Showing papers on "Mathematical model published in 2003"

Survey of maneuvering target tracking. Part I. Dynamic models

Abstract: This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target motion. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among models and insight to the pros and cons of models are provided. Some material presented here has not appeared elsewhere.

A generalized acoustic analogy

Abstract: The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out

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.

Applied Partial Differential Equations

Abstract: Partial differential equations are a central concept in mathematics. They arise in mathematical models whose dependent variables vary continuously as functions of several independent variables (usually space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This is an enthusiastic and clear guide to the theory and applications of PDEs. It deals with questions such as the well-posedness of a PDE problem: when is there a unique solution that changes only slightly when the input data is slightly changed? This is connected to the problem of establishing the accuracy of a numerical solution to a PDE, a problem that becomes increasingly important as the power of computer software to produce numerical solutions grows. This book is intended for final year undergraduates and graduate students in applied mathematics and engineering.

2001 Presidential Address: Working with Imperfect Models.

Abstract: Since the early years of psychological research, investigators in psychology have made use of mathematical models of psychological phenomena. Models are now routinely used to represent and study cognitive processes, the structure of psychological measurements, the structure of correlational relationships among variables, the nature of change over time, and many other topics and phenomena of interest. All of these models, in their attempt to provide a parsimonious representation of psychological phenomena, are wrong to some degree and are thus implausible if taken literally. Such models simply cannot fully represent the complexities of the phenomena of interest and at best provide an approximation of the real world. This imperfection has implications for how we specify, estimate, and evaluate models, and how we interpret results of fitting models to data. Using factor analysis and structural equation models as a context, I examine some implications of model imperfection for our use of models, focusing on f...

History of Quantitative Structure–Activity Relationships

Abstract: This chapter gives an overview of the historical development of the quantitative structure–activity relationship (QSAR) paradigm with a particular emphasis on the past 50 years. Parameters used to formulate various mathematical models are described as originally delineated. Refinement and fine-tuning of these variables as they evolved and were utilized, is also described. They are sequestered according to their electronic, hydrophobic, steric, and molecular orbital properties. Recent emphasis on molecular descriptors in high-throughput screening mandates their inclusion in this chapter. Various QSAR models spanning two-dimensional space to six-dimensional space are described and applied to various chemicobiological systems in isolated receptors, in vitro systems and in vivo systems. The presence of outliers in QSAR is also discussed in this chapter. Validation methods that are pertinent to QSAR model development are also addressed. The development of databases that encapsulate significant data on variables and models that allow for rapid retrieval, usage, and validation of chemical reactions and biological interactions is included in this analysis of QSAR. Keywords: bilinear model; Hammett equation; hydrophobicity; lateral validation; molar refraction; multiregression analysis; partition coefficient; sigma constants

Mathematical models in biology : an introduction

Abstract: This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Incorporation of variability into the modeling of viral delays in HIV infection dynamics.

Abstract: We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations (as is done in the method of stages). We discuss modeling from first principles, introduce several classes of non-linear models (including discrete and distributed delays) and present a discussion of theoretical and computational approaches. We then use the resulting methodology to carry out simulations and perform parameter estimation calculations, fitting the models to a set of experimental data. Results obtained confirm the statistical significance of the presence of delays and the importance of including delays in validating mathematical models with experimental data. We also show that the models are quite sensitive to the mean of the distribution which describes the delay in viral production, whereas the variance of this distribution has relatively little impact.

Modelling approaches in biomechanics.

Abstract: Conceptual, physical and mathematical models have all proved useful in biomechanics. Conceptual models, which have been used only occasionally, clarify a point without having to be constructed physically or analysed mathematically. Some physical models are designed to demonstrate a proposed mechanism, for example the folding mechanisms of insect wings. Others have been used to check the conclusions of mathematical modelling. However, others facilitate observations that would be difficult to make on real organisms, for example on the flow of air around the wings of small insects. Mathematical models have been used more often than physical ones. Some of them are predictive, designed for example to calculate the effects of anatomical changes on jumping performance, or the pattern of flow in a 3D assembly of semicircular canals. Others seek an optimum, for example the best possible technique for a high jump. A few have been used in inverse optimization studies, which search for variables that are optimized by observed patterns of behaviour. Mathematical models range from the extreme simplicity of some models of walking and running, to the complexity of models that represent numerous body segments and muscles, or elaborate bone shapes. The simpler the model, the clearer it is which of its features is essential to the calculated effect.

