Showing papers on "Mathematical model published in 1980"

The inverse problem of electromagnetic induction: Existence and construction of solutions based on incomplete data

Abstract: A theory is described for the inversion of electromagnetic response data associated with one-dimensional electrically conducting media. The data are assumed to be in the form of a collection of (possibly imprecise) complex admittances determined at a finite number of frequencies. We first solve the forward problem for conductivity models in a space of functions large enough to include delta functions. Necessary and sufficient conditions are derived for the existence of solutions to the inverse problem in this space. The approach relies on a representation of real-part positive functions due to Cauer and an application of Sabatier's theory of constrained linear inversion. We find that delta-function models are fundamental to the problem. When existence of a solution has been established for a given set of data, actual conductivities fitting the measurements may be explicitly constructed for various special classes of functions. For a solution in delta functions or homogeneous layers a development as a continued fraction is the essential idea; smoothly varying models are found with an adaption of Weidelt's analytic solution.

Candelinc: A General Approach to Multidimensional Analysis of Many-Way Arrays with Linear Constraints on Parameters.

Abstract: Very general multilinear models, called CANDELINC, and a practical least-squares fitting procedure, also called CANDELINC, are described for data consisting of a many-way array. The models incorporate the possibility of general linear constraints, which turn out to have substantial practical value in some applications, by permitting better prediction and understanding. Description of the model, and proof of a theorem which greatly simplifies the least-squares fitting process, is given first for the case involving two-way data and a bilinear model. Model and proof are then extended to the case ofN-way data and anN-linear model for generalN. The caseN = 3 covers many significant applications. Two applications are described: one of two-way CANDELINC, and the other of CANDELINC used as a constrained version of INDSCAL. Possible additional applications are discussed.

Principles of mathematical modeling

Abstract: Preface Acknowledgments Part A: Foundations 1. What is Mathematical Modeling? 2. Dimensional Analysis 3. Scale 4. Approximating and Validating Models Part B: Applications 5. Exponential Growth and Decay 6. Traffic Flow Models 7. Modeling Free Vibration 8. Applying Vibration Models 9. Optimization: What is the Best...? Index

Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements—Part 1: Formulation

Abstract: An efficient numerical (finite element) method is presented for the dynamic analysis of rapidly propagating cracks in finite bodies, of arbitrary shape, wherein linear-elastic material behavior and two-dimensional conditions prevail. Procedures to embed analytical asymptotic solutions for singularities in stresses/strains near the propagating crack-tip, to account for the spatial movement of these singularities along with the crack-tip, and to directly compute the dynamic stress-intensity factor, are presented. Numerical solutions of several problems and pertinent discussions are presented in Part II of this paper.

Strategies of Path Analysis

Abstract: Path analysis is a method for explicitly formulating theory, and attaching quantitative estimates to causal effects thought to exist on a priori grounds. There are four basic kinds of path models: recursive, block, block-recursive, and nonrecursive. Because some questions can be answered only under certain path analytic structures, the theoretical questions and research goals guide the selection of a particular model. Knowing what sorts of questions each model addresses, educational researchers will be in a better position to formulate hypotheses in model-specific terms. Four illustrations are provided, presenting strategies of analysis typical of each kind of model.

Geotrack model for railroad track performance

Abstract: In order to provide a basis for predicting track performance, an analytical model is necessary that will realistically represent the actual behavior of the track system subjected to vehicle loading conditions. The model should adequately characterize the three-dimensional nature of this problem; the various soil and ballast layers can be distinguished and be given proper material properties. In this paper a model is presented that incorporates both of these requirements with a feature which permits loss of contact between tie and ballast when the rail springs up. This model, named GEOTRACK, was developed primarily to characterize the geotechnical aspects of the track behavior. The predictions of this model are in good agreement with measured stresses, strains, and displacements from field experiments at the government test track in Pueblo, Colo.

Comparative study of saturation methods in synchronous machine models

Abstract: The paper investigates the use of various mathematical models to represent saturation in a synchronous machine. For the first time special attention is given to quadrature axis saturation. Calculated transient-response results are compared in order to find an accurate and computationally economical method of allowing for saturation.

Mathematical models of thermal regulation.

