Computer Subroutines Research Articles

Computer generated scatter dose distributions for 6-MV radiotherapy photon beams.

The time required for accurate computer dose distributions is of major concern in radiation therapy. Isodose distributions were obtained by calculating the primary and scatter radiation reaching a point. A description of the primary dose distribution, especially at the edge of the beam, requires the calculation of the dose on a finely spaced grid. However, the scatter dose distributions can be described on a much coarser grid. The primary and scatter dose distribution calculations were separated into two computer subroutines which permitted choosing the appropriate grid spacing for each dose component. A more rational partition of the computing time for the primary and scatter dose was obtained. In addition, the separation of the calculation of the scatter dose from the total dose allows one to examine the calculated scatter dose distribution as the radial and angular increments used in the Clarkson-Cunningham summation are varied. Accurate scatter dose distributions were generated with a tenfold time reduction by optimization of grid spacing and radial and angular increments.

Exact conditional tests for cross-classifications: Approximation of attained significance levels

A procedure is proposed for approximating attained significance levels of exact conditional tests. The procedure utilizes a sampling from the null distribution of tables having the same marginal frequencies as the observed table. Application of the approximation through a computer subroutine yields precise approximations for practically any table dimensions and sample size.

Analysis of shear walls using higher order finite elements

Shear walls can be simply and conveniently modelled by using higher order plane tress finite elements which have a higher degree of variation in the displacement (and consequently the stress) function. The derivation and generation of the stiffness matrices by a computer subroutine for a series of higher order plane stress rectangular elements with any number of nodes is explained in detail and the elements are applied in the idealization of different types of shear walls in which the spandrel beams and openings are treated as a continuum. Three examples of shear wall problems are analysed to illustrate the simplicity, versatility and accuracy of this method as compared with the results of other available methods.

Simulation procedures for Box‐Jenkins Models

New simulation procedures are presented for generating synthetic data from either a nonseasonal or a seasonal Box‐Jenkins model. The simulation techniques are designed so that random realizations of the underlying stochastic process are employed for starting values. Because fixed beginning values are not utilized, systematic bias is not introduced into the synthetic trace. When the data have been transformed by a Box‐Cox transformation, the inverse transformation can be conveniently incorporated into the simulation process. Also a new algorithm is presented for simulating integrated models. A method is developed for incorporating parameter uncertainty into simulation studies, and it is explained how this technique can be used in the design of reservoirs. Practical applications are presented to demonstrate the efficacy of the aforesaid simulation methods. In addition, the Fortran computer subroutines for the simulation procedures are included in an appendix with the microfiche edition of this paper.Appendix is available with entire article on microfiche. Order from American Geophysical Union, 1909 K Street, N.W., Washington, D.C. 20006. Document W78‐006; $1.00. Payment must accompanyorder.

Network layout procedure for printed - circuit design

This paper describes a heuristic solution procedure for laying out the conductors of a printed circuit on the two sides of a plate of nonconducting material. There must be no overlap between conductors on the same side of the plate as they are uninsulated. For certain layouts it is necessary to drill holes in the plate and pass conductors through the holes to avoid overlap. The problem is to identify the layout which requires the minimum number of holes. The solution procedure uses a computer subroutine in conjunction with an iconic model of the plate. The subroutine is based on a method of Nicholson 1 which attempts to lay out a given circuit on one side of a plate to minimize the number of overlaps. The iconic model of the plate used in this research consisted of a pair of plastic sheets, representing the two sides of the plate, overlaid one on top of the other. The nodes and connections were drawn on them with felt-tip pens. The procedure is iterative and takes advantage of the fact that the problem can be viewed in terms of graph theory. The procedure is suitable for an interactive computer terminal system. Computational experience is limited but encouraging. However there is no guarantee that solutions produced by the procedure will be optimal in the sense that an absolute minimum number of holes will be required to be drilled.

Diurnal motion of the Sun as seen from Mercury

The quantitative description of the motion of the Sun as observed from Mercury is a problem suitable to a variety of classes. The only difficult aspect for introductory students is a determination of the position along the orbit for the planet. Two methods are described and a listing of a computer subroutine is included. The combination of slow rotation and high eccentricity of Mercury’s orbit makes this problem an interesting one.