System identification of the Vincent Thomas suspension bridge using earthquake records

Abstract: The Vincent Thomas Bridge in the Los Angeles metropolitan area, is a critical artery for commercial traffic flow in and out of the Los Angeles Harbor, and is at risk in the seismically active Southern California region, particularly because it straddles the Palos Verdes fault zone. A combination of linear and non-linear system identification techniques is employed to obtain a complete reduced-order, multi-input–multi-output (MIMO) dynamic model of the Vincent Thomas Bridge based on the dynamic response of the structure to the 1987 Whittier and 1994 Northridge earthquakes. Starting with the available acceleration measurements (which consists of 15 accelerometers on the bridge structure and 10 accelerometers at various locations on its base), an efficient least-squares-based time-domain identification procedure is applied to the data set to develop a reduced-order, equivalent linear, multi-degree-of-freedom model. Although not the main focus of this study, the linear system identification method is also combined with a non-parametric identification technique, to generate a reduced-order non-linear mathematical model suitable for use in subsequent studies to predict, with good fidelity, the total response of the bridge under arbitrary dynamic environments. Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non-proportional damping) as well as quantitative measures of the extent and nature of non-linear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identification procedure, the apparent non-linearities in the system restoring forces are quite significant, and they contribute substantially to the improved fidelity of the model. Also shown is the potential of the identification technique under discussion to detect slight changes in the structure's influence coefficients, which may be indicators of damage and degradation in the structure being monitored. Difficulties associated with accurately estimating damping for lightly damped long-span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identified mathematical models of structural systems with the broadest range of validity. Copyright © 2003 John Wiley & Sons, Ltd.

Macroscopic model and its numerical solution for two-flow mixed traffic with different speeds and lengths

Abstract: A new first-order traffic flow model is introduced that takes into account the fact that various types of vehicles use the roads simultaneously, particularly cars and trucks. The main improvement this model has to offer is that vehicles are differentiated not only by their lengths but also by their speeds in a free-flow regime. Indeed, trucks on European roads are characterized by a lower speed than that of cars. A system of hyperbolic conservation equations is defined. In this system the flux function giving the flow of heavy and light vehicles depends on total and partial densities. This problem is partly solved in the Riemann case in order to establish a Godunov discretization. Some model output is shown stressing that speed differences between the two types of vehicles and congestion propagation are sufficiently reproduced. The limits of the proposed model are highlighted, and potential avenues of research in this domain are suggested.

Development of a Hybrid Model for Dynamic Travel Time Prediction

Abstract: Travel-time prediction has been an interesting research subject for decades, and various prediction models have been developed. A prediction model was derived by integrating path-based and link-based prediction models. Prediction results generated by the hybrid model and their accuracy are compared with those generated by the path-based and link-based models individually. The models were developed with real-time and historic data collected from the New York State Thruway by the Transportation Operations Coordinating Committee. In these models, the Kalman filtering algorithm is applied for travel-time prediction because of its significance in continuously updating the state variables as new observations. The experimental results reveal that the travel times predicted with the path-based model are better than those predicted with the link-based model during peak periods, and vice versa. The hybrid model derives results from the best model at a given time, thus optimizing the performance. A prototype prediction system was developed on the World Wide Web.

A three-dimensional model for the lateral and vertical dynamics of wagon-track systems

Abstract: Lateral and vertical dynamics of the wagon and track affects the maintenance and safety of the heavy haul railway operation. With a view to understanding this aspect comprehensively, a three-dimensional wagon-track system dynamics (WTSD) model is developed and presented. The model consists of a full wagon with 37 degrees of freedom (DOF), a four-layer track with discretely supported rails and a wheel-rail interface representing Kalker's creep and Hertzian contact parameters. The model has been validated using two sets of field data: one dealing with vertical impact due to the flat wheel and the other dealing with lateral hunting. The effect of detailed track modelling on lateral hunting is discussed, and the capability of the three-dimensional WTSD model in predicting lateral impact is demonstrated.

Information-based complexity

Abstract: Many of the mathematical models used in fields such as the physical sciences, engineering, economics, and mathematical finance use continuous mathematical models. These models typically require the numerical solution of multivariate problems (often in a very large number of variables) such as integrals, ordinary and partial differential equations (q.v.), optimization, approximation, integral equations, and nonlinear equations. The study of the computational complexity of continuous mathematical problems is called information-based complexity (IBC). This is a branch of computational complexity (q.v.) which studies the minimal computer resources (typically time or space) needed to solve mathematically posed problems.

