Digital Computer Calculations Research Articles

Digital computer calculation of the electric potential and field of a rod gap

The electric field and potential distribution in the gap between a cylindrical rod having a hemispherical tip and an infinite plane perpendicular to the cylinder axis was determined using a charge simulation technique. This method assumes a charge at the center of the hemisphere and a finite number of semi-infinite axial charges in the cylindrical portion of the rod electrode. Boundary conditions in the cylindrical and spherical portions enabled the formulation of simultaneous equations whose digital solution yielded the assumed lumped charges. The digital computer program provided values of the potential and both field components anywhere in the gap with an accuracy of about 2 percent.

Calculation of right and left cardiac ventricular volumes. Method using standard computer equipment and biplane angiocardiograms.

A method has been described for the digital computer calculation of intracardiac ventricular volumes from orthogonal biplane x-ray images. It is directly applicable to both left and right ventricles and uses equipment commonly found in medium size computer centers. Validation of the method is presented using data from geometrical shapes and casts of human ventricular cavities.

Design Considerations for a Semiiconductor Sandwich Fast Neutron Spectrometer

Semiconductor sandwich fast neutron spectrometers, using the Li6 or He3 reactions, are considered for use in measuring reactor type neutron spectra. Extensive digital computer calculations were performed in order to analyse the performance of these spectrometers. Areas treated were: 1. Response Functions - Characteristic resolution response functions were calculated for various layer thicknesses of Li6F and gold at a number of different energies. Results compare favorably with existing experimental data; 2. Detection Efficiency - The relative detection efficiency, for detection of the reaction products in coincidence, was calculated for both Li6 and He3 spectrometers as a function of energy, detector orientation angle and low level discriminator setting. The net relative detection efficiency, for any incident angular neutron distribution, can be obtained by weighted integration of these curves. The detection efficiency effect was found to be significant, especially for the He3 spectrometer; 3. Silicon Background Response - The true coincidence background response, due to reactions occurring in the silicon of the diodes, was calculated for the cases of incident fission and incident Pu-α-Be spectra. The background was found to be primarily due to the ground state (n,p) and (n,α) reactions. The results are in good agreement with available experimental data. A circuit arrangement, using fast (<30 nsec) electronics to minimize gamma ray pileup effects, low level discriminators to eliminate thermal neutron response if desired, and fast gates to minimize pulse pileup in the microsecond part of the electronic chain (multichannel analyser), has been designed and built for use with Li6 spectrometers.

Analogous studies of simultaneous conductive and radiative heat transfer

The process of radiative heat transfer is electrically simulated by using voltage-dependent resistors in conjunction with current transference circuits, and so an analogue is devised which shows how the overall uni-directional heat transfer by simultaneous conduction and radiation across a transparent gas space is a function of the positions of radiation shields which may be interposed between the bounding surfaces. The results for single and double shield systems are in close agreement with digital computer calculations and suggest a relatively simple procedure for establishing a favourable set of positions of any number of shields.

Natural Convection in a Rectangular Cavity with Internal Heat Generation

Applications to nuclear reactors have revived interest in natural convection. A rectangular closed cavity with internal heat generation and wall-cooling roughly simulating a channel of an internally-cooled homogeneous reactor core has been studied theoretically and experimentally.The basic equations of continuity, Navier-Stokes, and a modified energy relation including a volumetric heat source are normalized to show the dependence on the following nondimensional parameters: i) Nusselt number based on width; ii) Prandtl number, and iii) product of Rayleigh number based on width and aspect ratio, a/b, of the cavity. The complexity of these equations allows only numerical solutions, which are obtained following a modified Squire’s method consisting in assuming temperature and velocity profiles. These are substituted into the nondimensional equations, and integrated across the cavity, resulting in a still complex system of differential equations in which the dependent variables and unknown functions are the thickness, velocity, and temperature of the rising core of fluid. The coefficients in the equations are functions of the core thickness, more or less complicated according to the velocity and temperature profiles assumed. Two cases are considered: a simplified temperature profile, as used by Lighthill; and a more sophisticated profile with a positive maximum. Both velocity profiles are Lighthill’s. Digital computer calculations using a fourth-order Runge-Kutta method yielded solutions that follow the typical one-fourth power law: Nu = C(m, σ)[(a/b)Ra]1/4, where 1/2m is the slope of the wall temperature distribution, assumed linear. To include liquid metals, C was computed for 0.01 ≤ σ ≤ 10.The parallel experimental study confirms the existence of a positive maximum in the temperature profile, previously not reported. Introduction of this innovation in the theoretical treatment leads to excellent agreement with experimental results, and has the general effect of lowering the theoretical curves Nu = f[σ,(a/b)Ra]. Semiquantitative experimental data on the velocity field also indicate the existence of a positive maximum in the velocity profile until now not reported.

