bluuebunny/crossref_metadata_2025 huggingface dataset:
In-Plant Applications for Analog Computers
Authors: Mitchell E.E.L. , Marr George R.
Published: March 2008

Improvement in the versatility and reliability of an alog computing equipment has allowed a much broader view of potential applications in control problems. This paper summarizes some of the many applications and illustrates some especially new and unique programs that are now possible.
The Parallel Digital Differential Analyzer and its Application as a Hybrid Computing System Element
Authors: Reichardt Otto A. , Hoyt Merlin W. , Lee W. Thad
Published: March 2008

TRICE hybrid computing systems are currently in volved in aerospace simulations that are interesting and sophisticated. Indeed it would seem that these applications are so successful that an increasing wave of interest can be expected in such DDA applications. Unlike earlier DDA's, the parallel digital differential analyzer, we believe, combines more of the best fea tures of analog and digital machines: It boasts speed, accuracy, and ease of programming.

Because the machine itself is entirely digital, it couples naturally and inexpensively with convention al digital computers. Unlike other digital machines with central memory and sequential operation, all elements of this DDA operate simultaneously, thus providing rapid solutions to nonlinear differential equations characteristic of analog computers. And like its analog cousin, our DDA is programmed read ily via a patchboard, by connecting its computing elements in direct correspondence to the elements of differential equations.

In one sense, TRICE is more properly a hybrid— a unique combination of analog and digital machine characteristics—than are the combinations of analog and digital computers currently being interfaced. Yet it can also be connected with analog and/or digital computers.

Here we would like to explain how TRICE works, compare its advantages as a hybrid element, and con clude with a review of some current applications.
Quaternion Parameters in the Simulation of a Spinning Rigid Body
Authors: Mitchell E.E.L. , Rogers A.E.
Published: March 2008

The use of quaternions in describing the orientation of a rigid body allows all possible attitudes to be sim ulated. The problem of gimbal lock encountered when using the more commonly understood Euler angles is avoided. The analog implementation of the quaternion description is given together with the transformations between quaternion parameters and Euler angles in order that the latter may be available for display.
Hybrid techniques in statistical analysis I
Authors: Mitchell B.A.
Published: March 2008

Hybrid computation has been with us for a few years, and now techniques, procedures and applica tions are beginning to develop rapidly. We believe great strides can be expected in hybrid simulation now that many equipments are in the field and people are beginning to appreciate the value of bringing the respective qualities of analog and digital computers to bear on individual problems. This column is intended to disseminate information on hybrid simulation and tricks of the hybrid trade. We also hope to stimulate equipment users to provide us with contributions and comments we can publish.

At present the subject of special interest to us in the field of hybrid computation is that of sampling effects at the analog-digital interface. We would en courage anyone who has anything to say on this subject—be it with regard to equipment, technique, program control, or the analysis of sampling-to write to us.

The use of logic elements, gates, flip flops and counters, is foreign to most simulation people, and we are sure tricky circuits have evolved. Although the drive for hybrid came originally from the people with aerospace problems, many developments are occurring in other fields. These should be noted and made available to all who are interested.

As a start this month, we present a short descrip tion by Baker Mitchell of his automatic correlator, which provides nice displays to watch and saves lots of time.
Grounds, grounds, and more grounds
Authors: Stewart E.L.
Published: March 2008

This paper discusses the need for proper grounding of electrical equipment from the standpoint of safe ty and performance. Seventeen diagrams are em ployed to illustrate the most important points.

The discussion follows a fundamental vein in illus trating the proper connections of electrical apparatus to specifically avoid difficulties from common im pedances and "ground loops."

Some of the many so-called grounds that are en countered in instrumentation are illustrated and defined according to function, in an attempt to clar ify what appears to be a somewhat confusing array of grounds. A computer grounding system is illus trated, as is a so-called hub ground method of in tegrating several computers (or other devices) into a compatible system.

Emphasis is placed on the interconnection of elec trical devices, and attention is called to the need for thought concerning the circuit(s) formed by the casual treatment that is often given to such appar ently simple things as ground connections.

This paper was written to provide information for operators who do not have specific electrical back grounds, and as a reminder to the electrical prac titioner that the most important connection of all is frequently the one called ground.

"Ground," with its many connotations and impli cations, seems to raise some degree of confusion whenever it appears. There are grounds and grounds and grounds such as: signal ground, shield ground, power ground, relay ground, etc. This paper will at tempt to clarify this situation by examining the case from the ground up (wherever that is).
Noise reduction on interconnect lines
Authors: Stewart E.L.
Published: March 2008

This paper is concerned with the electrical "noise" on interconnect lines, particularly as applicable to analog equipment. The discussion summarizes the effects of magnetic, electric, and electromagnetic fields. Also considered are common impedances and ground loops in producing electrical interference on analog circuits.