Design method for ultrasound transducers using experimental data and computers

An approach is described for designing thickness mode ultrasound transducers. A computer subroutine is used to simulate the frequency response of a transducer in the transmitting or receiving mode. The physical parameters of the piezoelectric ceramic required for the design are obtained with conventional instrumentation. Two of the parameters (e33 and an equivalent resistance to represent losses) are calculated with the aid of a computer program which makes use of the measured impedance versus frequency. An example of design is presented.

A problem-oriented mathematical optimization course

A one-semester applied mathematical optimization course has been developed at the University of Wisconsin-Green Bay. The problems for the course were derived from the current research literature in environmental sciences. The use of computer subroutines for problem-solving is a key feature of the course.

The computer aided design of structural concrete sections subjected to combined loading

The paper describes a Computer Subroutine that may be employed to design the reinforcing steel of reinforced and prestressed concrete sections subjected to vertical shear, lateral shear, vertical bending, lateral bending, torsion and axial load. The Subroutine, called DEVAST ( Design by the Variable Angle Space Truss) is based on a space truss model that is capable of predicting the post-cracking behavior of rectangular structural concrete sections subjected to combined loading. Since the space truss model can be used to predict the full post-cracking response of concrete beams under combined loading (i.e. strain in the longitudinal and web reinforcement, as well as the various deformations of the beam at all load levels), it is possible to predict the load combination that will result in yielding of either the longitudinal or the hoop steel. As a simple and conservative design criterion for use in Sub-program DEVAST, the reliable capacity of the section is taken as the load corresponding to first yielding of the steel. Although conceived as a Sub-program to be used in conjunction with a Main Program that performs the structural analysis, this Subroutine may very simply be modified for use as a self-contained design program. A listing of Sub-program DEVAST written in FORTRAN IV is provided in the paper.

Unit algorithms

A computer subroutine implementing the Householder QR algorithms for diagonalizing real symmetric matrices is presented. The subroutine differs from previous versions in requiring only a single N × N array for storage in order to diagonalize an N × N matrix.

A computer-aided snowmelt model for augmenting winter streamflow simulation in a southern Ontario drainage basin

A lumped-parameter mathematical model is formulated to represent the physical processes of the accumulating and melting snowpack within a drainage basin. Common theoretical descriptions of the processes represent snow accumulation and melt at a point, but computer-aided procedures facilitate spatial distribution of the model inputs and thus provide for a digital simulation of the basin-wide snowpack condition and melt with time. The model is treated on the basis of the energy flux and mass transfer processes relating to the average snowpack, across the snowpack–atmosphere and snowpack – ground surface interfaces. An awareness of the likely lack of the extensive meteorological data usually required for proper application of such models, necessitates reliance on a number of literature-cited and locally derived empirical snowmelt relationships in order to ensure a practical and viable model. Thus, auxiliary computer subroutines are formulated to provide for applicable options, depending on the availability of real-time data. The purpose of the snowmelt model is to serve as a monitor of net basin input, complementing an overall comprehensive integrated hydrologic system model for use in streamflow simulation. The model is calibrated and tested with real-time data in a Ministry of the Environment-IHD Representative Drainage Basin in southern Ontario. Its applicability in estimating maximum flood flows during spring runoff periods is demonstrated by imposing meteorological conditions favourable for continuous melting upon maximum snowpack storage conditions.

Dynamic response of soil/concrete interfaces at high pressure: Huck, PJ Liber, T Chiapetta, RL IIT Research Inst Report, April, 1974, 308P, AD-778101

Abstract : Although finite element programs capable of dealing with free field soil behavior and structural response currently exist, little is known of soil/concrete interfaces dynamically loaded at high stress levels. It was the purpose of this study to conduct dynamic interface experiments at normal stresses up to 1500 psi, devise from first principles an analytic interface response model, and write a subroutine to include the model in existing finite element programs. The experimental work was accomplished in a simple shear device using two soil types (sand and clay). A method for describing concrete surface texture quantitatively was devised. The analytic model was founded on basic frictional mechanisms as applied to particulate mechanics. The computer subroutine written for the model was exercised against the experimental data. (Author)