Automatic digital data acquisition and computer calculation in amino acid analysis

Amino acid analysis data acquisition and computation have been automated by ( 1) measuring the ninhydrin color with a spectrophotometer which is linear with respect to optical density, ( 2) digitizing the data directly from the photometer circuit by means of a digital voltmeter, and ( 3) formating and punching the digital data in paper tape so that each data word is identified as to channel of information (i.e., cuvet position and wavelength), and processing the punched data on a computer using a FORTRAN program. The program edits the data with regard to noise, compensates for baseline changes of various types, splits unresolved peaks, and calculates peak areas over a range of optical densities from 0 to 3.000. This system, in daily use in our laboratory, provides increased accuracy and saves approximately 2 man hours per analysis.

PRECISION OF FIELD EXPERIMENTS WITH VEGETABLE CROPS AS INFLUENCED BY PLOT SIZE AND SHAPE: III. POTATOES

Uniformity trial data together with certain cost assumptions for potatoes indicate that long narrow plots are the most efficient. The basic unit was 4 ft long and 3 ft wide. A minimum of two basic units would be necessary for most potato studies with a maximum of six basic units depending upon the requirements for each experiment. Thus the optimum plot size could range from 3 ft wide and 8 to 18 ft long. Where smaller size becomes optimum more replications are required. Long narrow replicates likewise appear to be more efficient than either wide or square ones.The logical analysis and a generalized flow diagram for digital computer calculation of these data are presented.

An Analogue Computer Study of the Collapse Stage of the Linear Z-plnch†

A special-purpose analog computer, that solves the so-called snow-plough equation describing the initial collapse stage of the linear Z-pinch discharge, is described. Collapse curves, generated by the computer for a low energy (5.4 kJ) Z-pinch in argon and nitrogen, are presented. These compare favorably with digital-computer calculations and with photographic measurements of the discharge development. (auth)

Digital Computer Calculation of Transients in Electric Networks

This paper describes a new digital computer program for the solution of transients in linear electric networks. The program eliminates a number of obstacles uncovered through studying an earlier, published digital computer program. It is being applied to the solution of single-phase transient problems in power systems by several independent groups. The program may be applied directly to the solution of 3-phase problems, although further work in network reduction is required to this end.

On the Thermodynamic Properties of Solutions of Polar Polymers. Theory

In this paper we present a simple analysis of the thermodynamic properties of solutions of polar polymers. It is found that: (a) In the dilute solution regime, a cluster analysis identical with that used in the theory of solutions of nonpolar polymers can be developed, but with the thermodynamic parameter z now dependent on the dipole moment, dielectric constant, etc. (b) In the concentrated solution regime, a continuum theory can be developed based on the assumption of uniform mixing of polymer chains and the use of cavity field and reaction field arguments. (c) For dilute solutions of a polar polymer in a nonpolar solvent, or a nonpolarizable polar polymer in a polar solvent, the system is equivalent to an ordinary nonpolar polymer-poor solvent system. (d) It is generally true that the solvent becomes poorer as the dipole moment and/or polarizability of the segment are increased. Also, the solvent becomes better as its dielectric constant increases. (e) In the case of concentrated solutions of a polar polymer in a nonpolar solvent, the polar contribution to the Flory-Huggins free-energy parameter, χp, decreases with increasing concentration. (f) In the case of concentrated solutions of a nonpolar polymer in a polar solvent, χp increases with increasing concentration. (g) The dilute solution theory and concentrated solution theory predict the same functional form for χp in the limit of zero polymer concentration, but the numerical coefficients differ. (h) The results of extensive digital computer calculations are presented in terms of the predicted concentration dependence of χp with varying properties of both polymer and solvent. Agreement between theory and experiment is examined in detail in the following paper.

Digital Computer Calculation of the Operation of Nonlinear Devices with Energy Storage Elements

This paper presents results on digital computer calculation of the operation of some tube and transistor circuits which combine nonlinear operation with energy storage elements. The Class C amplifier, the frequency multiplier and the blocking oscillator are all circuits of this type. This approach allows many of the conventional restrictions on analysis procedures to be removed. For instance, in the case of the Class C amplifier, it is not necessary to assume that the plate and grid voltages are sinusoidal and the circuit at steady state. Additional features of computer use are the automatic calculation of efficiencies, plotting of waveforms and calculation of harmonic content; the facility of studying the effects of transients and modulation; the possibility of allowing the circuit parameters to take on any values or vary with time or with the voltages and currents; and the possibility of allowing the circuit associated with the device to be more complicated than usually allowed by other methods. Limitations to this approach lie in the cost of programming the problem, and the cost of running the program on an available computer. Questions of numerical accuracy sometimes arise, but can usually be handled with additional programming or running time. If a translator is available which can accept programs in the form of algebraic equations, the programming cost is often negligible. However, running time costs may be appreciable, particularly in the case of a complicated circuit with many storage elements.

