bluuebunny/crossref_metadata_2025 huggingface dataset:
Simulation of Human Problem-Solving Method
Authors: Johnson D.L. , Holden A.D.C.
Published: March 2008

One of the most intriguing and potentially important applications of the digital computer is in the simula tion of human thought processes. The objects of thought when suitably coded can be transformed, classified and stored within the computer at will.

The predominant charactertistic of human thought processes is their generality. To make any progress in the simulation of such processes, it is first necessary to isolate a small region and examine it in isolation. As progress is made in one region, it can be ex panded and generalized to include a wider field, and it is likely that many of the methods used in a re stricted field will be susceptible to modification for use in a larger area. It is desirable to work initially in a region in which the relationships between the ob jects of thought are clearly defined.

This report deals with the problem of finding se quences of transformations which constitute proofs of trigonometric identities. The method described need not be confined to this particular problem, but could easily be used in other fields if the allowable transformations are known. The behaviour of a ma chine which has been programmed to carry out this process is described in detail and its responses, when several identities were presented to it for proof, are given.

No attempt is made to use the method of finding proofs by exhaustive search, even though in this case such a search is quite feasible, since the number of "basic" trigonometric transformations which can be applied to a given function is relatively small. It is considered here that such repetitive "trial and error" methods are less interesting than the methods which we shall discuss. It is desirable to decide on the best transformation for a particular problem by compar ing the characteristics of the problem with the prop erties of each transformation in such a way that the machine's performance will improve with experi ence. Exhaustive search methods become useless when the number of possible decisions at each step becomes large.
Limitations due to Noise, Stability and Component Tolerance on the Solution of Partial Differential Equations by Differential Analysers
Authors: Fisher Michael E.
Published: March 2008

The solution of partial differential equations by a differential analyser is considered with regard to the effects of noise, computational instability and the deviation of components from their ideal values. It is shown that the 'serial' method of solving parabolic, hyperbolic and elliptic equations leads to serious in stability which increases as the finite difference interval is reduced. The truncation error (due to the difference approximations) decreases as the interval is made smaller and consequently an 'optimal' ac curacy is reached when the unstable noise errors match the truncation errors. Evaluation shows that the attainable accuracy is severely limited, especially for hyperbolic and elliptic equations.

The 'parallel' method is stable when applied to parabolic and hyperbolic (but not elliptic) equations and the attainable accuracy is then limited by the accumulation of component tolerances. Quantitative investigation shows how reasonably high accuracy can be achieved with a minimum of precise adjustments.
Substitution Methods for the Verification of Analog Solutions
Authors: Meissinger Hans F.
Published: March 2008

Substitution of analog computer solutions into the original differential equations followed by an iter ative or a variational procedure can be employed as a practical verification technique and as a method for improving solution accuracy. The method has the advantage of utilizing information contained in the analog solution and, therefore, yields results more rapidly than the conventional procedure of deriving an independent numerical check solution. It is also valuable as an aid in locating the source of computer errors.

Theoretical and practical aspects of the substitu tion check method are discussed and illustrative examples are presented in this article.
Computer Programming
Authors: Hammond Joseph L.
Published: March 2008

State variable techniques are reviewed and applied to analog computer programming. The concise rep resentation for ordinary differential equations made possible by this technique is used to formulate a gen eral program for all such equations. It is shown that an analog computer program based on state variables will not have redundant integrators.

The fact that the use of state variables facilitates the choice of variables internal to an analog com puter program is illustrated by two techniques, namely, (1) a technique for avoiding derivatives of the forcing function in programming a large class of ordinary differential equations, and (2) a technique for simulating certain systems in such a way that the effect of each characteristic root is placed in evi dence.
A New Numerical Method for Simulation
Authors: Fowler Maury E.
Published: March 2008

This paper illustrates a method of digitally simulating the motion and control of vehicles. This method of simulation has been used for the simulation of a large variety of systems, including a six-degree-of- freedom simulation of Gemini reentry with guidance and control, a six-degree-of-freedom aircraft simula tion, missile control simulations including bending modes, trajectory problems, and many others.

The major advantage of the method, in addition to the speed of computation, is that a detailed an alysis of the system is carried out during the develop ment of the simulation.

Although, for small problems, simulations using this method can be derived by hand, large simula tions generally require a computer program to com pute root locus points and z-transforms.
Transistors in Current-Analog Computing
Authors: Kerfoot Branch P.
Published: March 2008

A system of electronic analog computing is described in which current is used as the variable. The paper indicates that the circuit properties of transistors make them especially suitable for use in operational amplifiers for this computing technique.

