Complicated Mathematical Models Research Articles

Computer Control Laboratory

The paper describes a three semester course of the Computer Control Laboratory. Didactic program of the laboratory addresses all aspects related to the design and application of real-time computer control systems: software development technology, system development, and specialized controllers application. The run-time environment used in most laboratory exercises is a multi processor microcomputer controlled by a real-time operating system. The system is able to model different types of intertask communication procedures. Some details on the hardware structures and the operating system are discussed. Process models used as a real-world during the laboratory projects are presented. Some of them are relatively simple, while the others are characterized by a complicated mathematical models.

The Place of Modelling in Ecology

The Place of Modelling in Ecology

Expert systems in management science

Decision support software as we know it has failed in its goal of bringing managers and the management sciences closer together. Conventional software requires computer literacy and detailed technical modeling skills. Top managers, on the other hand, are prized for an entirely different set of skills: experienced judgment, innovative thinking and the ability to see the “big picture”. Even if they could build complicated mathematical models, work closely with computers and had timely access to relevant details, most managers would not have the time. This paper contends that the gap between managerial and analytic/computer competence can be bridged with expert systems meeting the following criteria: 1. 1. Require no user training 2. 2. Interact and explain themselves 3. 3. Learn from and adapt to users 4. 4. Incorporate state-of-the-art analytic techniques Palladian Software, Inc., of Cambridge Massachusetts is using artificial intelligence technology to build such expert systems for managers. An example of one application is provided.

Dynamic response of a thin-wall structure to axial loading

Because of the extensive application of thin-walled structures of composite materials in various branches of modern technology (rocket and aviation engineering), it is important to develop reliable methods ofpredicting their stress--strain and vibration state in the conditions of the effect of high-speed external loading (force, thermal, acoustic). Recently, there have been a number of detailed theoretical and experimental investigations of the nonstationary deformation of real structures which usually consist of several sections and are characterized by the presence of reinforcing elements, a locally attached weight, weakening holes, etc. The need to describe adequately the dynamic behavior of shell systems with a complicated geometrical rheological structure results in the development of comparatively complicated mathematical models. For example, the authors of [1-4] used the relationships of improved theory of Timoshenko's type for numerical simulation of the wave processes in compound shell-rod structures subjected to axial pulsed loading. In this work, we shall construct a mechanicomathematical model and a conservative difference scheme for determining the force and kinematic characteristics of wave fields in thinwalled structures with holes. The time dependences of the acceleration of combined masses are presented, and the analysis of these dependences makes it possible to estimate the effect of internal reinforcing elements, structural damping, and weakening and other factors on the evolution of transition processes. i. Formulation of the Initial Boundary-Value Problem. We shall examine thin-walled compound structures (Fig. i) whose left end is subjected to the effect of a nonaxisymmetric pulse f(~, t). The ends of the sections (shells of revolution) are rigidly fixed in thin nondeformed disks with the masses M~ ... M4. The walls of the shells are weakened with rightangled and circular holes with free or rigidly fixed edges. Each section has a constant wall thickness hj (j = i, 2, 3) and can be made of various materials (metals, composites). We shall introduce an orthogonal coordinate system s, y, z with unit vectors directed respectively along the generating line, around the circle and along the normal to the median surface of the shells, and also the radius-vector of the arbitrary point P: r(s,~ ) = [R(s) r R(s) sin ~, z(s)] T, where R(s) = AP, z(s) = OA, y = R(s)~.

Statistische Modellierung aus experimentell gewonnenen Daten MODAK

Mathematical modelling based on measurable data obtained by experiments is gaining increasing importance. One of the reasons of it is the type of hardware now available in form of microelectronics enabling complicated mathematical models to be applied for controlling management and production processes and facilities.Already in the modelling of one-dimensional dependencies by means of conventional methods some problems were encountered in the identification of parameters for complicated functions such as $$y = a_0 + a_1 \circ x^{a_2 }$$ unless all parameters could be determined simultaneously (e.g. by Gauss approximation). Simple iterative methods for the additional parameters do not yield any applicable results. By means of MODAK a methodology of modelling is now available which is able to compute multi-dimensional non-linear mathematical models from experimentally obtained data in a quality not achieved so far. Previous considerations on the functional equations in the individual planes are not required. The very function describing the particular single correlation in an optimum way is selected for each plane.MODAK is suited to mathematical and statistical modelling, compaction and analysis of data encountered in the activity and system analysis as well as for the evaluation of test results.

