Showing papers on "Mathematical model published in 2000"

Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences

Abstract: A general concept is presented which allows of setting up mathematical models for stochastic and quasi-deterministic dynamic processes in social systems. The basis of this concept is the master equation for the probability distribution over appropriately chosen personal and material macrovariables of the society. The probabilistic transition rates depend on motivation potentials governing the decisions and actions of the social agents. The transition from the probability distribution to quasi-meanvalues leads to in general nonlinear coupled differential equations for the macrovariables of the chosen social sector. Up to now several models about population dynamics, collective political opinion formation, dynamics of economic processes and the formation of settlements have been published.

Hysteretic Models for Deteriorating Inelastic Structures

Abstract: The modeling of deteriorating hysteretic behavior is becoming increasingly important, especially in the context of seismic analysis and design. This paper presents the development of a versatile smooth hysteretic model based on internal variables, with stiffness and strength deterioration and with pinching characteristics. The theoretical background, development, and implementation of the model are discussed. Examples are shown to illustrate the features of the model. Many inelastic constitutive models in popular use have been developed independently of each other based on different behavioral, physical, or mathematical motivations. This paper attempts to unify the concepts underlying such models. Such a holistic understanding is essential to realize limitations in application of inelastic models and to extend 1D models to 3D models featuring interaction between various stress resultants.

Applied parameter estimation for chemical engineers

Abstract: This book determines adjustable parameters in mathematical models that describe steady state or dynamic systems, presenting the most important optimization methods used for parameter estimation. It focuses on the Gauss-Newton method and its modifications for systems and processes represented by algebraic or differential equation models.

Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth

Abstract: In this paper we develop a general technique for establishing analyticity of solutions of partial differential equations which depend on a parameter e. The technique is worked out primarily for a free boundary problem describing a model of a stationary tumor. We prove the existence of infinitely many branches of symmetry-breaking solutions which bifurcate from any given radially symmetric steady state; these asymmetric solutions are analytic jointly in the spatial variables and in e. 1. THE MODEL AND MAIN RESULT In this paper we present a general technique for establishing analyticity of solutions of systems of partial differential equations which depend analytically on a parameter e. The method works not only for boundary value problems but also for free boundary problems. In this latter context it can be used to establish long time existence of transient solutions, and also to study the existence of spatially asymmetric steady solutions. Since free boundary problems are typically more challenging than their boundary-value counterparts, we shall concentrate here on a free boundary problem from developmental biology, namely, a model of tumor growth. To further exemplify the generality of our approach an instance of a boundary value problem (in a fixed domain) is presented in the last section of the paper. A variety of other problems are amenable to the same analysis, including, in particular, the Hele-Shaw model of fluid flow [11]. Within the last several decades a number of mathematical models have been developed that aimed at describing the evolution of carcinomas (see. e.g., [1, 5, 6, 8, 12, 13] and the references cited there). The main objective of these models has been to qualitatively describe, under various simplifying assumptions, the growth and stability of tumor tissue. Analysis and simulations of such models are helping to assess the relative importance of various mechanisms affecting tumor growth as well as the efficacy of certain cancer treatments. On the other hand, the description of the stationary (dormant) configurations that arise from the models has only been addressed in the case of spherical tumors, but otherwise it remains largely unexplored. In this paper we develop a method for establishing analyticity of Received by the editors August 17, 1999. 1991 Mathematics Subject Classification. Primary 35B32, 35R35; Secondary 35B30, 35B60, 35C10, 35J85, 35Q80, 92C15, 95C15.

Three-Dimensional Mathematical Model of Suspended-Sediment Transport

Abstract: This paper presents the basic equations for a mathematical model of sediment-laden flow in a nonorthogonal curvilinear coordinate system. The equations were derived using a tensor analysis of two-phase flow and incorporate a natural variable-density turbulence model with nonequilibrium sediment transport. Correspondingly, a free-surface and the bottom sediment concentration are employed to provide the boundary conditions at the river surface and the riverbed. The finite analytic method is used to solve the equations of mass and momentum conservation and also the transport equation for suspended sediment. To demonstrate the method, the sediment deposition for the Three Gorges Project is considered. The mathematical model specifies the boundary conditions for the inlet and outlet using data from physical model experiments. The results for the mathematical model were tested against laboratory measurements from the physical model experiment. Good agreement and accuracy were obtained.

Evaluation of unsteady flow resistances by quasi-2d or 1d models. technical note

Abstract: This note considers the evaluation of resistances in unsteady flow by means of a one-dimensional (1D) unsteady friction model. The model is applied for the case of a water hammer, both in a single gravity pipeline and in a single pumped pipeline. Comparisons with experimental results show that the model does not predict the exact shape of the oscillation, but it gives, with high precision, the maximums and minimums of the pressure head oscillation if correct values of the parameter of the model are used. Because experimental evaluations can be made only for a few cases and can give rise to very different values depending on experimental conditions, the sensitivity of the model to physical and numerical parameters that influence the phenomenon is examined by comparison with the results of a quasi-2D model previously proposed.

