cognitive spaces are described with focus on experiment design, objectives, statistical analysis, results, and conclusions. The hypothesis is advanced that an individual can be characterized as having a master cognitive space for a set of alternatives. When the context changes, the individual appears to change the dimension weights to give a new spatial configuration. Factor analysis was used in the interpretation and labeling of cognitive space dimensions.
Dupnick, E. G.↗
Comparative analysis of various approaches to evaluating the parameters of multidimensional models
The problem of evaluating parameters of a multidimensional model according to measurement results is examined. The conditions on which the problem solution depends are itemized.
Guran, L. S.↗
Stability theory of difference approximations for multidimensional initial boundary value problems
An attempt is made to generalize results for arbitrary multidimensional difference schemes. Severe obstacles are encountered, however, for dissipative difference schemes the problem may be resolved.
Michelson, D.↗
Integration of multidimensional regions with applications to finite element analysis
Alternatives to Gaussian integration methods for multidimensional regions are presented. These rules preserve the convergence behavior of the exact integrated element but require fewer evaluation points than the Gauss methods. Numerical examples are given to verify the behavior of the new integration rules.
Mullen, R. L.↗
Development of a dynamically adaptive grid method for multidimensional problems
An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.
Holcomb, J. E.↗
A full-implicit-continuous-Eulerian (FICE) scheme for multidimensional transient magnetohydrodynamic (MHD) flows
A full implicit continuous Eulerian (FICE) scheme is developed for solving multidimensional transient MHD flow problems. The physical system under consideration is a general case of a transient MHD flow in which an initial steady state is subject to a finite amplitude disturbance. The governing equations are described, their finite difference formulation is presented and the FICE algorithm is given. The boundary conditions are treated by classifying them into physical and computational ones. The usefulness of the FICE algorithm is demonstrated using a physical example concerning the dynamical response of the static solar atmosphere due to a representative photospheric disturbance.
Wu, S. T.↗
Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.
Roe, P. L.↗
Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.
Roe, P. L.↗
The use of multidimensional scaling for facilities layout - An application to the design of the Space Station
Before an optimum layout of the facilities for the proposed Space Station can be designed, it is necessary to understand the functions that will be performed by the Space Station crew and the relationships among those functions. Five criteria for assessing functional relationships were identified. For each of these criteria, a matrix representing the degree of association of all pairs of functions was developed. The key to making inferences about the layout of the Space Station from these matrices was the use of multidimensional scaling (MDS). Applying MDS to these matrices resulted in spatial configurations of the crew functions in which smaller distances in the MDS configuration reflected closer associations. An MDS analysis of a composite matrix formed by combining the five individual matrices resulted in two dimensions that describe the configuration: a 'private-public' dimension and a 'group-individual' dimension. Seven specific recommendations for Space Station layout were derived from analyses of the MDS configurations. Although these techniques have been applied to the design of the Space Station, they can be applied to the design of any facility where people live or work.
Tullis, Thomas S.↗
A multidomain and multidimensional numerical analysis of flow in fuelside preburner, high pressure turbine, hot gas manifold and main injector assembly of the Space Shuttle main engine
The Space Shuttle Main Engine (SSME) consists of a large number of critical components each serving a special purpose. Any design change in one of these components not only alters its performance but also the performance of the ones in the upstream and in the downstream. To evaluate the effects of such a design change on the flow fields and on SSME's overall performance a multidomain and multidimensional analytical procedure has been developed and applied here to the series of components on the fuel side of the SSME. The results obtained from the multidomain analysis and their comparison with the single-domain solution when the SSME is operating at Full Power Load indicates that the multidomain model shows greater realism. It is concluded that this modeling technique would assist the designer significantly to achieve still higher performance levels of the SSME.
Mukerjee, T.↗