Application of the aquifer's average characteristics for determining the onset of thermohaline convection in a heterogeneous aquifer

Due to layered deposition of sedimentary rocks, the aquifer's characteristics usually vary with the depth. Such variations are mainly significant in thick aquifers. The variable characteristics cause the aquifer to be heterogeneous. The basic equations used for the simulation of transport phenomena in the heterogeneous aquifer are nonlinear. Therefore, simulation of thermohaline convection in such a stratum requires complicated mathematical models. The present study considers the application of the aquifer's average characteristic method for such a simulation. According to this method, the model considers constant average characteristics of the aquifer, instead of considering variable local characteristics of the saturated porous medium. Such an approach considerably simplifies the calculations. The study verifies the applicability of the method for the predictions concerning diffusive thermohaline convection in a heterogeneous aquifer. On this basis the study presents an analysis of important features of dispersive thermohaline convection in a heterogeneous aquifer by applying the method of the aquifer's average characteristics.

Compex, a computer system for bleaching control based on direct measurements

This article contains a discription of a new computer system for the bleaching process which has been developed by Kajaani Co. It’s mode of operation differs from other corresponding systems in that all control functions for chemical dosage are based on direct process measurements.The desired variables, e.g. colour, brightness, residual and pH, are measured from the process, either directly or from continious samples with the help of a sampling system. The aim of this is to measure those important variables, which are necessary to control the process, as early as possible. Now the control will be done as a rapid feedback control, and it is not required to use complicated mathematical models which try to predict the process behaviour. With this system it is possible to achieve an accurate, but first of all a rapid control, which has the possibility to observe changes in the process. The system is based on an HP-45 desktop computer.

Compex, A Computer System for Bleaching Control Based on Direct Measurements

This article contains a discription of a new computer system for the bleaching process which has been developed by Kajaani Co. It’s mode of operation differs from other corresponding systems in that all control functions for chemical dosage are based on direct process measurements. The desired variables, e.g. colour, brightness, residual and pH, are measured from the process, either directly or from continious samples with the help of a sampling system. The aim of this is to measure those important variables, which are necessary to control the process, as early as possible. Now the control will be done as a rapid feedback control, and it is not required to use complicated mathematical models which try to predict the process behaviour. With this system it is possible to achieve an accurate, but first of all a rapid control, which has the possibility to observe changes in the process. The system is based on an HP-45 desktop computer.

The effects of compaction on retaining walls

It is widely recognized that compaction of fill behind earth retaining structures can induce lateral earth pressures that vary considerably in magnitude and distribution from those predicted using classical earth pressure theory. This Paper presents a simple analytical method which relates induced lateral earth pressures to the effective line loading imposed by compaction plant. Although by no means definitive, the method proposed permits a meaningful assessment of compactioninduced lateral pressures without recourse to complicated mathematical models. Predicted pressures are compared with observed pressures from two case histories, in a third case history the performance of a retaining wall is compared with predictions made using classical theory and the proposed method. A comparison is made between the factors of safety assumed to exist in conventional retaining wall design and those resulting when compaction effects are taken into account. II est couramment admis que le compactage du remblai derrière les ouvrages de souttnement peut occasionner des poussées de terre latérales qui varient considérablement en valeurs et en par rapport aux poussées calcultes en utilisant la théorie classique sur les poussées des terres. Cet article présente une méthode analytique simple qui compare les pousées latérales des terres et la charge linéaire efficace imposbe par I'appareil de compactage. Bien que nullement définitive, la méthode proposée permet d'évaluer de manière significative les poussées latérales dues au compactage sans qu'il y ait besoin d'avoir recours à des modéles mathématiques compliqués. Les pressions calculées sont comparées aux pressions effectivement enregistrées dans deux cas historiques et, dans un troisième cas, la comportement d'un mur de souténe ment est comparée aux prévisions établies suivant une théorie classique et la méthode proposée. Une comparaison est faite entre les coefficients de sécurité admis lors de la conception de murs de soutènement classiques et les coefficients obtenus lorsque les effets de compactage sont pris en considération.