Experimental direct-coupled amplifiers are shown which have been built and evaluated using low- power, low-frequency transistors. The amplifiers have been employed under laboratory conditions to per form the operations of summation, scale-change, integration, and differentiation.

The factors which determine computing accuracy are analyzed, and a new technique of error predic tion (based on square-wave output) is discussed.

The paper concludes that the current-analog meth od promises to use transistors effectively.
Electronic simulation of daily rhythm in nocturnal animals
Authors: Sage Andrew P. , Melsa James L.
Published: March 2008

The term biological clock is used to designate the phenomenon, displayed by organisms, of pacing activity in a cyclic manner related to environment. Many nocturnal animals, for example, are capable of entraining the onset of their activity with the light-to- dark transition in a periodic light-dark regime in which the period or ratio of light to darkness varies widely. This paper presents the development of an electronic model for simulation of the adaptation of the endogenous circadian rhythm of nocturnal ani mals due to light stimuli.
Tracking system simulation with variable delay
Authors: Robb R.E.
Published: March 2008

This paper describes the analog simulation developed to evaluate a digital control program. The digital pro gram is a doppler prediction program which updates a ground transmitter so that the input frequency to an airborne transponder is held constant.

It describes the simulation of the transmitter, re ceiver, transponder and the air-to-ground links be tween the transponder and the transmitter and re ceiver.

One of the unique features of the simulation is the dynamic time delay between the transponder and its ground stations.

The simulation is an example of direct modeling of the real-time transfer functions.
EASL ... a digital computer language for "hands-on" simulation
Authors: Schlesinger S.I. , Sashkin L.
Published: March 2008

EASL was developed to provide a simple language which would be easy to use by the occasional computer user, whether his background was analog or digital computing, and yet be powerful enough for use in programming com plicated computer applications. The language borrows liberally from the concepts of both analog and digital com puting in order to provide a framework in which a pro grammer from either field would feel at home. At the same time, the user has available the advantages of both disciplines so that he can operate as if he has a very sophis ticated hybrid system in which analog and digital com ponents can be readily intermixed.

In order to facilitate the use of EASL for engineering simulation studies, the capability of loading data and pro ducing graphical and tabular reports is provided in a man ner which is easily implemented by the user. Convenient algebraic representation is provided by FORTRAN state ments, and a simply-applied integration operation permits solution of systems of differential equations. The inherent simplicity of data input and output, where all references are made by the variable's name (which is provided by the user), lends itself to the adaptation of consoles to en able the user to monitor and control his computation. These consoles provide a "hands-on" capability for rapid control of computation based upon visual inspection of graphical output.
MIDAS III...a compiler version of MIDAS
Authors: Burgin George H.
Published: March 2008

The original MIDAS program (MIDAS I, Wright Patterson AFB1) and the enlarged version of MIDAS (MIDAS II, North American Aviation2) proved to be effective tools for the digital solution of comple,, engineering problems. For large problems, however, running times for these programs were excessive and means were sought to improve the run-time efficiency. This is achieved in MIDAS III, which is no longer an interpretive type program as are MIDAS I and II, but rather a pre-compiler generating a FORTRAN program which is then compiled and assembled into an efficient machine language program. The execution times for this program are on the average between four and ten times shorter than in the earlier versions of MIDAS. This ap proach not only reduces computer execution time, it also gives the program more flexibility and expansion capa bility. A fourth order Runge-Kutta Merson integration method with automatic stepsize adjustment is used for the solution of the differential equations. As an application of MIDAS III, a two point boundary value problem is solved.
New Approaches To the Design of Active Filters
Authors: Hansen Peter D.
Published: March 2008

Operational amplifiers can greatly simplify the design of high performance signal filters because they elimi nate the need for inductors and for impedance matching. Furthermore, use of active filters can result in reduc tion of weight, size, and cost. Filters designed to satisfy sophisticated mathematical criteria can be realized without resort to "equalization" or trimming.

In this issue we discuss the design of operational amplifier and analog computer circuits suitable for use as low pass filters. We also discuss the commonly used mathematically designed filters, i.e. Butterworth, Chebyshev, and Bessel. In addition, we present two new types of theoretical filters, the Paynter and the Aver aging filters. Design data necessary for realizing these theoretical filters with amplifier circuits is provided.