Atmospheric emission and opacity at millimeter wavelengths due to oxygen

The theory of Van Vleck and Weisskopf has been used to compute the emission and opacity of the earth's atmosphere in the wavelength region from 7.5 to 3.7 mm. Equal pressure broadening was assumed for the 25 oxygen transitions which occur in this spectral region. The line-broadening parameter Δv was set equal to 600 Mc/s for T = 300°K and P = 1 atmosphere, and the temperature dependence was assumed to be proportional to T−0.85. Digital computer calculations were made of τo, the total zenith opacity of the atmosphere as a function of frequency v. In these computations the ARDC model atmosphere was used, and excellent agreement was found with measured values of τo at 6-mm and 4.3-mm wavelengths. Emission was computed similarly in terms of To (theta), the antenna temperature contributed by oxygen for observation at a zenith angle θ. Computations were made of τo and To for elevations of 0, 2.5, 3.5, 8, and 30 km above the earth in order to determine the advantages of various sites for astronomical observations in this wavelength region. The radiation from the atmosphere into space was also computed, and the oxygen lines were found to appear in emission.

Resonant Beam Extraction from an A. G. Synchrotron

The resonant extraction method previously proposed for the normally constant gradient synchrotron has been extended to alternate gradient accelerators. It is found that perturbation field gradients which contain circular functions of arguments 2νx, 2νx+1, 2νx+2 are particularly effective in causing the radial betatron oscillations to grow exponentially at a particular azimuthal position. The analytical procedure for predicting which perturbations give optimum results, and digital computer calculations verifying these predictions, are presented.

A solution to the periodic-flow regenerative heat exchanger problem

An analytic solution to the problem of the periodic flow, regenerative heat exchanger is presented. The closed form solution based upon the usual simplifying assumptions permits rapid digital computer calculations of the heat exchanger design characteristics and effectiveness. The regenerator effectiveness calculated from this solution is compared with the result using the finite difference numerical technique.

Computation of the Equilibrium Composition of Burnt Gases

The multicomponent chemical equilibrium composition problem is discussed generally and a formulation of it is presented in a form suitable for digital computer calculations. A geometric interpretation of the equations used to specify the chemical system is also given.

The Quantum-mechanical Calculation of One-electron Properties

Two-center moment integrals for SLATER-type atomic orbitals are explicitly expressed in terms of a general formula involving the three quantum numbers and the effective nuclear charge of each of the two orbitals, the internuclear distance, and the usual A and B functions. A corresponding expression for one-center moment integrals is also given. The use of the one- and two-center moment integral formulae in digital computer calculations is discussed.

Synchronous-Mackine Design Using a Digital Computer

Digital computers have revolutionized electric machine design procedures for transformers and induction motors, yet little has been written on the application of digital computers to synchronous machine design. This paper converts one synchronous machine designer's method into a computer program, showing the steps and logic involved. The design method chosen, while admittedly not the latest nor considered the best, is not proprietary but the procedure developed does result in a complete machine design. The heart of a digital computer calculation is the flow chart giving the detail of the calculations to be performed and the logic steps involved. A flow chart resulting in a workable digital computer program is developed in as much detail as possible. Finally comments are made upon implementing the flow chart on a large digital computer.

Quantum-Mechanical Calculation of One-Electron Properties. I. General Formulation

For a one-electron operator, general formulas for weighted transition functions, weighted density functions, and their integrals are introduced. A detailed treatment is given of the expressions that are obtained from these formulas when they are applied to a system whose wave functions are expanded in a series of determinants of one-electron spin orbitals. Explicit consideration is given to the nonorthogonality problem and a method for the exact inclusion of overlap terms is formulated. The simplifications resulting from the use of the single determinant approximation and orthonormal functions are discussed. A brief evaluation of the suitability of the formulation for digital computer calculation is given.

Molecular Beam Resonances in Oscillatory Fields of Nonuniform Amplitudes and Phases

Molecular beam resonances are discussed for molecules subjected to various combinations of nonuniform fixed and oscillatory fields. The transition probability equations are reduced to forms which are suitable for digital computer calculations. A UNIVAC computer program for the calculation of the shapes of the resonances has been developed which is applicable to systems involving simultaneous transitions between two or three different energy levels and to cases where the magnitudes of the fixed fields, the amplitudes of the oscillatory fields, and the phases of the oscillatory fields vary arbitrarily throughout the transition region. The calculation is applicable to systems perturbed at as many as nine different frequencies simultaneously and to arbitrarily determined molecular velocity distributions. Curves are shown for molecular beam resonances with two, three, and four separated oscillatory fields and for resonances with a gradually applied single oscillatory field. The effects of phase variation along the beam in distorting a separated oscillatory field resonance are discussed.

The digital computer and power system short-circuit calculations

Precalculation of short-circuit currents is necessary in order to provide effective protection of power systems against possible short circuits. A method for determining these currents by means of a digital computer is described. Among its advantages are speed, accuracy, and the ability to be operated without highly trained professional personnel.