Hybrid cascade model-based predictive control system

Abstract: A hybrid cascade Model-Based Predictive control (MBPC) and conventional control system for thermal processing equipment of semiconductor substrates, and more in particular for vertical thermal reactors is described. In one embodiment, the conventional control system is based on a PID controller. In one embodiment, the MBPC algorithm is based on both multiple linear dynamic mathematical models and non-linear static mathematical models, which are derived from the closed-loop modeling control data by using the closed-loop identification method. In order to achieve effective dynamic linear models, the desired temperature control range is divided into several temperature sub-ranges. For each temperature sub-range, and for each heating zone, a corresponding dynamic model is identified. During temperature ramp up/down, the control system is provided with a fuzzy control logic and inference engine that switches the dynamic models automatically according to the actual temperature. When a thermocouple (TC) temperature measurement is in failure, a software soft sensor based on dynamic model computing is used to replace the real TC sampling in its place as a control system input. Consequently, when a TC failure occurs during a process, the process can be completed without the loss of the semiconductor substrate(s) being processed.

Numerical solution of coupled flow in plain and porous media

Abstract: The present thesis deals with coupled steady state laminar flows of isothermal incompressible viscous Newtonian fluids in plain and in porous media. The flow in the pure fluid region is usually described by the (Navier-)Stokes system of equations. The most popular models for the flow in the porous media are those suggested by Darcy and by Brinkman. Interface conditions, proposed in the mathematical literature for coupling Darcy and Navier-Stokes equations, are shortly reviewed in the thesis. The coupling of Navier-Stokes and Brinkman equations in the literature is based on the so called continuous stress tensor interface conditions. One of the main tasks of this thesis is to investigate another type of interface conditions, namely, the recently suggested stress tensor jump interface conditions. The mathematical models based on these interface conditions were not carefully investigated from the mathematical point of view, and also their validity was a subject of discussions. The considerations within this thesis are a step toward better understanding of these interface conditions. Several aspects of the numerical simulations of such coupled flows are considered: -the choice of proper interface conditions between the plain and porous media -analysis of the well-posedness of the arising systems of partial differential equations; -developing numerical algorithm for the stress tensor jump interface conditions, coupling Navier-Stokes equations in the pure liquid media with the Navier-Stokes-Brinkman equations in the porous media; -validation of the macroscale mathematical models on the base of a comparison with the results from a direct numerical simulation of model representative problems, allowing for grid resolution of the pore level geometry; -developing software and performing numerical simulation of 3-D industrial flows, namely of oil flows through car filters.

Modeling of washout of dams

Abstract: The laboratory experimental work has been conducted to investigate the process of dam-breach erosion. The physical pattern of washout of dams is developed and on this basis a mathematical model and its analytical solution are derived for both simulating the process of dam-breach erosion and estimating important characteristics of the process which are necessary for evaluation of dam-break wave parameters. Carrying out theoretical calculations needs only a minimum set of input data for reservoir, dam geometry and embankment material characteristics, so the mathematical model is convenient in practice for predicting purposes. The mathematical model consists of a reservoir water-mass depletion and a rate of breach-width enlargement equations. The closed form of the mathematical model is achieved by using the experimental data. Breach erosion is described from the formation of an initial breach with its bottom reaching the base of the dam. Breach shape is assumed to be rectangular. Experimental and historical...

Two-dimensional bifurcation diagrams: background pattern of fundamental dc–dc converters with pwm control

Abstract: One of the usual ways to build up mathematical models corresponding to a wide class of DC–DC converters is by means of piecewise linear differential equations. These models belong to a class of dynamical systems called Variable Structure Systems (VSS). From a classical design point of view, it is of interest to know the dynamical behavior of the system when some parameters are varied. Usually, Pulse Width Modulation (PWM) is adopted to control a DC–DC converter. When this kind of control is used, the resulting mathematical model is nonautonomous and periodic. In this case, the global Poincare map (stroboscopic map) gives all the information about the system. The classical design in these electronic circuits is based on a stable periodic orbit which has some desired characteristics. In this paper, the main bifurcations which may undergo this orbit, when the parameters of the circuit change, are described. Moreover, it will be shown that in the three basic power electronic converters Buck, Boost and Buck–Boost, very similar scenarios are obtained. Also, some kinds of secondary bifurcations which are of interest for the global dynamical behavior are presented. From a dynamical systems point of view, VSS analyzed in this work present some kinds of bifurcations which are typical in nonsmooth systems and it is impossible to find them in smooth systems.