In the next issue we shall discuss the design of band pass, band reject, high pass and all pass active filter circuits.
Hybrid techniques for generation of arbitrary functions
Authors: Rubin Arthur I.
Published: March 2008

A discussion of the implementation of a true hybrid func tion generator module is presented. Included is a detailed description of how two of these modules, when used in conjunction with a hybrid computer, are used simultane ously to generate a continuous function of two variables, and how four modules are used to generate a continuous function of three variables. From a variety of possible con figurations, an optimum choice for a general-purpose HFG module is made, taking into account digital coefficient storage requirements and analog multiplier requirements.

A detailed error analysis compares the errors produced in generating an arbitrary function using the HFG module with the errors produced by the classical hybrid (or purely digital) method of generating an arbitrary function by table look-up and interpolation for discrete values of the argu ment. The conclusion is reached that the hybrid method can be an order of magnitude more accurate than the classical discrete method for generating arbitrary functions and has further advantages in that the hybrid method does not require a 100°lo duty cycle in the digital processor for accurate function generation.
Circle test evaluation of a method of compensating hybrid computing error by predicted integral
Authors: Deiters Robert M. , Nomura Tamiya
Published: March 2008

In a real-time hybrid computing system using an analog and a digital computer joined by ADC and DAC linkage, the continuous analog signals are inevitably sampled and delayed by the ADC-digital computer-DAC execution time. We propose a method of compensating for this error in which the digital computer predicts the integral of the ideal continuous output over each delayed sample period. This predicted integral, then, determines the DAC output having the same integral value over the delayed sample period. Here we have considered only the zero- order hold DAC, but the method is easily extended to other types of hold circuits. The digital prediction algo rithm is based on backward difference extrapolation of the values derived from present and past DAC samples. We tested the effectiveness of this method in a hybrid circle test. Z-transform numerical calculations indicate that sampling rates as low as 20 samples per cycle of oscilla tion and digital execution time as long as 9/10 of a sample period are permissible when backward differences up to the fifth order are used. An actual hybrid circle test with only 10-bit rounded off accuracy in the converters con firmed the effectiveness of the method, even in the pres ence of errors in the analog error range.

Using numerical inversion of the z-transform model we computed a number of charts to guide hybriders in select ing a suitable order of the compensation algorithm and sampling frequency. The graphs show the divergence (due to uncompensated time delay) and frequency error (due to loop gain error) as functions of sampling frequency. The parameters for these graphs are digital execution time and the order of the backward difference algorithm.
Analog simulation of satellite times-in-view
Authors: Bryan Roger N.
Published: March 2008

During the planning stages of any communication or com mand/control system utilizing satellites, it is necessary to examine the ground-terminal/satellite geometry for many proposed configurations in order to find the one most suitable. By "most suitable," I mean the configuration exhibiting the greatest ground-terminal-to-satellite acces sibility as demonstrated by a maximum time-in-view.

The procedures I describe in this paper provide a means for rapidly generating ground terminal/satellite visibility records via an analog computer simulation of the Earth's surface/satellite orbit geometry. The analog simulation has several significant advantages relative to similar digital computer approaches-(1) it is significantly faster (easily 15,000 times real-time) and less expensive to operate; (2) the output, ink-on-paper strip-chart recordings, is directly interpretable without further data reduction; (3) system parameter changes are readily introduced while a simula tion is in progress; (4) the Systems Analyst can maintain a decidedly greater rapport with his configuration analysis. The disadvantages are: (1) diminished accuracy, and (2) exclusion of Earth/orbit non-linearities and anomalies—in a real-time tracking or scheduling simulation, these dis advantages are serious; in a systems analysis tool such as this time-in-view simulation, they are not of great con sequence.

I have devoted the first five sections of this paper to a description of the development of the vector-matrix model underlying the simulation. The sixth section describes the mechanization of the model using an electronic analog computer.

The equations from which the computer potentiometer settings are derived are quite tedious to manipulate man ually—even aided by a desk calculator. In an appendix, I describe the simple digital computer (in my case, a RE- COMP II) program used to obtain the desired potentiom eter settings.

It strikes me that, while lack of simultaneity in the usage of the analog and digital machines precludes the use of the word hybrid, we may validly coin the expression "syner getic computing" to describe this simulation.
Fields, and methods of their simulation and exploration
Authors: Soudack Avrum , Uhlig C.A. Edward
Published: March 2008

Since the treatment of the general field concept seems to be missing in the literature, and since methods of field ex ploration and of simulation are scattered in a great number of domestic as well as foreign papers, this paper presents, first, a brief survey on fields and on methods of their analy sis and simulation, and then reports on the state of the art in the area of simulation of electrostatic fields by means of a conductive-sheet analog or electrolytic tank.