The use of lines of low susceptibility is discussed together with the effects obtainable by suitable shielding. Circuits known to have been used are illustrated and their characteristics discussed.

Proper system grounding is emphasized as is the fact that interference control is obtained only by the system approach.

The paper should serve as a reminder that elec trical interference is minimized through the prin ciples of good wiring practice, separation, and proper attention to the circuit details during design and fabrication.
A demonstration hybrid computer for real-time flight simulation
Authors: Connelly Mark E.
Published: March 2008

A hybrid, real-time simulation facility has been de signed, constructed, and demonstrated, using as a test vehicle the complete aerodynamic and engine equations for a high-performance military aircraft. The analog-digital configuration employs peripheral analog equipment to represent a linear, skeleton version of the aircraft and the PDP-1 digital com puter to carry out engine simulation, decision man agement, and corrections for nonlinear effects.

To provide an all-digital reference against which the hybrid simulation could be compared, the air craft model was also simulated in real-time on the PDP-1 alone. It was found that the solution rate of 20 per second employed in the all-digital study could be reduced substantially without deleterious effects when the hybrid configuration was used. Such a re duction demonstrates that supplementing a digital computer by relatively inexpensive analog peripheral equipment greatly increases the real-time capacity of the digital computer in complex simulation appli cations. Moreover, because a number of key variables are computed continuously in the analog domain, the introduction of analog equipment results in a net decrease in the complexity of the interface.
Software for hybrid computers
Authors: McGhee R.B. , Lew A.Y.
Published: March 2008

Efficient use of a hybrid computer for the solution of a wide variety of problems requires that the computer hardware be complemented by a comprehensive software package. Such software ought to assist not only in the preparation of programs, but in their execution as well. For open-shop operation of a hybrid facility, it is important that a widely- understood high-level procedure-oriented language be made available to users. From a practical point of view, FORTRAN and its various derivatives are the only lan guages satisfying this requirement at the present time.

Expansion of a purely digital programming language into a hybrid programming language may be accomplished either by rewriting the processor or by attaching a suitable subroutine library. The software system of the System Simulation Laboratory at the University of Southern Cali fornia furnishes a concrete example of the latter approach.
Analysis of a vibrating heat engine using PACTOLUS
Authors: Smith H.J.
Published: March 2008

The purpose of this paper is to investigate the theoretical feasibility of a proposed vibrating heat engine. This engine, intended for small cryogenic refrigerators, is hoped to be more reliable than existing ones. The thermodynamics of the process is described and analyzed, and a final differ ential equation relating the pressure and volume of the gas in the engine is obtained. This equation is solved and its parameters are investigated using the PACTOLUS analog simulator on an IBM 1710 computer. The results of these calculations are shown, and from them have been calcu lated the heat engine efficiency as a function of its pa rameters.
Midwestern Simulation Council meeting
Authors: Kohr Robert H.
Published: March 2008

This report marks a transition in associate editors from the MWSC. P. J. Hermann, who replaced Ben Clymer, has retired from the field of battle to the flatlands of lowa, where he will sit in his rocking chair, stroke his beard, and again consider, if only briefly, writing his PhD thesis. Your current editor is associated with the School of Mechanical Engineering at Purdue.
Space trajectory computation at the University of Michigan
Authors: Fogarty L.E. , Howe R.M.
Published: March 2008

Extensive investigation of methods of real-time and fast- time computation of earth orbits and reentry trajectories has been conducted for both analog and digital computers. Integrator drift and multiplier errors in the case of analog computers preclude the use of direct computation in in ertial frames or geocentric coordinate systems. Such co ordinate systems can also lead to serious digital computer problems due to truncation and roundoff errors. Introduc tion of a vehicle-centered rotating coordinate system with variables referred to a nominal orbit permits greatly im proved computer scaling which, in turn, very substantially improves the absolute computational errors. In addition, the use of angular momentum and energy constraints is shown to reduce greatly the effect of integrator drift on the in-plane motion. Analog solutions to orbital and re entry problems have been obtained in real-time, fast-time, and high-speed repetitive operation using the above co ordinate system.
Some examples of the parametric technique in programming an analog computer
Authors: Butler Richard F.
Published: March 2008

A standard approach in programming an analog computer is to define a linear relationship between the independent problem variable and real time, i.e., computer time. This approach is not always necessary, as illustrated by the ex amples presented here. Quite often, an alternate approach utilizing a parametric technique is more convenient and makes it easier to obtain function values near singular points and points at which a function is indeterminate.
The DIAN digital I simulation program
Authors: Farris George J. , Burkhart Lawrence E.
Published: March 2008

Although DIAN can be used for almost any type of simula tion problem, it has been used most where it had a particu lar advantage over other available methods of solution. Thus, it has been used to transfer an analog problem to a digital computer when the problem grew too large for the existing facilities, where a large number of transport delays or where long transport delays were involved, and when the simulation problem was very large.