Process training derived from a computer simulation theory

Kotovsky and Simon (1973) identified four basic subprocesses in their computer simulation of adult and adolescent performance on Thurstone letter series completion problems. In Experiment I, children from Grades 1 to 6 were pretested on those problems, and then experimental subjects were trained on two of the four processes as an attempt to experimentally support a correspondence between the computer subroutines and human cognitive processes. A posttest administered in the experimental and control conditions revealed a significantly greater improvement for experimental subjects, although both groups made significant gains. The children's distributions of errors were consistent with Kotovsky and Simon's predictions. In Experiment II, children from Grades 3 and 5 took four series completion tests without intervening training. The additional practice was sufficient for Grade 5 subjects to make improvements similar in magnitude to those produced by training. Grade 3 subjects, however, made no gains. These results are related to Tulving and Pearlstone's (1966) distinction between the availability and the accessibility of memory traces.

UNIT HYDROGRAPHS – A COMPARATIVE STUDY1

ABSTRACT. Unit hydrographs derived by using two methods, linear programming and least squares, are compared. Test data comprise rainfall and runoff information from four storms over the North Branch Potomac River near Cumberland, Maryland. The mathematical bases of these methods for unit‐hydrograph derivation are explained. The linear programming method minimizes the sum of absolute deviations, and the least squares method minimizes the sum of the squares of deviations. Computer subroutines are readily available for application of these methods. The unit hydrographs derived with the two methods are practically the same for storms 2 and 3, but differ somewhat for storms 1 and 4. However, the reconstituted direct surface runoff hydrographs are similar to those observed with the exception of the hydrograph for storm 4 which had a relatively more non‐uniform rainfall excess of a considerably larger duration.

Data Processing in Three‐Dimensional Texture Analysis

To the background of purely computative problems of three‐dimensional texture analysis, the characteristics of an extensive system of computer subroutines, which allow certain standard calculations to be carried out, are presented. These subroutines are written in FORTRAN, and are easily adapted to any computer possessing a FORTRAN compiler.

Numerical Calculation of Psychrometric Properties in SI Units

ABSTRACT THREE computer subroutines for numerical calculation of psychrometric properties are discussed. Input parameters required are wet- and dry-bulb temperatures, dew point and dry-bulb temperatures, or relative humidity and dry-bulb temperature. All results are in SI units. Restrictions on the use of certain relationships are discussed.

Post-experiment introduction of constraints on parameters

An extension or modification of the output of least-squares computer subroutines is proposed in order to enable the researcher, who is confronted with an unreasonable parameter estimate, to investigate the effect of changing this value on the other parameter estimates and the estimated residual variance by simple hand computation.

Efficient FORTRAN subprograms for the solution of elliptic partial differential equations (abstract)

The purpose of this paper is to describe technical note, NCAR TN/IA-109, which is intended to provide scientists with a package of computer programs which make use of current methods for solving elliptic partial differential equations. Computer models of geophysical processes often require the numerical solution of elliptic partial differential equations. This is particularly true for models which make use of stream functions, velocity potentials, or vorticity equations, or in which the pressure of an incompressible fluid is computed. The numerical solution of elliptic equations can be a formidable programming task. Also, the equations are often time-dependent, requiring repeated solutions and, hence, considerable computing resources. Efficient, reliable, and well-documented computer subroutines for solving such equations are needed. With recent advances in computing methods, it became apparent to the authors that a very large class of elliptic equations (separable) could be solved rapidly and with minimal storage. Of particular importance was the fact that, as a result of work on singular problems, this class was free of special cases for which solutions could not be obtained numerically.