Although the paper has been written primarily with the needs of electric power engineering in mind, the treatment of the subject has been held as interdiscipli nary as possible. The paper will thus be useful also to those working in aerodynamics, elastic stress analysis, heat transfer, astronomy, acoustics, atomic physics, and ma terial sciences. Furthermore, for the electrical engineer, it may be helpful to know that electrical problems sometimes may be solved more easily or more conveniently by the use of nonelectrical methods.

In the specialized section on the application of the electrolytic tank and the conductive-sheet analog to the solution of electrostatic field problems, little-known as well as new techniques are discussed, such as (1) plotting of infinite fields on a double analog, (2) determining of force lines or surfaces by means of the dual analog, (3) simulation of areas of different dielectric constants and of continuously variable dielectric constants by means of jellified dielectrics, (4) plotting of areas of low current density by the use of consecutive field mapping, (5) the possibility of plotting fields with rotational symmetry on isotropically conducting sheets and graphically transpos ing the map so obtained, and (6) solution of distributed source problems.

A comparison of advantages, disadvantages, and limita tions of the electrolytic tank method and the conductive sheet analog is also presented.

Finally, an appeal is made for teaching and use of field analog methods for future developments.
A simulation study of the effect on simple ecological systems of making rate of increase of population density-dependent
Authors: Garfinkel David , Korn Granino , Garfinkel David
Published: March 2008

A simulation study has been carried out of the effect on Lotka-Volterra type ecological systems of the presence of density-dependent terms (of the type population-square) in the corresponding differential equations. It is found, as previously believed, that such terms do stabilize such a system, but the extent of the stabilization depends on the characteristics of the species to which they are applied. The lower trophic levels of a system are more important than the upper ones, herbivores collectively usually being the most important level. The numerical properties of the several species compare in importance with the organiza tion of the system: the importance of any individual species increases with the flux of protoplasm through it; the im portance of a pair of species increases with the flux of protoplasm between them. A possible method of extending this study to approach the status of a proof is suggested.
Digital simulation of general control systems
Authors: Trauboth Heinz H. , Burgin George H.
Published: March 2008

A numerical method and a program for the computation of the time responses of any complex multiloop control system are described in principle. The control systems are represented by block diagrams which are formed by the linear and nonlinear blocks well known in control engi neering. The properties of these blocks are given by simple relations between input and output signals in the time domain at discrete and equal intervals. Any number of input signals may be fed into the system at any point of the system. Initial conditions may be treated in a simple way like input signals. The input signals and weighting functions may be arbitrary time functions or impulse func tions given in analytical or numerical form. There is no need for special treatment of algebraic loops and of se quencing. The mathematical method is especially suited for programming an electronic digital computer.

The simulation program makes the work on the digital computer very easy. It computes the signals as functions of time at all points of the system. Several examples of linear systems were simulated on a Siemens-2002 with favorable results. Among others, a medium-size control system was simulated on this relatively slow computer in 3.2 minutes (compared to a real time of 26 minutes) and with more accuracy than on a medium-size analog com puter.
Sensitivities by the state variable approach
Authors: Kerlin Thomas W.
Published: March 2008

The well-known procedures for calculating transient-re sponse sensitivities, frequency-response sensitivities, and pole sensitivities have been successfully and profitably applied for several years. However, the usual formulations are not well suited for analysis of large systems on modern analog or digital computers. Expressions for these sensitivi ties are developed in this paper using simple matrix ma nipulations (usually referred to as the state variable ap proach). The state variable formulation illustrates clearly the structure of the sensitivity equations and provides an efficient procedure for computer calculations.
Regression analysis and parameter identification
Authors: Rubin Arthur I. , Driban Stanley , Miessner Wayne W.
Published: March 2008

The steps necessary to derive the regression differential equations for a set of unknown parameters are presented. A simple straight-line algebraic regression problem is re viewed. A real problem, that of finding the aerodynamic stability derivatives for the lateral equations of motion of an airplane, is presented. Preliminary results, using real airplane transient time histories, are compared with simu lated transients obtained using wind-tunnel values for the stability derivatives.
The simulation of structural and thermal systems via flow graphs
Authors: Feeser Larry J. , Feng Chuan C.
Published: March 2008

This paper presents a study of simulation of structural systems and heat flow problems by use of oriented flow graphs. Linear elastic structural systems are transformed into graph representation using two kinds of parametric analyses. In one case, flexibility parameters of structural components are used as branch transmittances of the or iented graphs, and geometric displacements are the ex ternal sources or inputs to the graph. In the other ap proach, stiffness coefficients as graph transmittances and unbalanced residual loads as source inputs lead to relax ation operations which can be represented by feedback analysis. Each of these approaches is the dual of the other in a topological sense.