The DIAN flowsheet is almost the same as an analog computer flowsheet, the coding of the input cards is straightforward, and except for a boundary value problem, no compilation is necessary. Iterative solutions of boundary value problems can be solved using DIAN and several problems can be handled sequentially in a multifile run. The use of DDA-type integrators permits flexibility in non linear function generation and output format may be var ied since the format is supplied as input information with each problem.
A computational compensation for measuring system dynamics
Authors: Mason Maughan S. , Clary George W.
Published: March 2008

This paper is concerned with the general problem of de termining the time history of an unknown input signal, given only the recorded response of a known physical sys tem excited by the unknown input. The particular case considered is determination of true thrust from the re corded test stand response, with the physical system re sponse noise superimposed upon the thrust data. Passive or numerical filtering can smooth the trace, but these methods will attenuate the signal within a particular fre quency band, and thus may distort the data content of the recorded response.

The paper describes analog computer techniques that can be used to reconstruct data distorted by such physical system response. The data may be recovered through an "active filtering" process, even when it contains compo nents of a higher frequency than the response noise being removed. Several examples are shown, including one case where the original signal was recovered intact even though the input signal excited a system resonance by passing through the natural frequency of the simulated test stand.

The method described is not restricted to linear systems, but can take into account such nonlinearities as changing rocket booster mass, and nonlinear damping and spring force versus deflection relationships. The major require ment is to obtain sufficient information to permit deriva tion of a realistic mathematical model of the physical sys tem used for test and measurement purposes.
A new digital attenuator system for hybrid computers
Authors: Pracht Conrad Paul
Published: March 2008

Digital attenuators are simple multiplying digital-to-analog converters used to replace coefficient-setting potentiome ters in modern analog/hybrid computers. This report de scribes a new digital attenuator system employing low- phase-shift miniature metal-film ladder networks. They are switched by latching reed relays which give the system a nondestructive coefficient memory even when the com puter is switched off. New digital control logic employs serial data transmission and requires only one address line per 14-bit attenuator. It permits one to set all 200 attenuators of a typical hybrid computer installation within 20 milliseconds. For maximum contact life, relay contacts are switched only when no current is flowing. The digital computer static-check routine can readily check individual relays to simplify maintenance.

Particular emphasis in this report is on a digital-attenu ator system designed for a very fast repetitive computer in the Analog/Hybrid Computing Laboratory at the Uni versity of Arizona. The same design approach is readily applied to "slow" analog computers and appears to be even more advantageous there.
Educational demonstration
Authors: Soudack Avrum , Greenberg David B.
Published: March 2008

A year has now passed since the initiation of this section, Computers in educa tion. During this time we have published articles on analog and digital simu lation in undergrad programs, on a prototype hybrid computer for undergrad use, on conducting tank and conducting sheet analogs, and on a student's research project.

With the beginning of the second year of CIE, we are inaugurating a sub section of CIE entitled Educational demonstrations and experiments. The object of this section will be to present in detail upper level experiments suitable for in-class demonstrations and in-lab projects. We hope to complement the excel lent job John Evans of ACEUG is doing in publication of the ACEUG applications.

A second object of our second year is to solicit and publish material from both graduate and undergraduate students. In this way, we hope to get fresh viewpoints and ideas.

To continue the success of CIE, we require the interest and enthusiasm of all those concerned with the educational aspects of computers. I thus ask my colleagues to submit interesting and meaningful experiments and extend the opportunity to students who wish to express their ideas and discuss their work.
Simulation languages
Authors: McNeley John
Published: March 2008

Based on a paper presented at the Computer Science and Statistics Symposium held February 1, 1967 in Santa Monica, California, to focus on the development of the interface between two related principles.
Mermaid... the development of a medium scale hybrid monitor
Authors: Anderson Tom
Published: March 2008

In the Fall of 1965, it was decided that an existing facility of adjacent analog and digital computers would be up graded to provide hybrid computation capability. The Mermaid Monitor System, which provides the executive control functions and hybrid communications features, was developed in the very brief period during which the interface equipment was built. The initial version of Mer maid was written by digital systems programmers with no direct experience with analog computation who consulted with analog programmers with no digital or hybrid expe rience. Despite the general lack of knowledge and expe rience, the initial version was a workable monitor system which was used for over a year.

