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Showing papers on "Mathematical model published in 2008"


Journal ArticleDOI
11 Feb 2008-Theoria

239 citations


Journal ArticleDOI
TL;DR: In this paper, an integral form of the shallow-water equations suitable for urban flood modeling is derived by applying Reynolds transport theorem to a finite control volume encompassing buildings on a flood plain.

174 citations


Journal ArticleDOI
TL;DR: A review of various efforts that researchers have made to mathematically model the coupled heat and mass transfer process occurring within the wheel is provided in this paper, where various models consisting of ideal assumptions, governing equations, auxiliary conditions, solution methods and main results are presented.
Abstract: In the solid desiccant wheel air-conditioning system, the performance of the desiccant wheel is critical to the capability, size and cost of the whole system. Constructing mathematical model is an effective method for analyzing the performance of the rotary wheel as well as the system. The model can also be used to guide system operation, interpret experimental results and assist in system design and optimization. The overall objective of this paper is to provide a review of various efforts that researchers have made to mathematically model the coupled heat and mass transfer process occurring within the wheel. The paper first briefly describes desiccant wheel including fundamental principle, heat and mass transfer mechanism and the method of model establishment. Then various models consisting of ideal assumptions, governing equations, auxiliary conditions, solution methods and main results are presented. The models can be classified into two main categories: (1) gas-side resistance (GSR) model; (2) gas and solid-side resistance (GSSR) model which can be further subdivided into pseudo-gas-side (PGS) model, gas and solid-side (GSS) model and parabolic concentration profile (PCP) model. It shows that GSSR models are higher in precision and more complex compared with GSR models. In addition, the simplified empirical models based on measured data are briefly discussed. This review is useful for understanding the evolution process and status quo of the mathematical model and highlighting the key aspects of model improvement such as taking account of pressure loss or air leakage.

173 citations


Journal ArticleDOI
TL;DR: Comparison between the responses of the overall turbine-generator model and the response of real plant indicates the accuracy and performance of the proposed models over wide range of operations.

160 citations


Book
04 Sep 2008
TL;DR: Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method useful.
Abstract: Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as uid ow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical nance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. The author bridges theory and practice by developing algorithms, concepts, and analysis from basic principles while discussing efficiency and performance issues and demonstrating methods through examples and case studies from numerous application areas. Audience: This textbook is suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Gradute students at the beginning or advanced level (depending on the discipline) and researchers in a variety of fields in science and engineering will find this book useful. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method. Contents: Preface; 1 Introduction; 2 Methods and Concepts for ODEs; 3 Finite Difference and Finite Volume Methods; 4 Stability for Constant Coefficient Problems; 5 Variable Coefficient and Nonlinear Problems; 6 Hamiltonian Systems and Long Time Integration; 7 Dispersion and Dissipation; 8 More on Handling Boundary Conditions; 9 Several Space Variables and Splitting Methods; 10 Discontinuities and Almost Discontinuities; 11 Additional Topics; Bibliography; Index.

144 citations


Journal ArticleDOI
TL;DR: A Monte-Carlo-based identifiability analysis is suggested for the sake of comparing among different experimental schemes, and the use of a robust global nonlinear programming solver is proposed.
Abstract: Mathematical models of complex biological systems, such as metabolic or cell-signalling pathways, usually consist of sets of nonlinear ordinary differential equations which depend on several non-measurable parameters that can be hopefully estimated by fitting the model to experimental data. However, the success of this fitting is largely conditioned by the quantity and quality of data. Optimal experimental design (OED) aims to design the scheme of actuations and measurements which will result in data sets with the maximum amount and/or quality of information for the subsequent model calibration. New methods and computational procedures for OED in the context of biological systems are presented. The OED problem is formulated as a general dynamic optimisation problem where the time-dependent stimuli profiles, the location of sampling times, the duration of the experiments and the initial conditions are regarded as design variables. Its solution is approached using the control vector parameterisation method. Since the resultant nonlinear optimisation problem is in most of the cases non-convex, the use of a robust global nonlinear programming solver is proposed. For the sake of comparing among different experimental schemes, a Monte-Carlo-based identifiability analysis is then suggested. The applicability and advantages of the proposed techniques are illustrated by considering an example related to a cell-signalling pathway.

123 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated parameters that may significantly affect water-hammer wave attenuation, shape and timing, and showed how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system.
Abstract: This two-part paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water-hammer theory include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Part 1 of this two-part paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system. Each case study compares the obtained results with the standard (classical) water-hammer model, from which conclusions are drawn concerning the transient behaviour of real systems

105 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated key parameters that may affect the pressure waveform predicted by the classical theory of water-hammer, and proposed a method of characteristics transformation of the classical waterhammer equa...
Abstract: This two-part paper investigates key parameters that may affect the pressurewaveform predicted by the classical theory ofwater-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equa...