Two-dimensional problems governed by the Laplacian partial differential equation are solved by using first-order central difference analysis to transform the governing equation into an oriented graph. The graph networks of physical systems of this type can be constructed by in spection of the mesh network without recourse to the difference equations. Initial boundary values are treated as independent source inputs to the graph. A solution of the steady-state heat flow in a thin plate is presented.

The simulation of physical systems by oriented flow graphs treats the system as an entity in which the physical characteristics are transformed topologically into graph representations. Oriented graphs are essentially analog setups from which numerical results can be obtained by analog computers. If use is made of the loop-rule equa tions of graph theory, efficient use of the digital computer is indicated. The nature of design of structural systems is complex because of the range of parameters to be con sidered and because of required accuracy. Flow graph simulation can give information on the effect of variation of parameters by way of sensitivity analysis and can be an aid in the study of design.
Log cards to raise a variable to a power
Authors: Walker R.E.
Published: March 2008

The technique described was found effective for raising a variable to a power, especially when the variable goes through zero. Over the range of exponents that was tested, the suggested circuit has better accuracy than the conven tional log-antilog circuit with automatic scaling. The tech nique described uses more equipment, but it can be modi fied to handle negative powers, varying powers, and com puter calculation of scale factors.
A passive network method of compensating an analog integrator for dielectric absorption errors
Authors: Guyton Robert D. , McKay Joe M.
Published: March 2008

A passive network that will compensate for dielectric ab sorption in the feedback capacitor of analog integrators is developed and its limitations are given. A modified net work that relaxes some of the restrictions encountered in the first network is developed. Dielectric absorption in the compensating capacitors is shown to be negligible. It is suggested that the performance of the integrators of an existing analog computer can be improved by the addition of a passive input network. It is also suggested that com puting capacitors other than polystyrene would give good results when compensated for dielectric absorption by the technique developed. A bibliography is included to give an information source on other compensation techniques and on methods of determining the constants for the fixed-parameter capacitor model.
Microwave radar and electronic environment simulator
Authors: Katsura Tomio
Published: March 2008

A facility capable of direct synthesis of radar systems and their electromagnetic environments operating concurrently with missile flight simulations, range instrumentation sim ulations, and related test-range experiments has been needed for many years.

This paper describes the design, development, and ap plication of a general-purpose Radar and Electromagnetic Environment Simulator operating under the combined control of digital and analog computers. This simulator is one of the more recent developments of the Analyses and Computation Directorate, White Sands Missile Range.

In this system the combined operation of computers and microwave hardware is utilized to create realistic dynamic radio-frequency environmental effects based on time de lay, doppler shift, and RF-signal-power equations com bined with simulated radar and missile flight geometry dynamics and kinematics. Associated radar antenna pat terns, target backscatter patterns, clutter, and other target- induced RF phenomena are included.

The simulator includes a flexible system for simulating RF signal generation and receiver signal-processing and provides a broad range of adjustment of radar parameters. The simulated transmitter signals are propagated through the computer-controlled environment simulation and are received and tracked by the receiver signal-processing equipment as in normal radar operations.

Prototype radar subsystems and components, tracking beacons, jammers, counter-countermeasure receivers, and many other devices can be coupled into the simulator to be studied within the confines of the simulation laboratory.
A modified Runge-Kutta method
Authors: Chai A.S.
Published: March 2008

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values.

Experimental results are shown in verification of the for mula.
Techniques for the design of linear digital simulations
Authors: Gagné R.E. , Baxter D.C.
Published: March 2008

This paper presents an operational approach to the design of digital simulations of linear dynamic systems which allows the design to be carried out using concepts familiar to the engineer. Traditional evaluations of numerical ap proximations to continuous operations are generally diffi cult to interpret in the engineering environment, and the operational approach presented allows discrete system evaluation using more familiar methods.