Compressibility of Natural Gases

Abstract A new correlation for the compressibility of sweet and sour natural gases ispresented. This correlation is derived from an equation of state whichadequately represents the Standing-Katz Z-Factor chart. The algebraicexpression for compressibility presented here is suitable for computercalculations. A FORTRAN subroutine to perform this computation is alsopresented, along with a graphical form of the correlation. INTRODUCTION IN THE PRESSURE ANALYSIS of transient or pseudo-steady-state flow Dataacquired during gas well testing, a knowledge of the variation of fluidcompressibility with pressure and temperature is essential. For liquid flow, the compressibility is small and is usually assumed to be constant. For gasflow, the compressibility is neither valid nor necessary of a real gas can becomputed readily. Trube (1957) has presented graphs from which the compressibility of natural gases may be obtained. This correlation is, however, difficult to usein a computer program. Recent developments have made possible a more consistentand convenient approach. The purpose of this paper, therefore, is to present An analytical technique forcalculating the compressibility of natural gases. The procedure may be readilycomputerized and was used to generate curves of pseudo-reduced compressibility, which are useful for manual calculations. Theory (Equation in full paper) Graphical Presentation The computer subroutines mentioned above were used to generate cr as a function of Pr and Tr. Figure 1 is aplot of c r versus pr for various values of Tr. In this figure, the curves are too close together for easy andunambiguous reading. In order to increase the separation of the isotherms, especially for the low-pr range, c r T r wasgenerated and plotted versus Pr for various values of Tr as shown in Figures 2 and 3. The separation between the isothermsin these figures is sufficient to make them easy to read and hence suitable forreasonably accurate manual calculations of compressibility. Sour Gases The correlation developed for c r in terms of (aZapr) and the graphical representation of cr Trare applicable to sour as well as sweet natural gases. A simple method has beendeveloped by Wichert and Aziz (1972) to account for the presence of H.S and CO2 in the use of the Standing-Katz Z-Factor chart. Inthis method, the pseudo-critical properties of a sour gas are adjusted togive: (Equation in full paper) The calculation procedures are then exactly the same as discussed previously, except that T12 and p1c must beused instead of T2 and po respectively. Discussion Figure 4 compares some of the isotherms for reduced compressibilitydeveloped by Trube (1957) with corresponding isotherms from Figure 1 Thedifference between the two methods is no doubt due to the different techniquesutilized to obtain Z and (aZ/a2r)Tr. Trube used the Standing-Katz Z-Factor chart re- produced by Brown et al.(1948, p.38) to obtain values of Z and (aZ/apr)substituted thesevalues into Equation (4), and calculated c, as a function of pr and Tr.

Further On the Calculation of Friction Factors For Use In Flowing Gas Wells

Abstract A comparison of two computer subroutines to calculate friction factors from the Moody(2) chart has been made. The comparison shows that, contrary to the claim of Dranchuk and Abou-Kassem(1), their method and that of Aziz et al.(5) give identical results in the partially-rough-wall and the fully-rough-wall turbulence regions. The transition from the former to the latter is predicted to occur at slightly different Reynolds numbers in the two methods because of the choice by Dranchuk and Abou-Kassem of an arbitrary transition criterion. Both routines are suitable for computer calculation of friction factors, but the Aziz et al. method is more efficient, requiring fewer iterations. IN A RECENT TECHNICAL NOTE, Dranchuk and Abou Kassem(l) recommend the use of the Moody chart(2) instead of approximate relationships to determine friction factors in pressure-drop calculations for flowing gas wells. Without doubt, fundamental equations with a properly chosen friction factor based on the correct reynolds number and the best estimate of the relative roughness will yield more accurate pressure-drop predictions than equations incorporating approximations for the friction factor(3). (Equation in full paper) Dranchuk and Abou-Kassem compare Darcy-Weisbach friction factors calculated by their own and the Aziz et al. method and arrive at the following conclusions: The Aziz-Govier-Fogarasi method:generates Fanning friction factors;yields values which are higher than Colebrook at low values of Re and lower than Colebrook at high values of Re;yields values which are higher than Moody at low values of Re and lower than Moody at high values of Re when flow is in the transition zone) but higher than Moody at low values of Re and lower than Moody for high values of Re when flow is fully turbulent;cannot generate values for smooth pipe." These conclusions seem unwarranted. Table 1 shows a comparison of Darcy-Weisbach friction factors calculated by the two methods for a wide range of relative roughnesses and Reynolds numbers. The comparison shows that:the friction factors are exactly the same in the PRW and FRW regions, as they should be, because both routines use the same equations;a slight difference (half a per cent or less) at the transition from PRW to FRW turbulence due to the difference in the transition criterion chosen by Dranchuk and Abou-Kassem and the assymptotic approach used in the Aziz et al. routine;the Aziz et al. routine is more efficient, requiring fewer iterations. (Table in full paper) Keeping in mind that Moody indicated that his chart would predict friction factors with no better than 10 per cent accuracy, the small differences are insignificant. The friction factors, for practical purposes, are the same. Finally, the Aziz et al. method was not intended for the calculation of friction factors in smooth pipes. It was designed only to deal with the practical problem of estimating pressure drops in actual gas wells, which may always be expected