Abstract: The thermal characteristics of animal and human tissues determine in important ways the absolute temperature of such tissues and organ systems in response to varying ambient conditions and different levels of metabolic activity. The presence of the circulatory system adds convective heat transport to the other thermal characteristics governing heat transfer such as conduction and heat capacitance. Most tissues exhibit a high degree of anisotropy in their structure and in addition may have a variable rate of heat production and blood flow. Many organs, in addition, are involved in the system that regulates the body temperature of homoiotherms, and this can result in such tissues changing important thermal characteristics in response to neural commands originating in other parts of the body. All animals, including man, live in a constantly changing thermal environment, with a widely varying internal heat production. As a result, the thermal gains and losses are constantly varying, with different factors participating at different times. Although responses to a given set of environmental conditions can be measured in a test exposure, the universe of possible conditions is so great that it is not feasible to test all such conditions. Mathematical simulation models have been constructed by a number of investigators. These models incorporate insights from anatomy, physiology, and mechanical engineering and provide a simplified system that reacts to internal and external thermal stimuli in essentially the same manner as the real system does. One of many such systems was developed at the John B. Pierce Foundation Laboratory, New Haven, Connecticut. An early version was formulated for implementation on an analog computer.' Since then, advanced versions have been described by this Laboratory\" as well as by a number of authors who have adapted or expanded this later version for special applications. Gagge et al.' developed a very simplified version for assessment of complex thermal environments. Montgomery' adapted the advanced model for the simulation of heat transfer in divers wearing diving suits. Azer and Hsu6 adapted various models to the prediction of thermal sensation. The National Aeronautics and Space Administration used simulations of various physiological control systems including the thermoregulatory system quoted above.

On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations

Abstract: It is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission-line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission-line network models used in the steady-state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two-dimensional example.

New method for extracting static equilibrium configurations in general relativity

Abstract: We investigate the static equations of general relativity for spherical symmetry in Schwarzschild coordinates A new formalism is discussed which allows integration of the equations for an isotropic fluid under a broad range of initial assumptions We are able to derive many previous solutions using this technique, and find as well a number of new solutions to the equations A process is discussed whereby already known solutions can be generalized to increase their flexibility and usefulness with regard to the mathematical modeling of ultradense objects such as neutron stars

Mathematical Models for High-Intensity Discharge Lamps

Abstract: Mathematical models have been determined for mercury and high-pressure sodium electric discharge lamps. The models consist of a set of nonlinear differential equations. They reproduce the electrical characteristics of the lamps from dc to the high audio frequencies with good accuracy. They permit computer simulation of electronic or reactive ballasting circuits. Also, they yield a better qualitative understanding of the properties of a discharge lamp as an electric circuit element. The methods by which these models were determined are described, and the pertinent lamp properties are measured.

A Framework for Constructing Network Equilibrium Models of Urban Location

Abstract: Recent advances in network equilibrium modeling provide efficient algorithms for solving the urban trip assignment problem. These models can be extended to incorporate the trip distribution problem with two types of variable demand functions. By reinterpreting the zone-to-zone trip variable, these models can be viewed as urban location models. This paper synthesizes these results, and shows how several urban location models can be derived from the mathematical framework based on the network equilibrium problem.

Uncertainty in the context of highway appraisal

Abstract: Transport planning is based on traffic forecasts which are subject to great uncertainties. These uncertainties have generally been ignored or, at least, not explicitly included in the planning process. This paper describes the principles behind the estimation of the uncertainty (or range of error) of the forecasts of a traffic model and discusses the means by which this information can be absorbed into the decision-making in transport planning projects. These principles have been applied to the appraisal of a British highway project and throughout the paper reference is made to this project in order to illustrate the results of the practical application of an explicit treatment of uncertainty. It is believed that this approach can and should be developed for application in most areas of transport planning, leading inevitably to an improvement in the quality of the decisions taken.

Improved boundary–integral equation method for time‐dependent inelastic deformation in metals

Abstract: Efficient solution of boundary-value problems for time-dependent inelastic deformation in metallic structures are generally solved by finite element methods and separate descriptions for time-independent plasticity and time-dependent creep are normally used. The boundary-integral equation method was recently applied for the first time to such problems. A very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler type time-integration scheme with automatic time-step control for time integration is presented. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor--corrector scheme for time-integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time-histories of loadings. The numerical results presented in the paper are for certain illustrative problems.

A model for predicting the effect of moisture content on the modulus of elasticity of soybeans.

Abstract: A functional relationship has been proposed foi describing the effect of moisture content on the modulus of elasticity of remoistened soybeans. Based on experimental results, constants in the model have been determined by non-linear regression. Data from the ex-periments and the proposed function are graphically compared.