104 citations


Journal ArticleDOI
19 Nov 2008-PLOS ONE
TL;DR: Extended Kalman Filter (EKF) is applied to the estimation of both states and parameters of nonlinear state-space models for modeling dynamic biochemical networks and preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinearstate-space equations.
Abstract: It is system dynamics that determines the function of cells, tissues and organisms To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli In general, biological dynamic systems are partially observed Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks

104 citations


Journal ArticleDOI
TL;DR: The results suggest that the proposed approach is more effective and robust than presently available methods for deriving metabolic models from time-series data and its avoidance of error compensation among process descriptions promises significantly improved extrapolability toward new data or experimental conditions.
Abstract: Motivation: At the center of computational systems biology are mathematical models that capture the dynamics of biological systems and offer novel insights. The bottleneck in the construction of these models is presently the identification of model parameters that make the model consistent with observed data. Dynamic flux estimation (DFE) is a novel methodological framework for estimating parameters for models of metabolic systems from time-series data. DFE consists of two distinct phases, an entirely model-free and assumption-free data analysis and a model-based mathematical characterization of process representations. The model-free phase reveals inconsistencies within the data, and between data and the alleged system topology, while the model-based phase allows quantitative diagnostics of whether—or to what degree—the assumed mathematical formulations are appropriate or in need of improvement. Hallmarks of DFE are the facility to: diagnose data and model consistency; circumvent undue compensation of errors; determine functional representations of fluxes uncontaminated by errors in other fluxes and pinpoint sources of remaining errors. Our results suggest that the proposed approach is more effective and robust than presently available methods for deriving metabolic models from time-series data. Its avoidance of error compensation among process descriptions promises significantly improved extrapolability toward new data or experimental conditions. Contact: eberhard.voit@bme.gatech.edu Supplementary information: Supplementary data are available at Bioinformatics online.

97 citations


Journal ArticleDOI
TL;DR: In this paper, Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak presented a deterministic sensitivity analysis on the cardiovascular model using 11 differential state equations with 52 parameters.
Abstract: The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523–1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.


Journal ArticleDOI
TL;DR: System algebra provides a denotational mathematical means that can be used to model, specify, and manipulate generic system problems, particularly system architectures and high-level system designs, in computing, software engineering, system engineering, and cognitive informatics.
Abstract: Systems are the most complicated entities and phenomena in abstract, physical, information, and social worlds across all science and engineering disciplines. System algebra is an abstract mathematical structure for the formal treatment of abstract and general systems as well as their algebraic relations, operations, and associative rules for composing and manipulating complex systems. This article presents a mathematical theory of system algebra and its applications in cognitive informatics, system engineering, software engineering, and cognitive informatics. A rigorous treatment of abstract systems is described, and the algebraic relations and compositional operations of abstract systems are analyzed. System algebra provides a denotational mathematical means that can be used to model, specify, and manipulate generic “to be†and “to have†type problems, particularly system architectures and high-level system designs, in computing, software engineering, system engineering, and cognitive informatics.

Journal ArticleDOI
TL;DR: G gap time, the time taken for a following vehicle to travel at its current speed the distance between its head position and the position of the rear of its leading vehicle, is introduced as a fundamental parameter for modeling some prominent features of congested traffic, namely the scatter of the fundamental diagram and the growth and decay of traffic disturbances on highways.
Abstract: We introduce in this paper gap time, the time taken for a following vehicle to travel at its current speed the distance between its head position and the position of the rear of its leading vehicle, as a fundamental parameter for modeling some prominent features of congested traffic, namely the scatter of the fundamental diagram and the growth and decay of traffic disturbances on highways. In the model, traffic waves propagate in a stochastic manner and their speeds are determined by the relative differences between gap times and the reaction times of drivers. The scatter on the fundamental diagram and the growth and decay of perturbations are explained by random fluctuations of gap time and random transitions of traffic states on the fundamental diagram, respectively. Empirical data are used to validate the model and the evaluation shows close correspondence between model predictions and field observations.

Book ChapterDOI
01 Jan 2008
TL;DR: The most widely used approach to mathematical modelling involves the construction of mathematical equations based on physical laws that are known to govern the behaviour of the system.
Abstract: Mathematical models of dynamic systems are required in most areas of scientific enquiry and take various forms, such as differential equations, difference equations, state-space equations and transfer functions. The most widely used approach to mathematical modelling involves the construction of mathematical equations based on physical laws that are known to govern the behaviour of the system. Amongst the drawbacks to this approach are that the resulting models are often complex and not easily estimated directly from the available data because of identifiability problems caused by over-parameterisation. This complexity also makes them difficult to use in applications such as control system design.