Since the initial version of Mermaid was not an ideal monitor, a two-stage updating was undertaken to incor porate additional equipment and to strengthen Mermaid's capabilities in the area of hybrid inputloutput. On com pletion of this development cycle, the system will be com pletely disk oriented, and it will provide a maximum of convenience in programming for hybrid applications.
On the stability of continuous parameter tracking systems
Authors: Jackson Glenn A.
Published: March 2008

Continuous parameter tracking systems utilizing the out put-error method have been analyzed by intuitive argu ments1 and by linearized equations2. This paper presents a method for analyzing the convergence properties of this type of system; it is applicable when the input signal is either a single sinusoid or a sum of sinusoids. The method is based on the technique advanced by Kryloff and Bogo liuboff3.
Optimization by parameter-perturbation correlation
Authors: Gonzalez Robert , Muterspaugh Milo
Published: March 2008

This paper describes a simple method of steepest-descent optimization of a criterion functional F(α1, α2,...) depend ing on the state variables y i(t;α1,α2,...) of a dynamic system with design parameters α 1, α 2.... The system is simulated on a fast analog computer and the parameters are given mutually orthogonal sequences of binary pertur bations during successive computer runs. Simple correla tion of each parameter perturbation with the criterion functional value at the end of each computer run yields ap proximations for the gradient components ∂ F/∂α k needed for steepest-descent optimization with a minimum- of dig ital logic. As an example, two- and three-parameter model- matching problems are solved by iterative computation at 1000 iterations per second.

A course term-paper for first-year graduate students
Hybrid simulation of speech waveforms utilizing a Gaussian wave function representation
Authors: Howard J.A. , Wood R.C.
Published: March 2008

Most of the prior research work concerned with the analysis and synthesis of speech has employed Fourier series and transforms as the mathematical framework for the characterization of live speech. Current studies at UCSB have taken a new approach, namely the time domain analysis of speech waveforms. This work, per formed under the direction of Dr. Glen J. Culler, is based on a Gaussian wave-function approach to the analysis, synthesis and decomposition of speech elements. This paper is concerned with the hybrid simulation of speech waveforms utilizing the wave-function representation. A speech simulator consisting of a hybrid interconnec tion of four TR-20 analog computers is described. Re sults of the simulation of two vowel sounds, the "o" in "on" and the "a" in "at," are presented and compared with the original speech data. The results form an im pressive check on the wave-function approach and have provided the impetus for the realization of a hybrid speech-synthesizer based on this technique.
Digital-computer interface systems
Authors: Korn Granino A.
Published: March 2008

Digital-computer interface design is of vital and increas ing importance in simulation, control, instrumentation, and data processing. Hybrid-computer linkage design deals only with a small facet of the interface world, but reflects many of its problems. This tutorial report re views the important techniques for transferring data and control signals between digital computers and the out side world and discusses, in turn, device selection and control for a party line I/O bus, device control, sensing, interrupts and automatic data channels with direct mem ory access. Interfaces for iterative analog computers, for combined simulation, and for simple graphic displays are described as examples. Finally, special interfaces for random-process measurements and interfaces employ ing an intermediate digital processor are discussed.
Four-gimbal systems for simulation display
Authors: Wilson John W.
Published: March 2008

The utility of a four-gimbal system for positioning two reference frames with respect to each other without gim bal lock has long been recognized. As early as 1954 such a system to isolate an inertial platform was proposed by Arnold and Schlesinger1 . However, the exact law for driving the fourth angle has been a question. The situa tion had not improved through 1962 where, in Reference 2, "gimbal flip" (an instantaneous rotation of 180 de grees in two axes, similar to the three-axis gimbal be havior at gimbal lock) appears as an inherent part of the fourth angle's driving law. Clearly this behavior is not desirable for platform isolation or visual display systems used for vehicle motion cues in simulation.

This paper describes developments made at Langley (NASA) in the last several years. A driving law for the fourth angle is developed for two different four-gimbal systems. The first is similar to the gimbal systems de scribed in References 1 and 2 and has advantages in design and implementation for platform isolation. The second is specifically designed to minimize occlusion in visual display systems3.

