Showing papers on "Computation published in 1971"

Computation of characteristic modes for conducting bodies

Abstract: A procedure for computing the characteristic modes for conducting bodies of arbitrary shape is developed. The method is applied to conducting bodies of revolution and to wire objects, and general computer programs are discussed. Illustrative examples of the computation of characteristic currents and characteristic fields are given for a cone-sphere, a disk, and a wire arrow. Modal solutions using these modes are computed for representative antenna and scattering problems to illustrate convergence of the solution as the number of modes is increased.

A Heuristic Algorithm for the Testing of Asynchronous Circuits

Abstract: This paper describes an algorithm for the computation of tests to detect failures in asynchronous sequential logic circuits. It is based upon an extension of the D-algorithm [1]. Discussion of experience with a program of the procedure is given.

Cause-Effect Analysis for Multiple Fault Detection in Combinational Networks

Abstract: The important problem of generating test patterns to detect multiple faults has received little attention, mainly due to their computational complexity. The theoretical results of this paper show that near minimal tests for multiple faults can be generated with complexity of computation comparable to that of single faults.

Uniform computation of the error function and other related functions

Abstract: Uniform methods of computation, to any required degree of accuracy, for the error and other closely related functions are given. from which the above quadrature formula was derived, were included in the contour c. This means that t was restricted to the range t > h2/47r2. In this paper, we extend the method to include the cases when h is such that the poles at z = -iw lie on and outside the contour c. The respective results are

Contribution to methods for calculating the flow about thin lifting wings at transonic speeds: Analytic expressions for the far field

Abstract: The problem of determining the small-disturbance flow about two-dimensional airfoils at transonic speeds has been successfully treated by the process of matching a numerical solution of the near field to analytic expressions for the far field. The three-dimensional problem, it would appear, can be treated in a similar way with the aid of algorithms adapted to high-speed and high-capacity computers. The far-field potential for both lifting and nonlifting three-dimensional wings at transonic speeds is developed herein for a subsonic free stream. This potential could be used for a three-dimensional-wing computation similar to the computation made for the two-dimensional wing.

A new method for reduction of dynamic systems

Abstract: A new method has been presented for the determination of a low-order model approximating a high-order system. It is based on the use of the matrix pseudo-inverse to estimate the parameters of the model which minimize the sum of the squares of the errors between the response of the actual system and that of the model at the sampling instants. One of the advantages of this method is that the description of the actual system dynamics need not be known, but only the measurements of the input-output data are required. As the algorithms are iterative, computation is fairly straightforward, and the requirement for storage of input-output data depends only on the order of the assumed model, not on the number of iterations in the interval considered for minimization. An example of the application of the method for the determination of an approximate second-order model of a seventh-order system has been given, and compared with the reduced model obtained using another method.

A problem in the theory of epidemics, II

Abstract: In an earlier article the authors considered a deterministic epidemic model that accounts for certain threshold phenomena occuring in the spread of infection. The present article includes a major modification of the earlier model that allows individuals recovered from the infection to eventually become susceptible again to the infection. A set of five integral equations is derived from the basic assumptions concerning the spread of the infection. The basic theorem asserts existence, uniqueness, and continuous dependence of a solution of these equations. The proof of these results is accomplished by a contraction mapping argument that also gives a simple proof of the earlier result. A minor modification of the earlier model also is included, which brings into the scope of this study some of the older epidemic models. Some numerical computation carried out for this problem is also described.

Rearranging Matrices to Block-Angular form for Decomposition (And Other) Algorithms

Abstract: The rows and columns of an arbitrary coefficient matrix of large numerical problems can often be permuted so that substantial time can be saved in computations. For example, if a large linear programming problem has a suitable block-angular structure, one of the time-saving decomposition algorithms can be used. This article presents a systematic method for effecting such a block-angular permutation. An example and the results of manipulations of matrices with more than 300 rows and 2500 columns are shown.

Tapered Floating Point: A New Floating-Point Representation

Abstract: It is well known that there is a possible tradeoff in the binary representation of floating-point numbers in which one bit of accuracy can be gained at the cost of halving the exponent range, and vice versa. A way in which the exponent range can be greatly increased while preserving full accuracy for most computations is suggested.

Realization of Optimum Discrete-Time Nonlinear Estimators,

Abstract: : The authors discuss the problems associated with the implementation of optimal discrete-time nonlinear filters on a digital computer. For storage of the conditional densities the authors consider a point mass representation on a peculiar form of floating grid. In order to implement the Bayes-law computation the authors introduced a simplifying ellipsoid tracking technique which eliminates most of the unnecessary points from the computation. The authors also discuss a method for handling multimodal densities and a simple illustrative example. (Author)

A small-signal calculation for one-dimensional transistors

Abstract: A computation method to obtain an exact small-signal solution of a one-dimensional transistor model for high-frequency operation is presented under the assumption of negligible bulk recombination effect. Basis for the small-signal calculation is 1) a dc solution at the operating point under consideration, 2) trial potentials (electrostatic potential and quasi-Fermi potentials for electrons and holes, respectively), and 3) frequency. A scheme for iterative computation can be constructed in a manner similar to that for dc steady state given by Gummel. Discussions are made on conservation of the total currents, terminal currents relationship, as on a simplified method to obtain terminal characteristics. Some computation results will be demonstrated for potentials, carrier densities, current densities, and the current transfer factor. In the Appendix the relation between the exact solution and low-frequency treatment will be discussed.