A method of digital modeling is derived which allows the digital transfer function of the discrete model to be obtained directly from the transfer function to be simu lated. From this digital transfer function can be obtained information on stability, frequency response, transient response, root mean square modeling error, as well as the numerical algorithm itself. The method is illustrated by examples of the digital simulation of several linear systems using several traditional numerical integration algorithms.
Digital simulation of space missions for Monte Carlo analysis
Authors: Mullin Frank J.
Published: March 2008

This paper describes a set of computer programs devel oped for Monte Carlo analysis of a complete space mis sion. The results of such an analysis are used in mission planning (for example, in the determination of how various errors affect the trajectory, midcourse-correction fuel re quirements, and other parameters).

In Monte Carlo analysis, a sample mission is simulated a large number of times, with the various stochastic pa rameters assuming different random values for each run. The resulting data is then processed statistically to yield useful probabilistic statements regarding output param eters of interest.

Three programs are described. The first derives, edits, and formats the input data required for simulation of a particular mission. The second is the simulation proper, generating a set of output parameters for each run. The third program processes the data from the simulation to derive the required statistical error-analysis data. The first and third programs are relatively straightforward and are briefly described; the simulation is described in more detail.

In general, the simulation operates by ordering all the events of the mission and using a set of standard mathe matical descriptions called PROP boxes to compute the state vector at the end of each event from its state at the beginning of the event. It uses the deviations of the pa rameters from those of a reference trajectory rather than the values of the parameters themselves, thereby simplify ing the mathematical treatment and reducing the comput ing time by orders of magnitude.
On the measurement of resistor dynamic characteristics
Authors: Single C.H. , King T.A.
Published: March 2008

This paper is a summary of two techniques for the meas urement of resistor dynamic characteristics. It is not a comprehensive paper in that it does not include a liter ature search or a review of well-established bridge tech niques. It does, however, present methods of measuring resistor high- and medium-frequency dynamic characteris tics, using only a square-wave generator, a sine-wave generator, and a high-speed oscilloscope. It emphasizes the use of models, both physical and mathematical, and completely avoids the use of analog computer measuring methods, even though the practical goal is analog-compu ter oriented.
Analog methods for on-line system identification using noisy measurements
Authors: Ricker D.W. , Saridis G.N.
Published: March 2008

Of current interest in the field of automatic control is the problem of system identification in the presence of measurement noise. Generally this problem has been dis cussed in the literature for the case of linear time-invar iant systems where the parameters to be identified are constant or slowly varying. This paper describes the ap plication of continuous stochastic approximation meth ods for the identification of a class of simple nonlinear systems. The two algorithms described are easily imple mented with analog equipment, although one of them requires some logic capability.
Digital simulation of frequency-limited random functions
Authors: Stearns Sam D.
Published: March 2008

Pseudo-random sequences with limited frequency con tent are often required in digital computing for the simu lation of various random processes. Such sequences can be generated by passing white noise samples through a digital filter. A family of filtering functions that par ticularly lends itself to this application is discussed, and a simple algorithm for producing the resultant time series is presented along with an example.
Simulation of geologic systems: an overview
Authors: Bonham-Carter Graeme , Harbaugh John W.
Published: March 2008

Systems philosophy provides the theoretical framework linking diverse applications of computer simulation. Natural systems and man-made systems may be regarded as end members of a spectrum of system types. Simula tion of man-made systems employs operations research techniques; the objectives of simulation are to optimize system design and to test the performance of models under differing parameter settings. Simulation of natural systems cannot readily utilize specialized simulation lan guages, as these are designed primarily for industrial and business applications. The objectives of simulating natu ral systems are normally to test alternative models and to see how they react under various conditions; the natural system itself cannot be changed (unless it is partly man- influenced)-only the model can.
Explicit forms of the rotational equations of motion for digital simulation
Authors: Economy Richard , Burgin George
Published: March 2008

The rotational acceleration for a rigid body has traditionally been represented by three simultaneous equations. Be cause of the computation time required for the iterative solution of simultaneous equations using a digital com puter, it is desirable to transform these equations to an explicit form for digital solution. The rotational equations are linear in the acceleration components. Thus, an explicit form can be obtained by either a determinate or a substi tution method. For problems where solution requires two or more of the cross-products-of-inertia terms, the determ inate method yields the most efficient equation form for digital solution. For the special case of body-plane sym metry (i.e., two cross-products-of-inertia terms are neg lected), the substitution method yields the most efficient form.
Mathematical programming in economics by physical analogies
Authors: Franksen Ole I.
Published: March 2008

This article is the first of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming.