In each system, the fourth angle driving law is a direct consequence of maximizing the angle between the two axes causing the singularity. Thus, a necessary differ ential constraint is found to maintain a nonsingular solu tion. A sufficiency condition for a nonsingular solution is also found. The second four-gimbal system that mini mizes occlusion has the interesting result that the maxi mum angle between the singularity-forming axes is not always 90 degrees.
Optimum generating schedule for a hydro-thermal power system/an analog computer solution to the short-range problem
Authors: Perera K.K.Y. Wije
Published: March 2008

An analog computer programme for solving the "co ordination equations" developed by Chandler, Dandeno, Glimn, and Kirchmayer 1 (CDGK) is formulated and tested. These coordination equations are wanting in that the plant maximum and minimum limits of operation have not been considered in CDGK's problem formula tion. 2 New coordination equations which consider plant operation limits are therefore derived. These new equa tions are reduced to a form suitable for analog compu tation. The practical feasibility of an iterative-type ana log solution to CDGK's equations as well as to these new equations is established.
Mathematical programming in economics by physical analogies
Authors: Franksen Ole I.
Published: March 2008

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

In the third article the concept of equilibrium is de rived from the basic notion of a static mechanical system at rest, and it is shown how, by refining this concept, it can be extended to dynamic physical systems. In this process it is also explained why an extremum value of a state-function determines an equilibrium state of a system.

From an economic viewpoint the physical concept of equilibrium is identified with that of a perfectly competi tive market, and it is demonstrated how this concept dif fers from the equilibrium concept of a monopolist. For comparison, industries with one and two outputs are considered.

From a mathematical programming viewpoint both linear and quadratic problems are discussed in terms of methods of classical mechanics. In particular it is shown that the simplex method can be derived from Fourier's inequality for equilibrium on a boundary and that the Kuhn-Tucker conditions are statements analogous to Kirchhoff's mesh law for an electrical network.
A decision procedure for selecting among proposed automatic analog computer patching systems
Authors: Gracon T.J. , Strauss J.C.
Published: March 2008

In the recent literature, a paper1 and a contract report2 indicate that automatic analog computer patching sys tems have become economically and technologically feasible. In anticipation of the development of a variety of proposed patching systems, a specific decision pro cedure is developed for the rational evaluation of com peting automatic analog patching systems.

The design procedure described in this paper facilitates selection of the patching system best suited for a partic ular computer and a particular problem class. Sufficient information is abstracted from a typical problem set to determine the number of relays required for (and thus to assign a cost figure to) each possible patching system without requiring the actual design of each system. Nom inally, the best system is that with the lowest cost figure. It is recognized, however, that there are many subjective decisions (e.g., captive vs. free pots) involved in the de sign process that are not quantified in this overall cost figure. This problem is met in part by providing inter mediate information relating to the optimal module size, combinations of proposed systems, etc. to help estab lish some of the sensitivity properties of the optimal system.

The procedure is illustrated by applying it to a particu lar case and evaluating a number of alternative switching systems.
Simpl-1
Authors: Benham R.D. , Cole C.R. , Dionne P.J. , Foote H.P. , Gerhardstein L.H. , Worth G.A.
Published: March 2008

This article briefly illustrates a new simulation concept called SIMPL-1 (Simulation Implementing Machine Programming Language — Version 1). Although the example illustrated is a trivial second-order system, the techniques are currently being used on a number of much larger simulation problems. We are currently evaluating the limits of the concept on a cross section of expensive scientific simulation problems. Early indications suggest that economic relief is just around the corner for many simulation areas (both hybrid and digital) when SIMPL tech niques are used.
A simulation model for evaluating the effectiveness of various stock market strategies
Authors: Krolak P. , Berquist R. , Conn R. , Gilliland H.
Published: March 2008

This paper develops a simulation model which can be used to investigate a wide variety of stock market invest ment strategies. A brief review of the literature of stock market forecasting is given. The paper describes the de tails that any simulation of a stock market investor would have to include if the model is to be realistically com pared to the performance of real investors. An outline of the necessary features of any program which is to be used to investigate may different combinations of invest ment strategies and forecasting devices is also given. The program is described in detail and a few preliminary results are given.
A general purpose digital traffic simulator
Authors: Blum A.M.
Published: March 2008

The described vehicle traffic simulator is designed to fa cilitate analysis of traffic flow and to experiment with postulated traffic control systems. It offers users a large amount of flexibility in specifying network, intersection, vehicle, and control parameters. The logical flow of ve hicles, as well as much of the control system, is prepro grammed. Vehicles varying in size may change lanes, turn, change velocity (including reaction and acceleration delays), and merge. Input volumes may be varied, turns may be eliminated, and vehicles may be routed through the network. The user supplies the geometrical character istics and input information unique to his particular net work in data cards for the program.