Computation of Sensitivities for Noncommensurate Networks

Abstract: The adjoint network approach to automated network design as presented by Director and Rohrer is extended for use in gradient calculations for noncommensurate networks. The networks can contain distributed elements such as uniform transmission lines and RC lines. An example investigates gradient computations for a noncommensurate microwave network having 13 variable parameters.

The meridional distance problem for desk computers

Abstract: Existing equations for computation of meridional distance from latitude and for computation of latitude from meridional distance are modified to forms which are suitable for programming for electronic desk computers. Certain constants are given for ellipsoids in common use. Some programming hints are also included.

Effective computation over the real numbers

Abstract: Extended Turing Machines We will obtain our simplest model, the ETM, by adding to Turing Machines the ability to add, multiply, and compare real numbers. We allow real parameters to appear in an ETM's program. In this manner the set of real numbers becomes the underlying domain of our computations much as a finite set of symbols is the domain of computation of a Turing machine. As successively deeper levels of GLB are allowed, successively stronger computational systems result. Functionals which can be approximated iteratively at one level (such as differentiation) can be computed exactly at a somewhat higher level. By closing our computation scheme under the GLB-operation we obtain a system closed under limiting operations in general, but one for which the question of effectively choosing elements from effectively defined sets is presently unanswered. Indeed, the solution to this last question may depend upon higher axioms of set theory. More explicitly, take as the definition of an (ordinary) Turing machine a device consisting of (1) an infinite tape divided into squares on which symbols from some finite alphabet are written. (2) a read-write head capable of moving one square left or right under the control of (3) a finite-state-control (fsc). We consider an fsc to be a flowchart consisting of an allowable interconnection of boxes of the following forms: multiply number on tape with that in s and store result in s branch according to sign of number in s the real number beneath the head is copied into s the real number in s is written on square of top track currently scanned by the head (for c some real number) the constant c is put into s add number on top track square currently scanned to that in s and store result in s (j) s+T-+ s (i) c-+ s (1) Test s (k) s*T-+ s (h) Store s (g) Load s flowchart Any number of arrows may enter a HALT box, but none leave it (c) TEST This box has 1 outgoing arrow for each symbol in the Turing machine's alphabet. TEST causes a branch according to the symbol being scanned; if the ith symbol of the alphabet appears beneath the head when ~ TEST box is entered , control passGs to the flow-chart box indicated by the ith arrow leaving the TEST box (d) Write symbol i The ith symbol of the Turing machine's alphabet …

Deterministic Pushdown Store Machines and Real-Time Computation

Abstract: A comparison is made of the computing capabilities of deterministic pushdown store machines and real-time iterative arrays of finite-state machines. The main result is that every deterministic pushdown store computation can be performed by some (multidimensional) iterative array in real-time. The latter are strictly more powerful since they can recognize the set of palindromes in real-time, which deterministic pushdown store machines cannot do even if permitted unlimited computing time. During the development of the main result, variants of pushdown store machines, the tabulator machines and the n-dimensional pushdown store machines, are introduced. By imposing a real-time constraint and letting the number of tabs and the number of dimensions vary, an infinite hierarchy of pushdown store (deterministic context-free) languages is obtained.

Numerical Integration of the Primitive Equations with a Floating Set of Computation Points: Experiments with a Barotropic Global MODEL1

Abstract: A Lagrangean-type numerical forecasting method is developed in which the computational (grid) points are advected by the wind and the necessary space derivatives (in the pressure gradient terms, for example) are computed using the values of the variables at all the computation points that at the particular moment are within a prescribed distance of the point for which the computation is done. In this way, the forecasting problem reduces to solving the ordinary differential equations of motion and thermodynamics for each computation point, instead of solving the partial differential equations in the Eulerian or classical Lagrangean way. The method has some advantages over the conventional Eulerian scheme: simplicity (there are no advection terms), lack of computational dispersion in the advection terms and therefore better simulation of atmospheric advection and deformation effects, very little inconvenience due to the spherical shape of the earth, and the possibility for a variable space resoluti...

The computation of supersonic flow fields about wing-body combinations by “shock-capturing” finite difference techniques

Abstract: Supersonic flow field computation for wing-body combinations by shock-capturing finite difference techniques, discussing improvement based on Runge-Kutta method

Mathematical models of computation using magnetic bubble interactions

Abstract: This paper considers the computational capabilities of different mathematical models of magnetic bubble interactions. A specific model was studied earlier by R. L. Graham, who showed that there exist combinational functions of 11 or more variables that cannot be computed by this model. This paper extends his results by introducing different types of interactions which seem to be practical and enable the computation of all combinational functions. The problem of efficient computation from the points of view of time and space requirements and the geometrical requirements imposed by the fact that interactions can occur only between physically adjacent locations are also examined. Finally, a model in which computations are carried out by applying uniform magnetic fields to the entire platelet, with individual access limited to locations along the periphery, is presented.