Basically, the first article is a reexamination of the fundamental assumptions underlying quasi-static models in economics and engineering, with a view to the estab lishment of a conceptual framework common to both disciplines.

At the microscopic level it is demonstrated that the assumptions of perfect competition can be cast in a form analogous to the one used in statistical physics.

At the macroscopic level it is shown that measurements in economics and physics can be classified in identical manners with the result that derived relationships, like Ohm's law and demand curves or electric power and total revenue, can be made analogous concepts. On this basis it is then asserted that underlying economics we find two basic laws which, apart from a single change in sign, are completely analogous to the well-known first and second laws of thermodynamics.
Mathematical programming in economics by physical analogies
Authors: Franksen Ole I
Published: March 2008

REVIEW OF PART I AND PREVIEW OF PART II

This article is the second of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming.

Basically, the first article (published in SIMULATION last month) was a reexamination of the fundamental assumptions underlying quasi-static models in economics and engineering, with a view to the establishment of a conceptual framework common to both disciplines.

At the microscopic level it was demonstrated that the assumptions of perfect competition can be cast in a form analogous to the one used in statistical physics.

At the macroscopic level it was shown that measure ments in economics and physics can be classified in iden tical manners with the result that derived relationships, like Ohm's law and demand curves or electric power and total revenue, can be made analogous concepts. On this basis it was then asserted that underlying economics we find two basic laws which, apart from a single change in sign, are completely analogous to the well-known First and Second Laws of thermodynamics.

The present article is primarily a reformulation of the Walrasian economic model, which underlies mathemati cal programming, into an analogue electrical network.

In accordance with the tradition of physics, the Wal rasian system of equations is derived from the postulates of the First and Second Laws of economics. The advan tage of this approach, which differs from conventional economic expositions, is that it permits a nearly auto matic establishment, term for term, of the corresponding electrical network model.

The constraints and state-functions of the electrical analogue are formulated by modern network techniques in order to separate, in the economic formulation of the Walrasian system, the analytical aspects from those more general aspects which are involved in the design of an economic production system.
Automatic measurement and plotting of probability histograms using an analog computer with digital logic
Authors: Kavanagh R.J.
Published: March 2008

A method of automatically measuring and plotting prob ability histograms is described. The equipment required consists of a small number of analog computer compo nents, a few digital logic elements, and an X-Y plotter. The technique may be applied to the analysis of either random or periodic signals.
Sampling errors in closed-loop hybrid computer programs
Authors: Hammond Joseph L. , Alford Cecil O.
Published: March 2008

This paper applies a previously derived equation for sampling error in hybrid systems to the case of hybrid computer systems which use first-order analog hold de vices. Explicit expressions for sampling error are ob tained for a general hybrid computer program and for several classes of programs corresponding to particular cases. The equations apply for most types of hybrid com puter operation including the case for which the digital computer is used to integrate one or more of the prob lem equations.

The error equations are used to examine the effect of various allocations of computing operations, both in general terms and through use of a particular example. The results, while providing no new insight into gross effects, give quantitative relations which sharpen intui tive guidelines for programming a hybrid computer.

The equations place in evidence the following facts which are not apparent from a qualitative study: (1) The major components of sampling error depend on the first power of the sampling period, making the hybrid computer a first-order numerical method. (2) Digital execution time has an effect on error which is similar to that of the sampling period, but is weighted twice as heavily. (3) A numerical integration method in the digi tal computer produces negligible error in relation to other error sources if it is of order 2 or higher.
Applications of simulation to traffic problems
Authors: Wigan M. Ramsay
Published: March 2008

The present state of the art of simulating traffic problems is reviewed in outline, and part of a briefly annotated bib liography of the work done on traffic simulation is pre sented. The full 206-item bibliography (available from the author) covers discrete event simulation of such situations as intersection and network flows, and also more general techniques such as 'car-following' models. Transportation survey techniques—such as assignment and distribution- are not specifically covered.
Expanded capabilities of CSMP graphics on the IBM 1130 digital computer
Authors: Schroer Bernard J.
Published: March 2008