Mathematical Head-Neck Models For Acceleration Impacts

Abstract: The objective of this thesis is to develop a detailed three-dimensional (3D) mathematical model describing the dynamic behaviour of the human head and neck in accident situations without head contact. Firstly, a relatively simple model (the global model) with few anatomical details was developed. Secondly, detailed segment models of the upper and lower cervical spine were developed as an intermediate step. Finally, the detailed head-neck model was formed by joining the segment models and adding muscle elements.The main conclusions are as follows: (1) Active muscle behaviour is essential to accurately describe the human-neck response to impacts; (2) The global model is a computationally efficient model and, therefore, especially suited for car safety improvement and dummy neck development; and (3) the detailed model is suitable for studying neck injury mechanisms and neck injury criteria, since it reveals the loads and deformations of individual tissues of the neck. Recommendations are given for additional experiments, model enhancements, and further validation. (A)

Modeling nonstationary longitudinal data.

Abstract: An important theme of longitudinal data analysis in the past two decades has been the development and use of explicit parametric models for the data's variance-covariance structure. A variety of these models have been proposed, of which most are second-order stationary. A few are flexible enough to accommodate nonstationarity, i.e., nonconstant variances and/or correlations that are not a function solely of elapsed time between measurements. We review five nonstationary models that we regard as most useful: (1) the unstructured covariance model, (2) unstructured antedependence models, (3) structured antedependence models, (4) autoregressive integrated moving average and similar models, and (5) random coefficients models. We evaluate the relative strengths and limitations of each model, emphasizing when it is inappropriate or unlikely to be useful. We present three examples to illustrate the fitting and comparison of the models and to demonstrate that nonstationary longitudinal data can be modeled effectively and, in some cases, quite parsimoniously. In these examples, the antedependence models generally prove to be superior and the random coefficients models prove to be inferior. We conclude that antedependence models should be given much greater consideration than they have historically received.

Recursive Prediction of Traffic Conditions with Neural Network Models

Abstract: This paper presents a recursive traffic flow prediction algorithm using artificial neural networks. The system prediction model is specified based on the understanding of how disturbances in traffic flow are propagated, and the order of the model is determined by correlation analysis. The parameters of the model, on the other hand, can be obtained through nonlinear optimization. Preliminary studies show that this approach can yield reasonably accurate results.

Prediction and optimization of weld bead volume for the submerged arc process - Part 1

Abstract: Because of its high quality and reliability, submerged arc welding (SAW) is one of the chief metal-joining processes employed in industry for the manufacture of steel pipes used for various applications. This paper highlights a study and analysis of various process-control variables and important weld bead quality parameters in SAW of pipes manufactured out of structural steel (IS: 2062). Mathematical models were developed for the submerged arc welding of 6-mm-thick structural steel plates using 3.15-mm-diameter steel electrodes. The models were developed using the five-level factorial technique to relate the important process-control variables -welding voltage, wire feed rate, welding speed and nozzle-to-plate distance - to a few important bead-quality parameters - penetration, reinforcement, bead width, total volume of the weld bead and dilution. The models developed were checked for their adequacy with the F test. Using the models, the main and interaction effects of the process-control variables on important bead geometry parameters were determined quantitatively and presented graphically. The developed models and the graphs showing the direct and interaction effects of process variables on the bead geometry are very useful in selecting the process parameters to achieve the desired weld-bead quality. Also, the precision ofthe results obtained with the mathematical models were tested by using conformity test runs. The test runs were conducted nearly two years after the development of mathematical models with the same experimental setup, and it was found the accuracy of the predicted results is about 98%. Further, these mathematical models help to optimize SAW to make it a more cost-effective process.

A Structural Modeling Approach to a Multilevel Random Coefficients Model

Abstract: A method for estimating the random coefficients model using covariance structure modeling is presented. This method allows one to estimate both fixed and random effects. A way of translating the general linear mixed model into a structural equation modeling (SEM) format is presented. In particular, a LISREL setup for the multiple group linear latent growth curve model is illustrated with suggestions on ways to parameterize more complex models. To illustrate the procedure, we apply the method to both simulated and real data. The method is shown to recover the simulated parameter values. Results and interpretation for the Belsky and Rovine (1990) marriage data are presented. Other applications of the more general model are suggested.