Numerical simulations of molecular multiphoton excitation models

Abstract: In this paper we report the results of numerical simulations of the intramolecular dynamics of a model system for multiphoton excitation of large molecules, where the low energy range is represented by a single discrete state, while the quasicontinuum is mimicked by two or three manifolds of molecular eigenstates. The random coupling model (RCM), where the radiative coupling matrix elements are assumed to be random functions of the level indices, yields conventional rate equations describing consecutive–reversible transitions for the populations with golden rule rates. In addition, numerical simulations were conducted for a constant coupling model (CCM) and for a separable random coupling model (SRCM), confirming the counterintuitive analytical results for these model systems. The time evolution of a RCM system is determined by the distribution function of the coupling elements and not by individual coupling terms, and the intramolecular dynamics is essentially determined by the lower moments (average and...

Optimal Sampling Strategies for Statistical Models with Discrete Dependent Variables

Abstract: The object of this paper is to improve the cost-effectiveness of data gathering procedures for models with discrete dependent variables. It is assumed throughout the paper that the true value of the parameter vector is approximately known and that, with that information, one must select a statistically optimal number of observations from different population subgroups to refine the accuracy of the estimate. It is shown that the problem can be reduced to a small mathematical program whose objective function can be written after a few preliminary algebraic manipulations. For binary choice models, these preliminary calculations are simple enough to be implementable on 1979 state-of-the-art programmable hand calculators. It is also shown that choice-based and mixed data can be optimally selected in a similar way; in particular, binary choice-based samples drawn from one single population group are so easy to analyze that all calculations can be performed by hand. Multinomial models are less amenable to hand calculations, except, perhaps, trinomial models which require evaluation of a double integral. The technique extends naturally to limited dependent variable regression models.

Game Theory-Mathematical Models of Conflict

Abstract: Part III contains most of the articles of direct interest to O.R. workers and fortunately they are of a uniformly high standard. The first three articles are particularly good, especially Fiacco's on Barrier Methods, which gives a clear exposition of the theory and applications of Barrier Methods in non-linear programming, together with nine pages of references. Similarly, anyone wishing to read up on the mathematical background to developments in integer programming could do worse than read the articles on Cutting Plane Methods & Bivalent (0,1) Programming. The paper on Decomposition Methods is comprehensive, covering tearing, non-linear equations and applications to dynamic pro? gramming. The final two papers can be taken together, with the transformation of linear and convex quadratic programming and bimatrix games into linear complementarity problems, and non-linear complementary problems being discussed in terms of Fixed Point methods.

On the Consistency of the Mathematical Models of Chemical Reactions

Abstract: There are two main principles according to which chemical reactions in a spatial domain are modeled: (i) global description (i.e. without diffusion, spatially homogeneous or ‘well-stirred’ case) versus local description (i.e. including diffusion, spatially inhomogeneous case), (ii) deterministic description (macroscopic, phenomenological, in terms of concentrations) versus stochastic description (on the level of numbers of particles, taking into account internal fluctuations).

Analytical method to predict noise radiation from vibrating machine systems

Abstract: A fundamental study of noise generation in high‐speed mechanical systems is undertaken. The objective being the development of modeling techniques for the prediction of mechanical system noise levels. Recently developed dynamical procedures are used to obtain the motions of linked mechanical systems with elastic elements and connection clearances. The ranges of critical system parameters are identified and classical acoustical analysis methods are used in determining the most significant acoustic sources. Detailed acoustic models are analytically developed for these significant sources. These methods and models are then used to predict the farfield radiation of a simple, yet representative, mechanical system; an elastic link with connection clearances in a nominal motion container.

Diffusion from solid cylinders

Abstract: The problem considered is the diffusion of material from a solid cylinder initially containng a uniform concentration and immersed in a well-stirred bath which maintains the external concentration at zero. The Fourier-Bessel series form of the fraction of the original material removed from the cylinder as a function of time converges very slowly for small time. An alternate form was obtained, which converges reasonably rapidly for small time. The convergence acceleration method of P. Wynn was also used to provide an efficient method for computation. Numerical examples and program listings are included.

Principles of the spin mode of combustion front propagation

Abstract: A mathematical model of the spin mode of combustion propagation on a cylindrical surface is developed. The model is a system of two-dimensional nonlinear partial differential equations, which are solved numerically by an implicit conservative two-dimensional difference scheme and a cross-drive method. Parametric effects in the spin combustion process are examined, and theoretical results are compared with experimental data.