Some applications to real traffic networks (including a validation procedure) and a simple control experiment are discussed. The model, programmed in a special version of GPSS II and in FAP for the IBM 7090/94 systems, can be used in the simulation of single intersec tions, arterial routes, grid networks, and, for some special cases, limited access roadways.
The translation and docking simulator
Authors: Williams Wayne K.
Published: March 2008

This article describes the Translation and Docking Sim ulator (TDS) used to support the Gemini as well as the Apollo space flight programs. The simulator was origi nally conceived, designed, built, and operated as a Gem ini simulator. The six-degrees-of-freedom relative mo tion of the crew station was simulated with an actual out-the-window view of docking and with the actual spacecraft controls as major parts of the simulation. Then at the conclusion of the Gemini program, the simulator was modified to simulate the Lunar Module (LM) active lunar orbital docking with the Command and Service Module (CSM) for the Apollo program. A LM crew station replaced the Gemini as the active vehi cle, and a CSM mockup replaced the Agena as the pas sive, or target vehicle. Again, primary attention was given to simulation of the out-the-window view of dock ing and to controls in the crew station. Typical opera tions consist of one-hour to one-and-a-half-hour train ing sessions. During the session lighting configurations are varied and system malfunctions are simulated.

In the Gemini and Apollo programs docking is ac complished by a crew member using onboard maneuver ing systems while relying on his own judgment of relative positions and rates as determined by viewing the target vehicle through a spacecraft window. To develop the skill required, crew members have used several training devices, one of which is the TDS.
General management simulations: an approach for the seventies
Authors: Hodgetts Richard M.
Published: March 2008

The great surge of enthusiasm and research in gaming during the sixties provided us with some of the most sophisticated general-management simulations ever. In the seventies we will undoubtedly witness even more interest in these games. However, the value of many of them is questionable because: (a) the time needed to memorize mechanistic rules is excessive and (b) the difficulty in interpreting feedback leads to an inability to draw cause-effect relationships. If these games are to be of real value we need more emphasis in game design upon giving the participants data that can be analyzed, cause-and-effect relationships that can be determined, and situations in which intelligent strategy can be devel oped. In short, less doing and more thinking.

The concept of Key Equations as used in TOP MAN AGEMENT SIMULATION, a general management game developed at the University of Nebraska, may serve as a model for these games during the seventies.
Simulation of the evolution of stellar systems
Authors: Hohl Frank
Published: March 2008

Computer models for isolated disk galaxies and for infi nite doubly periodic stellar systems are used to study the self-consistent motion of large numbers of interacting stars as they move in the plane of the galactic disk. The doubly periodic model is used to investigate the develop ment of the gravitational instability for a plane stellar system. The results obtained show that the initial con densations which form are about two Jeans lengths in diameter.

An isolated, initially cold, balanced disk is found to be violently unstable. Adding a sciffcient amount of ve locity dispersion will stabilize all small-scale disturb ances. Most disks investigated are found to be unstable against slowly growing long wavelength modes, and after about two rotations the disks tend to assume a bar- shaped structure. It is also found that the final mass distribution for most disks can be closely approximated by an exponential variation irrespective of the initial mass distribution.
Distributed system simulation using infinite product expansions
Authors: Goodson R.E.
Published: March 2008

Infinite product expansions for the transcendental terms in the transfer functions for linear distributed systems are developed. Simulation of the dynamic re sponse of such systems is indicated, using the product expansion. Comparisons are made between the classi cal eigenvalue and product expansion approximations. It is concluded that the product expansion is an ex tremum transient-amplitude-preserving approximation based on the correct characteristic roots.
The role of hybrid computers in simulation and control
Authors: Paul Frank W.
Published: March 2008

This paper discusses the present atzd futtsre of hybrid computation: Has it reached its zenith, or will it continue to develop as a powerful but specialized technique? The minicomputer has made current hybrid systems practical by providing a low-cost digital component. Unless the cost of the analog computer is reduced, the increasing power and decreasing cost of the minicomputer may severely limit future hybrid computer usage by providing an economic all-digital alternative. However, problems with alternative solution techniques indicate that for some important applications the hybrid computer will be the most cost- effective approach.
Interactive simulation language-8 (ISL-8)
Authors: Benham R.D.
Published: March 2008