A dynamic model of the rolling process. Part II: inhomogeneous model

Abstract: Mathematical models representing the static rolling process have attracted considerable attention in the past, resulting in analytical, numerical, or graphical solutions obtained under various degrees of simplification and constraints. Most models, however, can only be used under steady conditions, and therefore are not suitable for the study of rolling chatter. An enhanced analytical process model that can handle dynamic variations exerted by roll vibrations in multiple directions is proposed in this paper, and its linearized form established for easy analysis. Finally, experiments are presented that verify the accuracy of the proposed dynamic model of the rolling process.

Mathematical Models of Distribution of Sediment Concentration

Abstract: Mathematical models have been developed that can completely describe the distribution of sediment concentration from the channel bed to the water surface. These models can be used to estimate the mean (depth-averaged) sediment concentration by a quick, point sampling in river engineering practice. The developed models are products of a combined application of the deterministic and probabilistic concepts. The complementary nature of the two concepts strengthens the methodology of describing the various features of sediment transport. The models incorporate a velocity distribution equation that corresponds to a probability distribution derived by maximizing the information entropy. The probability distribution is a compact description of the system at a channel section, and its resilience or stability explains the applicability of the developed models of velocity and sediment distributions in a wide range of flows, steady or unsteady.

Neural networks in signal processing

Abstract: Nuclear Engineering has matured during the last decade. In research & design, control, supervision, maintenance and production, mathematical models and theories are used extensively. In all such applications signal processing is embedded in the process. Artificial Neural Networks (ANN), because of their nonlinear, adaptive nature are well suited to such applications where the classical assumptions of linearity and second order Gaussian noise statistics cannot be made. ANN’s can be treated as nonparametric techniques, which can model an underlying process from example data. They can also adopt their model parameters to statistical change with time. Algorithms in the framework of Neural Networks in Signal processing have found new applications potentials in the field of Nuclear Engineering. This paper reviews the fundamentals of Neural Networks in signal processing and their applications in tasks such as recognition/identification and control. The topics covered include dynamic modeling, model based ANN’s, statistical learning, eigen structure based processing and generalization structures.

Optimal estimation of roughness in open-channel flows. technical note

Abstract: The inverse problem of estimating the open-channel flow roughness is solved using an embedded optimization model. Measurement data for flow depths and discharges at several locations and times are used as inputs to the optimization model. The nonlinear optimization model embeds the finite-difference approximations of the governing equations for unsteady flow in an open channel as equality constraints. The Sequential Quadratic Programming Algorithm is used to solve the optimization model. The performance of the proposed parameter estimation model is evaluated for different scenarios of data availability and noise in flow measurement data. Solution results for illustrative problems indicate the potential applicability of the proposed model.

Correlating dynamic characteristics from field measurements and numerical analysis of a high-rise building

Abstract: Using the concept of lumped masses and rigid floor slabs, several mathematical models were built using a popular PC-based finite element program to model a tall building with a frame-core wall structural system. These models were analysed to obtain the first nine mode shapes and their natural frequencies which were compared with those from field measurements, using numerical correlation indicators. The comparison shows several factors that can have a significant effect on the analysis results. Firstly, outriggers connecting the outer framed tube system to the inner core walled tube system have a significant effect on fundamental translational mode behaviour. Secondly, detailed modelling of the core considering major and minor openings as well as internal thin walls has the strongest influence on torsional behaviour, whose measurements were shown to be an important aspect of the dynamic behaviour for the structure studied. Fine tuning of an analytical model requires not just considering variation in values of structural parameters but also attention to fine detail. Copyright © 2000 John Wiley & Sons, Ltd.

A Unified Model for Color Prediction of Halftoned Prints

Abstract: This study introduces a new model and a new mathematical formulation describing the light scattering and ink spreading phenomena in printing. The new model generalizes the classical Kubelka-Munk theory, and unifies it with the Neugebauer model within a single mathematical framework based on matrices. Results like the Saunderson correction, the Clapper-Yule equation, the Murray-Davis relation and the Williams-Clapper equation are shown to be particular cases of the new model. Using this new theoretical tool, the reflection spectra of 100 samples printed on high quality paper by two different ink-jet printers were computed with an average prediction error of about ΔE = 2.1 in CIELAB.