The 1130 Continuous System Modeling Program (1130 CSMP) with interactive computer graphics on the IBM 1130 digital computer has been in use at The Boeing Company, Huntsville, Alabama, since the middle of March, 1969. CSMP was introduced through a small research study to define the graphics requirements for Boeing Huntsville. By June 1, 1969, approximately 250 hours of CSMP utiliza tion had been logged on the 1130. As a result of this initial usage by various engineering disciplines, many new requirements have been identified for CSMP. The purpose of this paper is to present those modifications which have already been made to CSMP as a result of these require ments. Also noted in this paper are additional requirements which users feel should be met by further modifications of CSMP.
Simulation of the mechanical properties of a physiological tissue
Authors: Sakata K. , Parfitt G. , Pinder K.L.
Published: March 2008

The compressive behavior of a particular physiological tissue — sheepskin — was simulated on an analog com puter, the simulation being derived from a nonlinear me chanical model. The mechanical model, which consisted of elastic, viscoelastic, and ratchet or contractile elements, was developed from cyclic-stress fatigue data. By compar ing experimental data with the simulated results, it is shown that the proposed model satisfactorily describes the complex behavior of the tissue.
Hybrid computer simulation of xenon spatial oscillations
Authors: Wozny M.J. , Bartells P.S. , Bailey R.E.
Published: March 2008

This paper is concerned with a hybrid computer simulation of the space-time xenon oscillation problem. Such prob lems are important in large thermal nuclear power reactors.

The basic nuclear reaction is modeled by three slightly nonlinear partial differential equations-a diffusion equa tion describing the neutron flux concentration, and two first-order partial differential equations which contain only partials with respect to time and which describe the gen eration and decay of iodine and xenon.

The continuous-space discrete-time approximation is used to implement the equations on the hybrid computer. By discretizing the time variable the xenon and iodine equations are reduced to algebraic expressions and the flux equation is reduced to a boundary value problem. The algebraic equations are decoupled from the boundary value problem and, therefore, solvable on the digital computer, by invoking the assumption that the nonlinear flux terms change slowly with respect to the time step. This assump tion also simplifies the boundary value problem which is solved on the analog computer in conjunction with digital function storage.

The simulation effectively displays the space-time xenon oscillatory behavior resulting from an initial spatial per turbation of the flux shape. This information is used to study the stability of the local changes in the xenon con centration and, hence, the spatial variations of reactivity in the core.
On the simulation of distributed parameter systems
Authors: Schuchmann Heinz
Published: March 2008

This paper presents analog, hybrid, and digital simulation techniques for one-dimensional flow, diffusion, and wave- type systems. These techniques also provide the basis for the simulation of more complex distributed-parameter systems. Many of the techniques considered are well known; however some of them are just recently devel oped. The various techniques result from either discretiza tion and transformation of the original partial differential equations or from application of the method of charac teristics. From this point of view, it is possible to fit the

techniques into a general framework. It will be indicated by means of the properties of each technique which type of computer will best implement it and which system can be treated by it most advantageously.
Hybrid computation in the university
Authors: Strauss Jon C. , Greenberg David B.
Published: March 2008

One of the primary goals of the Carnegie-Mellon University Hybrid Computation Laboratory has been to study hybrid computation per se, from both an application and automation viewpoint. To date, the work has concentrated on automation of hybrid computer programming and on methods for solving partial differential equations.

During the course of the design, installation, and operation of its hybrid computation laboratory, CMU has obtained a wealth of experience (both objective and subjective) with the use of hybrid computation in the university environment. In light of growing univer sity interest in hybrid computation, this article describes the experience of CMU and presents certain conclusions concerning the appropri ateness of university use of hybrid computation.
Simple Memory Circuit for Iterative Analog Computation
Authors: Torfason L.E. , Crossley F.R.E.
Published: March 2008

This paper describes a memory circuit for iterative com putation on electronic analog computer that uses much less analog equipment than the conventional track-and- store circuit.
Computer simulation of human temperature control
Authors: Winton Henry J. , Linebarger Robert N.
Published: March 2008

A feedback control system model of human temperature regula tion is developed. Body thermal properties are represented by an electrical circuit analog. The sudomotor, vasomotor, and metabolic parameters in this circuit are made to be nonlinear functions of an error signal derived from hypothalamic and cutaneous thermoreceptors. The system state equations are de rived and a digital simulation of the model using System 360/ CSMP is discussed. An analog simulation of the same problem is also given, along with an evaluation of the advantages and disadvantages of each approach. Comparison of static and dy namic responses of the model with published data from physio logical experiments shows reasonable agreement over a broad spectrum of conditions, including exposure to heat and cold, humidity, ice ingestion, and exercise.