Showing papers on "Computation published in 1968"

Computer representation of excitation systems

Abstract: The availability of large digital computers has permitted more extensive computation of power system stability, a subject of increasingly greater importance. This paper suggests a common nomenclature and control system representation of the various excitation systems now available. It can be used to define input data requirements for computer programs, and can provide a consistent format in which manufacturers can respond to requests for excitation system data to be used for system studies.

The Use of a Square Grid System for Computer Estimation of Precipitation, Temperature, and Runoff

Abstract: Studies on water resources in the last few years have had the tendency to encompass larger and larger areas The increase in size and sophistication of these studies makes the use of computers almost mandatory To adapt computers to this type of study, the study area must be converted to a schematic representation which is easily manageable by computers A simple and reasonable way of doing this is to cover the study area with a square grid, which may then be considered as consisting of a matrix of squares This system can be used to store, process, and retrieve information and may have numerous applications in the fields of hydrology, hydraulic power, economics, etc The paper presents the application of the square grid system to the estimation of the precipitation, temperature, and runoff distribution in a large area and shows how the use of the system enables efficient combination of the meteorologic and hydrologic information available in assessing the precipitation, temperature, and runoff distribution An example of such a computation for a 43,000-square-mile area is shown and the advantages of the method over the usual techniques emphasized

Littoral drift as function of waves and current

Abstract: For the computation of littoral drift due to waves hitting a coast obliquely, most formulae are based upon the assumption that this longshore transport is some function of the energy flux of the waves towards the coast. For the actual computation the component of this flux parallel to the coast is introduced. Most of the available prototype data are incorporated m the formula of the U.S. Army Coastal Engineering Research Center (ref. 4 and 1). In this formula no reference is made to the gram size and the slopes of beach and foreshore. The explanation for the fact that nevertheless reasonable results are obtained is probably owing to the fact that variation of gram size and beach slope for sandy beaches is not so very great. A more serious disadvantage is, however, that it is not possible to take into account the influence of a possible longshore current which is not generated by the wave motion, such as for instance tidal currents. In this paper an attempt is made to compute the littoral drift, starting from the longshore current velocity as it is generated by the waves or as it may originate from other causes (ref. 4). For the actual computation of the bed load transport a normal bed load transport formula is used, in which, however, according to the method developed by the author in earlier studies, the bed shear is increased as a result of the wave motion (ref. 2). From the tests briefly described in the present paper it becomes clear that the transport may be treated indeed as a function of the longshore current, even when this current has a direction opposite to that of the component of the wave propagation parallel to the coast.

Analog methods for computation of the generalized inverse

Abstract: In this paper some properties of the generalized matrix inverse are discussed leading up to two analog techniques for its computation. Analog procedures are given for the computation of the unique vector x of least Euclidean norm that minimizes the Euclidean norm of the error vector Ax - b .

Analysis of Elastically Coupled Piezoelectric Resonators

Abstract: This paper presents an analysis of an elastically coupled piezoelectric resonator system consisting of a linear array of two or more counter electrode pairs placed on the major surfaces of a quartz crystal plate. Each pair of counter electrodes establishes resonator having a transverse thickness mode of motion. The equations describing this system are derived and applied to an array of n coupled resonators and specific numerical computations are made for the cases where n is equal to 2, 3, and 6. These results are plotted and show the dependence of the effective interresonator coupling on the dimensions of the electrode configuration.

Solution of Nonlinear Equations

Abstract: —A new approach to solving a set of nonlinear equations, described by fi(x1, x2, . . ., xn) = 0, i= 1, 2, ..., n, is presented. The computation is carried out by simple matrix inversion and matrix multiplication without evaluation of ∂fi/∂xj. Thus, computation time is saved. The method converges rapidly if the initial approximation is close to the solution. A specific example, using nonlinear equations with two variables, shows the application of the method.

Coulomb Integrals over Slater‐Type Atomic Orbitals

Abstract: New general analytical formulas are derived for the two‐center Coulomb integral between real, Slater‐type atomic orbitals of arbitrary integer quantum numbers. The integral is expressed as a finite sum over powers and certain auxiliary functions. Procedures are given for numerical evaluation which are particularly suitable for use with an electronic digital computer of large storage capacity. Computation times are quoted.