Estimating scalar sources, sinks, and fluxes in a forest canopy using Lagrangian, Eulerian, and hybrid inverse models

Abstract: A new method was developed to estimate canopy sources and sinks from measured mean concentration profiles within the canopy (referred to as the "inverse" problem). The proposed method combined many of the practical advantages of the Lagrangian localized near-field (LNF) theory and higher-order Eulerian (EUL) closure principles. Particularly, this "hybrid" method successfully combined the essential conservation equations of closure modeling and the robustness of the regression source inversion developed for LNF theory. The proposed method along with LNF and EUL were tested using measurements from two field experiments collected in a pine forest and published measurements from a wind tunnel experiment. The field experiments were conducted to investigate the vertical distribution of the scalar fluxes within the canopy and the temporal patterns of the scalar fluxes above the canopy. This comparison constitutes the first "inverse method" comparison performed using the same data sets on all three models. For the wind tunnel data, all three models well reproduced the measured flux distribution. For the field experiments, all three models recovered the measured spatial and temporal flux distribution in an ensemble sense. The agreement between these three models is desirable to the inverse problem because it adds the necessary confidence in the computed flux distributions. However, the agreement among all three models with the field measurements, on a 30-min time step, was less than satisfactory. Additionally, the divergence between models and measurements increased with departure from a near- neutral atmospheric state. Despite fundamental differences in these model approximations, this similarity in model performance suggests that the source information recovered from a measured one-dimensional mean concentration profile will not be further enhanced by a one-dimensional steady state, planar homogeneous model of neutral flows.

Modeling wells in porous media flows

Abstract: In this paper, we prove the existence of weak solutions for mathematical models of miscible and immiscible flows through porous medium. An important difficulty comes from the modelization of the wells, which does not allow us to use classical variational formulations of the equations.

Statistical models of at-grade intersection accidents - addendum

Abstract: This report is an addendum to the work published in FHWA-RD-96-125 titled "Statistical Models of At-Grade Intersection Accidents." The objective of both research studies was to develop statistical models of the relationship between traffic accidents and highway geometric elements for at-grade intersections. While the previously published report used only multiple-vehicle accidents in developing predictive models, this addendum presents models based on all collision types (including both multiple-vehicle and single-vehicle accidents). The statistical modeling approaches used in the research included lognormal, Poisson, and negative binomial regression analyses. The models for all collision types are similar to those developed in the previous report for multiple-vehicle accidents. The regression models of the relationships between accidents and intersection geometric design, traffic control, and traffic volume variables were found to explain between 16 and 39% of the variability in the accident data. However, most of that variability was explained by the traffic volume variables considered (major road and crossroad average daily traffic). Geometric design variables accounted for only a small additional portion of the variability. Generally, negative binomial regression models were developed to fit the accident data at rural, three- and four-leg, STOP-controlled intersections and urban, three-leg, STOP-controlled intersections. On the other hand, lognormal regression models were found more appropriate for modeling accidents at urban, four-leg, STOP-controlled and urban, four-leg, signalized intersections. The decision to use negative binomial or lognormal regression analysis was based on evaluation of the accident frequency distribution for the specific categories of intersections.

Nonideal transport of reactive solutes in heterogeneous porous media 6. Microscopic and macroscopic approaches for incorporating heterogeneous rate-limited mass transfer

Abstract: Two major approaches have been used to incorporate heterogeneous rate-limited mass transfer into mathematical models for solute transport. One focuses on processes operative at the microscopic scale and associated grain-scale heterogeneity, while the other stresses the macroscopic variability of the medium and the field-scale behavior of solute transport. In this paper, we examine the conceptual framework and model formulation of these two approaches in an attempt to evaluate potential commonality. Numerical solvers are developed for both sets of governing equations, and the performance of these two models is tested for two systems, each incorporating one of two types of mass transfer mechanisms. The results show that despite differences in conceptualization and formulation, the models produce comparable behavior for smaller-scale systems. However, greater deviations are observed at larger scales. This suggests that caution should be exercised when using mathematical modeling for elucidating the specific processes that may be influencing reactive-solute transport for a given system. We also evaluate the impact of microscopic-scale mass transfer heterogeneity on field-scale transport in systems for which hydraulic conductivity is spatially variable. The results show that inclusion of locally heterogeneous mass transfer does not appear to significantly influence the mean transport behavior for systems with field-scale heterogeneity. However, it does appear to influence low-concentration tailing. For simulations of reactive transport over extended distances, models with locally heterogeneous mass transfer may “preserve” the nonequilibrium effects associated with rate-limited mass transfer better than models incorporating locally uniform mass transfer when both pore-scale and field-scale heterogeneity coexist.

Development of Parking Demand Models in Hong Kong

Abstract: This paper describes the parking demand models for private cars and goods vehicles developed as part of a parking demand study that was completed in Hong Kong in 1995. In the model, it is assumed that there is a linear and additive demand function relating land-use variables in a zone (such as jobs, schools, or households) with parking demand. Further, the parking activity associated with each land-use variable is assumed to have a unique parking accumulation profile. Surveys were conducted to determine these profiles. A unitgraph, which is defined as the parking accumulation profile per parking activity, was constructed for each land-use variable. Given the land-use variables, the parking demand function, and the unitgraphs, the total parking accumulation profile in each zone is determined.