Proceedings ArticleDOI
TL;DR: Some of the mathematical challenges arising from modelling structured populations are outlined, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time model for the genealogical trees relating individuals in a sample from that population.
Abstract: Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical models we describe a special case of a new model introduced in very recent work with Nick Barton. A number of directions for future research are suggested.

Journal ArticleDOI
TL;DR: A novel Bayesian approach to model building is presented that takes advantage of breakthroughs in Monte Carlo sampling procedures and high performance computing to enable high fidelity mathematical modeling.

Journal ArticleDOI
TL;DR: This work considers natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty, and establishes not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution.
Abstract: Bilevel optimization models, and more generally MPEC (mathematical program with equilibrium constraints) models, constitute important modelling tools in transportation science and network games, as they place the classic ``what-if'' analysis in a proper mathematical framework. The MPEC model is also becoming a standard for the computation of optimal design solutions, where ``design'' may include either or both of network infrastructure investments and various types of tolls. At the same time, it does normally not sufficiently well take into account possible uncertainties and/or perturbations in problem data (travel costs and demands), and thus may not a priori guarantee robust designs under varying conditions. We consider natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty. In stochastic programming terminology, we consider ``here-and-now'' models where decisions on the design must be made before observing the uncertain parameter values and the responses of the network users, and the design is chosen to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed link pricing scheme that provides the best revenue for a given network over a given time period, where the varying traffic conditions are described by distributions of parameters in the link travel time and OD demand functions. For a general such SMPEC network model we establish not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution. We also provide convergence results for general algorithmic schemes based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution, the latter enabling the utilization of standard MPEC algorithms. Especially the latter part utilizes relations between the traffic application of SMPEC and stochastic structural topology optimization problems.

Journal ArticleDOI
TL;DR: An optimal-order error estimate is proved for a family of ELLAM-MFEM approximations, which simulates porous medium flow accurately even if large spatial grids and time steps are used.
Abstract: Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent nonlinear partial differential equations, which present serious mathematical and numerical difficulties. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The ELLAM-MFEM time-stepping procedure, in which an Eulerian-Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for a family of ELLAM-MFEM approximations.

Journal ArticleDOI
TL;DR: The main objective is to attain effective model calibration and rigorous uncertainty assessment by integrating environmental mathematical modeling with Bayesian analysis and underscores the lack of perfect simulators of natural system dynamics using a statistical formulation that explicitly accounts for the discrepancy between mathematical models and environmental systems.

Journal ArticleDOI
TL;DR: In this paper, the problem of solving the one-dimensional parabolic partial differential equation subject to given initial and nonlocal boundary conditions is considered, and the radial basis functions are used for finding an approximation of the solution of the present problem.
Abstract: Nonlocal mathematical models appear in various problems of physics and engineering. In these models the integral term may appear in the boundary conditions. In this paper the problem of solving the one-dimensional parabolic partial differential equation subject to given initial and nonlocal boundary conditions is considered. These kinds of problems have certainly been one of the fastest growing areas in various application fields. The presence of an integral term in a boundary condition can greatly complicate the application of standard numerical techniques. As a well-known class of meshless methods, the radial basis functions are used for finding an approximation of the solution of the present problem. Numerical examples are given at the end of the paper to compare the efficiency of the radial basis functions with famous finite-difference methods. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

Journal ArticleDOI
TL;DR: The paper aims to demonstrate the relative ease of algebraic sensitivity analysis in many cases and to discuss its advantages and limitations in situations typical of environmental models.
Abstract: The paper aims to demonstrate the relative ease of algebraic sensitivity analysis in many cases and to discuss its advantages and limitations in situations typical of environmental models. Sensitivity results for the operations in an equation can be combined to find algebraically the sensitivities of its output to variations in contributing factors. Algebraic sensitivity analysis has the advantage that it yields insight not readily available from numerical experiments alone. It exploits the fact that a simulation model is fully known and not a black box. By producing relations valid for changes of any size, it can save much computational experiment. The paper gives sensitivity results for common operations on one or more arguments (parameters and/or input variables). A second-order approximation is also given for each. An illustrative example of algebraic sensitivity analysis in a model of pathogen generation and transport in a catchment is presented. Two formulae useful in first- or second-order approximations to normalized sensitivity relations are presented: a Taylor expansion relating the proportional change in effect on a scalar variable to the proportional changes in a number of causal factors and a chain rule for propagating normalized sensitivities through a series of submodels.

Journal ArticleDOI
TL;DR: An original numerical model based on a new lumped formulation of the mixed finite element method for the fluid flow problem and a combination of Discontinuous Galerkin finite elements for advection and a Multipoint Flux Approximation method for dispersion is developed.