Microtremor site analysis study at Beatty, Nevada

abstract Current microzonation mapping procedures often call for the generation of complicated mathematical ground-motion models. These models require that expensive geophysical and geological surveys be performed to gather input information. A more desirable method of estimating ground motions would be to measure these effects directly. Microtremor analysis procedures provide such a direct method. Microtremor data were collected at several sites at Beatty, Nevada, and compared to nuclear event and mathematical model ground-motion spectra. The frequency at which peak amplitudes occurred on all spectra agreed. These frequencies appear at the resonance frequency of the surface layer when stimulated by compressional waves. Results of this experiment add validity to the use of microtremors in microzonation studies.

The Ruin Problem in Multiple-Line Insurance. Comment

Ruin Problem in Multiple-Line Insurance-A Simplified Model,' by Hofflander and Duvall, which appeared in the Journal of Financial and Quantitative Analysis, (June, 1967) is one of the more significant efforts in applying statistical techniques devise rules for testing the ratio of premiums written policyholders' surplus. The authors state that their purpose is to make use of a generally accepted statistical tool devise and explain a new rule for relating premiums written (i.e., sales) policyholders' surplus, taking the loss reserve and stock portfolio into account.2 They concluded at the end of their paper that under the worst possible conditions a property and liability insurance company could write up $9.10 of premiums for every dollar of policyholders' surplus with only the slightest probability of becoming insolvent. This was a rather astounding conclusion, given the emphasis on the traditional 2:1 rule which has been expounded in industry circles for years. The conclusion may have been so astounding as turn practical insurance men and women off from considering their model. (Just some more ivory tower professors playing with complicated mathematical models which have no applicability the real world.) Unfortunately, Hofflander and Duvall may have unknowingly blunted the importance of their efforts by a rather elementary arithmetic error. Rather than a 9.1:1 premiums policyholders' surplus ratio, it should have been .91:1. Apparently they misplaced the decimal by one place. A ratio of .91:1 is obviously much more realistic and certainly a more palatable result for practitioners in the industry. A brief look at their work will show where they went astray. In constructing their model, Hofflander and Duvall make the convenient assumption that the combined loss and expense ratios of the various lines of insurance are normally distributed. They propose techniques for estimating the mean and variance of the combined loss and expense ratio for a given property and liability insurance company. By making use of these estimates, they illustrate how establish standards of minimum policy-

Single Activity Accidents

T ADITIONALLY, tort law has been viewed as having two functionsdeterrence and compensation. Taxes and fines also serve the first purpose while private and social insurance join in the second (and naturally affect the first). Accidents fit neatly into the economists' framework of externalities, and the role of taxes and insurance has been examined in an equilibrium framework in this context. The purpose of this essay is to begin the extension of equilibrium models to include tort liability for accidents. Thus, the models developed represent an attempt to examine some of the elements of the way tort law affects resource allocation. This is not an analysis of the development of tort law nor a serious putting together of all relevant questions in a way appropriate for policy analysis. Any work in this area must be greatly influenced by the work of Guido Calabresi,1 and I started this project as an attempt to set Calabresi to mathematics, although the logic of my approach has drawn me away from that definition of the task. While the paper concentrates on developing successively more complicated mathematical models, I have attempted to make it readable by someone who omits the mathematical derivations, although he must follow the setting up of the models. The paper analyzes equilibrium behavior of all the participants in an activity, where participation exposes one to the possibility of accidents involving two (and only two) persons. For a world of risk-neutral expected-utility maximizers who do not engage in side transactions, equilibrium in the activity is related to the parameters (particularly the standard of due care) determining the outcomes of the tort law system. The focus is on the nature of equilibrium rather than the complexities of judicial decision-making. Although much of the paper is devoted to simple cases where equilibrium can be made

Numerical Evaluation of Spatially Dependent Dynamic Reactor Systems Using Pseudorandom Signals

The crosscorrelation method of determining the impulse response of a dynamic system, which has been widely used in experiments, is applied numerically to a complicated mathematical model of a spatially dependent reactor system, and is concluded to be a practical alternative to analog computer analysis.The method is applied using two families of periodic discrete level signals as the input perturbation. It is demonstrated that a relatively new class of signals, having three possible levels, which has had very limited use to date, leads to a more accurate determination of the impulse response in the presence of strong system nonlinearities than do the better known and more widely used binary signals.