Adaptive computing techniques
Adaptive local algorithm and convergence speed of multimodal multidimensional function
Schmitt, E.↗
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Decision making and pattern recognition of multi-dimensional data
Multidimensional data efficient decomposition for communication interface between man machine system, considering decision making and pattern recognition on digital computers with orthogonal transformations
Andrews, H. C.↗
Transformation coding for noise immunity and bandwidth reduction
Fourier and Hadamard transformation codings for multidimensional data channel noise immunity and bandwidth reduction
Andrews, H. C.↗
Line transfer in two dimensions
Radiative transfer equation for spectral line formed in multidimensional atmosphere, solving for two dimensional atmospheric model
Cannon, C. J.↗
A sequence solution to the Fokker-Planck equation
Sequence solution to multidimensional time varying Fokker-Planck equation for phase locked nonlinear systems
Mayfield, W. W.↗
The Measurement of Radiation Exposure of Astronauts by Radiochemical Techniques
The principal gamma-ray-omitting radioisotopes produced in the body of astronauts by cosmic-ray bombardment which have half-lives long enough to be useful for radiation dose evaluation are Be-7, Na-22, and Na-24. The sodium isotopes were measured in the preflight and postflight urine and feces, and those feces specimens collected during the manned Apollo missions, by analysis of the urine salts and the raw feces in large crystal multidimensional gamma-ray spectrometers. The Be-7 was chemically separated, and its concentration measured in an all Na(T1), anticoincidence shielded, scintillation well crystal. The overall sensitivity of the experiment was reduced by almost all variables such as low concentrations of excreted cosmogenic radionuclides, high concentrations of injected radionuclides, low sample sizes, long delay periods before analysis, and uncertain excretion rates. The astronaut radiation dose in millirads, as determined by this technique, for the Apollo 7, 8, 9, 10, 11, 12, and 13 missions was 330, 160, 315, 870 ? 550, 31, 110, and 250 respectively. In view of these limitations this technique would be best applied to cases of unusually high exposures, such as that encountered from solar flares.
R L Brodzinski↗
The measurement of radiation exposure of astronauts by radiochemical techniques
The principal gamma-ray emitting radioisotopes, produced in the body of astronauts by cosmic-ray bombardment, which have half-lives long enough to be useful for radiation dose evaluation, are Be-7, Na-22, and Na-24. The sodium isotopes were measured in the preflight and postflight urine and feces, and those feces specimens collected during the manned Apollo missions, by analysis of the urine salts and the raw feces in large crystal multidimensional gamma-ray spectrometers. The Be-7 was chemically separated, and its concentration measured in an all NaI (TL), anticoincidence shielded, scintillation well crystal. The astronaut radiation dose in millirads, as determined for the Apollo 7, 8, 9, 10, 11, 12, and 13 missions, was 330, 160, smaller than 315, 870 plus or minus 550, 31, 110, and smaller than 250, respectively.
Brodzinski, R. L.↗
The application of optimal control techniques to advanced manned missions, volume 2
The hybrid optimization techique for attitude control design is described in detail. The technque is capable of optimizing an n-dimensional adjustable parameter vector, but a 1-dimensional vector is used as an example to explain the procedure. This permits an easier explanation as opposed to a multidimensional case. The procedure used to derive the perturbation equations of motion describing the 6-DOF shuttle ascent phase is presented. These equations were programmed on the EAI 8800 analog computer to describe the perturbations of the shuttle vehicle from a nominal zero lift trajectory due to wind disturbances. Included are the control system equations, trim equations, and wind angle of attack equations. Analog wiring diagrams, raw data and time-varying coefficients, and state variable responses during shuttle ascent are also considered.
Connor, C. L.↗
An approximate theory of imperfect modeling with application to thermal modeling of spacecraft.
Proposal of a new concept of model testing which makes use of imperfect models and is based on the heuristic argument of representing the error states in a multidimensional Euclidean space when the errors in the modeling parameter are sufficiently small. By a separation of these errors into positive and negative groups, and from a consideration of the error paths in the hyperspaces, it is shown that the global effect of these errors may be evaluated with a good degree of approximation. Conditions under which the procedure would yield satisfactory results are discussed. To test the usefulness of the theory a computer experiment was conducted for the prediction of both transient and steady state thermal behavior of a hypothetical spacecraft using perfect, as well as imperfect, models.
Chao, B. T.↗
Generation of random hypersurfaces.
A technique to generate multidimensional random hypersurfaces with given statistical properties numerically on a digital computer is discussed in this paper. The technique is based on the linear filter theory. Using this technique, two-dimensional random surfaces are generated to illustrate the procedure. Statistics of these two-dimensional random surfaces are presented. Possible applications of these random surfaces in various physical problems are discussed.
Youakim, M. Y.↗
Computation of space shuttle flow fields using noncentered finite-difference schemes.
Second- and third-order, noncentered finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The advantages of noncentered methods over the more conventional centered schemes are: simpler programming logic, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. Second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability. These schemes are then used in a shock-capturing technique to determine the inviscid, supersonic flow field surrounding space shuttle vehicles (SSV). Resulting flow fields about typical pointed and blunted, delta-winged SSVs at angle of attack are presented and compared with experiment.
Kutler, P.↗
Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure.
Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.
Curry, D. M.↗
Computational efficiency achieved by time splitting of finite difference operators.
A technique is presented for computing multidimensional time-dependent flow fields that avoids much of the inefficiency typically found in finite difference calculations. The technique initially divides the flow field into regions, each containing a mesh of general quadrilateral cells chosen to provide spatial resolution of the local features of the flow. A finite difference operator of second order accuracy, consisting of a sequence of one-dimensional operators (each operating at near maximum Courant-Friedrich-Lewy number) is then constructed for each region. Numerical results illustrating the technique for inviscid flows about simple bodies that generate shock waves, embedded shock waves, and expansion fans are presented and compared with exact theory.
Maccormack, R. W.↗
Radiative cooling of shock-heated air in an explosively driven shock tube.
Results are presented of an experimental program to measure the effect of radiative cooling on the enthalpy distribution behind incident shock waves traveling in air. The shock velocity was nominally 16 km/sec and the preshock ambient pressure was varied from 0.4 to 1.6 torr. Shock-tube diameters of 4.7 and 9.4 cm were used to investigate the effects of varying optical depths. Radiative cooling rates were determined from spatially resolved measurements of the profile of the H sub alpha line and from absolute measurements of the continuum radiation. The measured enthalpy profiles are in good agreement with the theoretical predictions of Chien and Compton which account for both nongrey and multidimensional aspects of the radiative transport in the shock tube.
Cooper, D. M.↗
Additional comments concerning inversion techniques
The chronological development of multidimensional inversion techniques is reviewed briefly. Some current work in this area is described.
Shmoys, J.↗
Finite element solution for energy conservation using a highly stable explicit integration algorithm
Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.
Baker, A. J.↗
Source encoding of images for efficient transmission
A set of recursive rules which generate unitary transforms with a fast algorithm are presented. For each rule, simple relations give the number of elementary operations required by the fast algorithm. The common Fourier, Walsh-Hadamard, Slant, and Haar transforms are expressed with these rules. The framework developed allows the introduction of generalized transforms which include all common transforms in a large class of identical computation transforms. A systematic and unified view is provided for unitary transforms which have appeared in the literature and for a number of new transforms of potential interest. Generalization to complex and multidimensional unitary transforms is considered.
Algazi, V. R.↗
A sequence solution to the Fokker-Planck equation.
In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer.
Mayfield, W. W.↗