ISL-8 is the first single precision, parallel interactive simulation language available for a minicomputer. This paper illustrates ISL-8 programming procedures and opera tional conveniences for solving a second-order differential equation and three nonlinear problems from science and engineering. The relationship to integration step size and computational accuracy is also shown. The article con cludes that ISL-8 as implemented on any of the 4K PDP-8 family of computers can accommodate up to 25 nonlinear differential equations at computational speeds 10 to 50 times faster than languages using floating-point methods. (8K systems can accommodate up to 100 nonlinear equa tions.)
Application of multifactor experimental design plans in parametric studies of theoretical problems
Authors: Wedekind G.L.
Published: March 2008

A technique is proposed for reducing the number of repetitious solu tions required to carry out a conventional parametric study of a theoretical problem. The technique is potentially applicable to a particular class of problems which involve the numerical solution of differential equations. An applicability criterion is presented, along with a method for predicting the errors which may be expected in problems which do not satisfy the criterion exactly.
Time path of total society systems — the case of US society (1951—1972)
Authors: Rastogi P.N.
Published: March 2008

This paper seeks to structure the problem of mea surement and prediction in total society systems. A macrosociological model comprising a limited num ber of variables is developed and applied to five diverse societies of the globe - Brazil, France, India, Nigeria and the USA. The rationale of the model and the methodology are provided by cyberne tic concepts; it permits making qualified predic tions. The model that is developed can be run for ward or backward in time. In the latter use the results of the simulation were compared with available official data for prior years, and the agreement was found to be generally good.

The performance of the model is illustrated here with particular reference to US society for a period of over two decades. In the simulation the time path of a society consists of its viability status (Z)GS and essential variables as functions of time.

The predictions obtained by running the model forward in time depend for their validity on the fit of the simulation to historical data when time runs backward. For 1972 and the USA, this applies particularly to empirical variables like government change, economic growth, price rise, and unemployment. The generality and validity of the model are reinforced by the con sistent results obtained for the other four societies (which differ markedly from the USA) when the model for them is run backward in time.

The model encompasses exogenous pressures, internal system processes, and endogenous events. The latter are interpreted as processes extended in time.
Problems in the implementation of a combined continuous-discrete simulation language
Authors: Golden D.G. , Schoeffler J.D.
Published: March 2008

GSL (Generalized Simulation Language) is a combined continuous-discrete simulation language which permits the simulation of either type of system or a combin ation of the two. The combination leads to powerful new capabilities, including creating and dynamically controlling multiple instances of continuous systems, extensive control over execution and events, and extensive interprocess communication. These capabil ities in turn lead to implementation problems, primarily in the areas of scheduling of multiple continuous simulation blocks, control of interaction between simulation blocks, coordination with discrete blocks, and storage allocation. The resolution of these problems in the GSL implementation is described along with experience with typical problems.
A time-scaling rule for analog computers
Authors: Pessen D.W.
Published: March 2008

Two rules-of-thumb are presented for determining whether a change in time scale in the computer cir cuit is necessary. One rule is for the simulation of feedback systems by means of transfer functions, while the second applies to circuits solving differential equations. Each rule is illustrated by means of an example, and in the Appendix each rule is derived.
Digital simulation of the rotation of a moving triad with a known matrix spin vector
Authors: Massoud M.F. , Youssef Y.A.
Published: March 2008

This paper discusses the numerical evaluation of the elements of the transformation matrix of an orthogonal rectilinear triad moving with respect to a similar fixed system, when the former rotates with a known spin vector. Typical governing equations are formu lated in terms of Euler angles, in terms of quater nions, and in terms of direction cosines and their derivatives. Emphasis is placed on the latter formu lation for solution by digital computation.

The governing equations are reformulated into a homogeneous and linear matricial state variable equa tion of the first order, with a skew symmetric coefficient matrix called the rotation operator. The transition matrix of this state equation gives the required rotation matrix. The characteristics of the skew-symmetric matrices are used in the development of a suitable algorithm for the solution.

The exact rotation matrix can be obtained for cases of constant spin vector and for special cases of variable spin vectors. For the general case of a variable spin vector, a discrete-variable numerical solution based upon a mean coefficient value is used. The algorithm is based upon a recursive formula giving the elements of the rotation matrix at any arbitrary value of the independent variable. Errors resulting from the use of this method are compared (for a particular example) with those resulting from a fourth-order Runge-Kutta integration algorithm. The state equation for systems of higher degrees of free dom is discussed.
Generation of a pseudo-random set with desired correlation and probability distribution
Authors: Polge R.J. , Holliday E.M. , Bhagavan B.K.
Published: March 2008