Journal ArticleDOI
TL;DR: In this article, the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells is discussed, and a perturbation procedure, validated in previous studies, is used to derive a general expression for the vibration modes and the discretized equations of motion are obtained by the Galerkin method.

Journal ArticleDOI
TL;DR: In this paper, the influence of mathematical models in the optimal design of PV-Diesel systems has been studied, and a more complete general control strategy has been developed, one that also takes into account more characteristics than those usually considered in this kind of design.

Journal ArticleDOI
TL;DR: A model based on a discrete system of dynamical systems based on the kinetic theory of gases as well as microscopic models is presented and evaluated by comparing the efficacy of the model with real time data from monitoring facilities on a highway in Austin, Texas.
Abstract: After reviewing a variety of macroscopic models based on the continuum approach, cellular automata models, models based on the kinetic theory of gases as well as microscopic models, and delineating their usefulness and deficiencies, we present a model based on a discrete system of dynamical systems. We evaluate the efficacy of the model by comparing the predictions of the model with real time data from monitoring facilities on a highway in Austin, Texas.

Journal ArticleDOI
TL;DR: Neural models based on the time delay neural network (TDNN) are benchmarked with classical models, such as auto-regressive moving average (ARMA) models and show the suitability of these approaches for the management of SCs.
Abstract: In this paper, we present the use of different mathematical models to forecast service requests in support centers (SCs). A successful prediction of service request can help in the efficient management of both human and technological resources that are used to solve these eventualities. A nonlinear analysis of the time series indicates the convenience of nonlinear modeling. Neural models based on the time delay neural network (TDNN) are benchmarked with classical models, such as auto-regressive moving average (ARMA) models. Models achieved high values for the correlation coefficient between the desired signal and that predicted by the models (values between 0.88 and 0.97 were obtained in the out-of-sample set). Results show the suitability of these approaches for the management of SCs.

Journal ArticleDOI
TL;DR: In this article, the average circuit models for switch mode shunt converters coupled with power systems such as active filters and static compensators (STATCOM) are introduced, and the average operator is defined, and applied to the state equation to get averaged mathematical models.
Abstract: This paper introduces average circuit models for switch mode shunt converters coupled with power systems such as active filters and static compensators (STATCOM). These devices absorb or deliver reactive power to the utility network by employing either a fixed or a variable switching frequency (e.g., pulsewidth modulation voltage control or hysteresis current control). Analysis and simulation of these exact devices could be complex under transient and steady state conditions. Ongoing investigations on design of a practical STATCOM show that performing these kind of simulations (e.g., with PSpice) are very sluggish. Here both the fixed and variable switching frequency shunt devices are modeled using an averaging approach, by deriving their state-space equations. An average operator is defined, and applied to the state equation to get averaged mathematical models. Expansion of these models will eventually lead us to average circuit models. Further, the ripple is approximated to provide a correction to the average model. The resulting models produce much faster simulations than their exact devices. Theoretical considerations show that the averaged models agree well with the original system, and this is confirmed by PSPICE and MATLAB simulations. Additionally, experimental results are presented to validate the developed models.

Journal ArticleDOI
TL;DR: In this paper, an experimental and numerical investigation was carried out to optimize thin-walled conical shells for their use in design for energy absorption using LS-DYNA.
Abstract: Experimental and numerical investigations were carried out to optimize thin-walled conical shells for their use in design for energy absorption. Geometrical parameters, such as bottom diameter, height, and semi-apical angle were considered to obtain the design space. The numerical analysis and impact experiments were designed using design of experiments (DOE). A three-level, second-order Box–Bhenken technique was used to select the design points from the design space. Various set of numerical simulations were carried out using LS-DYNA. To investigate the influence of flow stress of the material on the energy absorption, numerical simulations were carried out using frusta made of aluminium, zinc, and mild steel. From the numerical results, mathematical models were created using response surface methodology (RSM). With the help of impact experiments carried out on specimens made of zinc on a drop mass test rig, a mathematical model has been developed using RSM. The mathematical models developed using experimental data and the numerical data were used as objective functions for optimization of the design. The non-dominated sorting genetic algorithm code NSGA II was used to optimize the design. The mathematical models were also used to predict the energy absorbed and deformation. The influence of various design parameters on energy absorption has been analysed and is discussed.

Journal ArticleDOI
TL;DR: In this paper, the posterior covariance matrix of difference between model predictions is taken into account during the design for model discrimination for the first time, and the obtained results show that the model discrimination power becomes much higher when the model prediction matrix is considered during the experimental design, increasing the capability of model discrimination and simultaneously leading to improved parameter estimates.