An exploration of the nature of the scatter in ground-motion prediction equations and the implications for seismic hazard assessment

Abstract: This paper reviews the modelling of the scatter in ground-motion prediction equations, and also explores the nature of scatter in strong ground-motion, using an extended database of European accelerograms and newly derived predictive equations Several statistical tests are used to confirm that the distribution of the residuals is genuinely lognormal over a certain range but appears to deviate from this model significantly in the tails of the distribution An alternative model, the upper limit lognormal (ULLN) distribution is found to provide a good fit to the data; the parameters of this model include an upper-bound on the distribution, which is effectively inferred from the statistics of the data itself However, it is clear that upper bounds established in this way do not provide a reliable ceiling on ground-motion amplitudes and physical constraints are required Investigative tools that could be used to explore the physical limits of ground-motion amplitudes are discussed In line with the underlying focus of the work, which is to explore the sometimes almost dominant influence that the scatter can exert on PSHA, and also to provide new data to prevent the overestimation of strong-motion parameters for design, the covariance in the scatter of different strong-motion parameters is also explored

Automated Generation of High-Order Partial Derivative Models

Abstract: A standard problem in science and engineering consists of developing mathematics and sensitivity models for complex applications for optimizing a candidate design. A chain rule-based evaluation technique is presented for analytically evaluating partial derivatives of nonlinear functions and differential equations defined by a high-level language. A coordinate embedding strategy is introduced that replaces all scalar variables with higher-dimensional objects. The higher-dimensional objects are defined by a concatenation of the original scalar and its Jacobian, Hessian, and higher-order partials. Exact sensitivity models are recovered for arbitrarily complex mathematical models. An operator-overloading technique is used to define generalized operators for basic and standard library functions. The generalized operators encode the chain rule of calculus and store the results of partial derivative calculations in the artificial dimensions used to redefine the scalar operations. Hidden operations automatically generate and evaluate exact first- through fourth-order partial derivative models, which are accurate to the working precision of the machine. The new algorithm replaces a normally complex, error-prone, time-consuming, and labor-intensive process for producing the partials with an automatic procedure. Module functions encapsulate new data types, and extended mathematic and library functions for handling vector, matrix, and tensor operations. Matrix operations are shown to generalize easily. The algorithm has broad potential for impacting the design and use of mathematical programming tools for applications in science and engineering. Several applications are presented that demonstrate the effectiveness of the methods.

Steady state models of stable isotopic distributions.

Abstract: This study reviews common calculations and mathematical models used in stable isotopic studies. Some approximations are adopted to simplify the algebra for use in steady state models, with more rigorous mathematics outlined in an Appendix. Review shows that steady-state isotopic models are easy to construct, provide good approximations of system behavior, and are very helpful in evaluating isotopic cycling in many kinds of systems.

A System Dynamics Approach to Land Use/Transportation System Performance Modeling Part II: Application

Abstract: This paper presents a system dynamics approach to simultaneous land use/transportation system performance modeling. A model is designed based on causality functions and feedback loop structure between a large number of physical, socioeconomic, and policy variables. The model system consists of 7 sub-models: population, migration of population, household, job growth-employment-land availability, housing development, travel demand, and traffic congestion level. The model is formulated in DYNAMO simulation language, and tested on a data set from Montgomery County, Maryland. In Part I: Methodology, the overall approach and structure of the model system is discussed and causal-loop diagrams and major equations are presented. In Part II: Application, the model is calibrated and tested with data from Montgomery County, Maryland. Least square method and overall system behavior are used to estimate the model parameters. The model is fitted with 1970–80 data and validated with 1980–1990 data. Robustness and sensitivities with respect to input parameters (birth rate, regional economy growth) are analyzed. The model performance as a policy analysis tool is also examined by predicting year by year impacts of highway capacity expansion on land use and transportation system performance. While this is a first attempt in using dynamic system simulation modeling in simultaneous treatment of land use and transportation system interactions, and model development and application are limited due to data availability, results show that the proposed method is a promising approach in dealing with complex urban land use and transportation modeling.