Pseudo-random sequences can be computed to approximate a distribution or a sample correlation function. How ever, conventional techniques do not allow the control of both distribution and correlation, except for a few special cases. This paper presents a more general and more accurate procedure, based on correlation transfer, to generate a pseudo-random set with select ed distribution and correlation. Two sets are com puted, an ordered set in which the sample values cor respond to the desired probability distribution and an auxiliary set with the desired correlation and arbi trary distribution. The auxiliary set provides the addresses to scramble the ordered set. Thus, the desired correlation is injected without changing the distribution. The representation of continuous and discrete distributions is optimum for a specified set size. An example illustrates the method.
Extension of the hybrid Monte Carlo method for boundary-value problems
Authors: Fahrmeir Ludwig
Published: March 2008

Hybrid Monte Carlo techniques for the solution of linear boundary-value problems have previously been developed. This paper is not primarily concerned with implementing these techniques., but extends the class of problems that can be solved by them and improves the method first described by Little, which in its original form is shown to be valid only in a special case and not generally applicable to linear boundary-value problems.
Simulation of Larval Populations of a Parasitic Nematode of Sheep
Authors: Barger I.A. , Benyon P.R. , Southcott W.H.
Published: March 2008

This paper describes a mathematical model of part of the life-cycle of Haemonchus contortus, a parasitic worm of sheep and other ruminants. The model simulates the free- living stages of the life-cycle, beginning with eggs passing out in the faeces of the sheep, and predicts the con centration of infective larvae on the pasture that will develop from these eggs according to the prevailing climatic conditions. The output from the model has been compared over a three-year period with data from a real experiment; the agreement is good enough to indicate that the model is basically sound. The authors intend to combine this model with a model of the epidemiological and physiological responses of sheep to various levels of contamination of their forage by infective larvae of H. contortus. Such a model is expected to be useful in devising management strategies to control this parasite.
Simulation of the motion of the heart
Authors: Tomek Ivan
Published: March 2008

This paper describes a simulation of the motion of the heart during the heart cycle. It considers the heart as a body with two cavities representing the combined atria and ventricles, respectively. It is coupled to the frame (chest) by viscoelastic eZe ments. In the first part of the paper this heart- frame system is described by equations for the relative translation and rotation of its parts. The factors affecting the motion are blood flows into and out of the heart, the changing shape and distribution of the mass of the heart, and the mechanical coupling. Two models were formulated. The first one included some nonlinear terms, and the second was linearized. Both were tested, and results obtained from the linearized model show that it describes the system adequately. This model can be incorporated into existing analog models of the circulation. It considers only one-dimensional translation and neglects the nonlinear effects of flows. The relationship between the position of the centre of gravity of the heart and its volume and shape is linearized. Results obtained from this model for the contribution of the heart to the human ballistocardiogram (the main purpose of the model) are shown and discussed. The main problem at this stage seems to be the lack of data describ ing the mechanical properties of the system.
Simulation of the effects of weather on an insect population
Authors: Loewer O.J. , Huber R.T. , Barrett J.R. , Peart R.M.
Published: March 2008

This paper describes a digital-computer simulation of the influence of weather on the population of the European corn borer (ECB). The program, which is written in a FORTRAN-based language, defines a basical ly continuous-system model that accommodates discrete events in the weather-ECB ecological system. The principal factors controlling the ECB population are temperature, the daily spread of temperature (i.e., maximum-minimum), and rainfall. The goal of the simu lation is to improve our understanding of crop-ECB ecology and to assist corn-pest managers in reducing crop damage by applying control measures when they will be most effective.
Documentation of CLEANX : a generalized model for simulating the open-water ecosystems of lakes
Authors: Scavia Don , Bloomfield Jay A. , Fisher John S. , Nagy James , Park Richard A.
Published: March 2008

This paper outlines the software for an open-water version of CLEAN, an ecosystem model for lakes. The modular program structure is described, examples of driving variables are given, and the output (including values of several parameters) is shown. The program, with extensive annotations to facilitate adaptation by potential users, is available from author Richard A. Park or from SCS.
Observations on some commonly used methods for identification of parameters in linear systems
Authors: Bekey George A. , Ung Man T. , Karuza Sarunas
Published: March 2008

This paper describes and compares the application of two alternative approaches to the identification of linear systems from input-output data. The first approach is based on fitting input and output data by sums of exponentials and deriving both the system structure and the parameter values from the resulting functions. The second approach is based on assuming a differential-equation structure and finding only the parameter values from the given data. The relative advantages, disadvantages, and computational aspects of both approaches are discussed with reference to a specific biological problem. The results are applicable to a variety of engineering and scientific problems described by systems of first-order linear differential equations.