On the evaluation of e Aτ

Abstract: The purpose of this letter is to present a method for computing the transition matrix of linear time-invariant systems. Due to the important role the transition matrix plays in linear system response, several methods have been put forward for its computation. A numerical computation method, which avoids the use of the eigenvalues, for the evaluation of the transition matrix is presented here.

Techniques for Analysis of Large Structures

Abstract: This paper attempts to evaluate the various methods available for the solution of large sparse linear systems from the point of view of minimizing the computer time required for their execution. First, the more obvious classical methods are considered. These are then related to the work of Kron and the various substructure techniques. Finally, the theoretical aspects of optimum computation are discussed in the light of the practical aspects of the problems of machine computation.

An elementary design procedure for digital filters

Abstract: The purpose of this paper is to parallel for digital filters the type of synthesis that might be found in a first course in circuit or control theory. The method described emphasizes the digital formulation as a separate entity rather than a carry-over from one domain to the other by means of conformal mappings. Implementation problems are considered, particularly that of the volume of computation required for operation of the filters.

Computation of minimal representations of a rational transfer-function matrix

Abstract: A new method is given for obtaining a minimal representation of a rational transfer-function matrix. The computation involved and the storage requirements are less than those for other methods.

Network-Flow Method Applied to Load-Flow Calculation

Abstract: This paper aims to apply a network-flow method for the load-flow calculation in electric power systems and to discuss a computer handling technique from the computational aspects. An attractive feature of the new method is its ability to handle calculation rapidly without requiring so large an amount of computer memory. The program based upon the proposed method has been developed, and a flow diagram for the algorithm is presented. A numerical example for the calculation is also described as well as the convergence characteristics of the solution of computational processes. The method is compared with a conventional one from viewpoints of computation time and data storage space.

A Ray‐Tracing Program and its Application to the Computation of Frequency Deviations in a High‐Frequency Signal

Abstract: A two-dimensional formulation based on Fermat's principle is used to compute electromagnetic rays in the ionosphere in geocentric polar coordinates. The geomagnetic field and electron collisions are omitted. Digital and analogue computers are used. The accuracy of the digital program is sufficient to compute frequency deviations due to ionospheric disturbances by a direct method.

Planck functions and integrals - Methods of computation

Abstract: Black body radiation - numerical solution for computer and hand calculation of total intensity over specified spectral range

A multi-level computer organization designed to separate data-accessing from the computation

Abstract: The computer organization to be described in this paper has been developed to overcome the inflexibility of computers designed around a few fixed data structures, and only binary operations. This has been accomplished by separating the data-accessing procedures from the computational algorithm. By this separation, a new and different language may be used to express data-accessing procedures. The new language has been designed to allow the programmer to define the procedures for generating the names of the operands for each computation, and locating the value of an operand given its name.

On the computation of transition matrices for time-invariant systems

Abstract: A method for calculating transition matrices for linear time-invariant systems is presented which is much faster than the direct series approach and which, because of the reduced computational requirement, provides better accuracy

Computation of backscattering cross section of plasma-clad metal cylinders by the "Layer method"

Abstract: A numerical method is presented for the computation of backscattering cross section per unit length for parallel polarization at normal incidence of a plasma-clad metal cylinder. The technique employed is well suited for use on present-day high-speed computers. The method is capable of handling plasmas varying in an arbitrary manner in the radial direction.

Statistical estimation in inertial navigation systems.

Abstract: Although navigation systems have generally been developed by solving exactly the dynamic equations of motion, in reality the navigation problem is a statistical one since there are unpredictable errors in the measurements. The advent of very powerful navigation computers makes it possible by using statistical filtering techniques to retrieve more of the information contained in the navigation measurements. The navigation system is thus developed here as an information-filtering problem rather than a simulation of a deterministic physical system. The Kalman optimum linear filter is found to apply to the navigation problem if some technique is used to account for possible non-Gaussian maneuver accelerations. A major problem in the application of statistical techniques is the tremendous amount of computation required. Two methods are suggested which greatly reduce the amount of computation with a minimum degradation in the performance of the system. In one method, physical considerations are used to divide the total filter into smaller, simpler filters. In the other method, the optimum gains are precomputed and approximated by simple functions in the flight computer. The details are given for the alignment and calibration of an inertial platform using statistical filtering.