Showing papers on "Mathematical model published in 1997"

Evaluation of Nonlinear Frame Finite-Element Models

Abstract: In recent years nonlinear dynamic analysis of three-dimensional structural models is used more and more in the assessment of existing structures in zones of high seismic risk and in the development...

High-Pressure Trickle-Bed Reactors: A Review

Abstract: A concise review of relevant experimental observations and modeling of high-pressure trickle-bed reactors, based on recent studies, is presented. The following topics are considered: flow regime transitions, pressure drop, liquid holdup, gas−liquid interfacial area and mass-transfer coefficient, catalyst wetting efficiency, catalyst dilution with inert fines, and evaluation of trickle-bed models for liquid-limited and gas-limited reactions. The effects of high-pressure operation, which is of industrial relevance, on the physicochemical and fluid dynamic parameters are discussed. Empirical and theoretical models developed to account for the effect of high pressure on the various parameters and phenomena pertinent to the topics discussed are briefly described.

Mathematical Models in the Applied Sciences

Abstract: Part I. Introduction: 1. Mathematical modelling Part II. Methods: 2. Non-dimensionalisation 3. Asymptotics 4. Perturbation methods Part III. Classical Models: 5. Heat transfer 6. Viscous flow 7. Solid mechanics 8. Electromagnetism Part IV. Continuum Models: 9. Enzyme kinetics 10. The Belousov-Zhabotinskii reaction 11. Spruce budworm infestations 12. Chemical reactors 13. Groundwater flow 14. Convection in a porous medium 15. River flow 16. One-dimensional two-phase flow Part V. Advanced Models: 17. Alloy solidification 18. Ice sheet dynamics 19. Chemosensory respiratory control 20. Frost heave in freezing soils References.

Landau fluid models of collisionless magnetohydrodynamics

Abstract: A closed set of fluid moment equations including models of kinetic Landau damping is developed which describes the evolution of collisionless plasmas in the magnetohydrodynamic parameter regime. The model is fully electromagnetic and describes the dynamics of both compressional and shear Alfven waves, as well as ion acoustic waves. The model allows for separate parallel and perpendicular pressures p∥ and p⊥, and, unlike previous models such as the Chew–Goldberger–Low theory, correctly predicts the instability threshold for the mirror instability. Both a simple 3+1 moment model and a more accurate 4+2 moment model are developed, and both could be useful for numerical simulations of astrophysical and fusion plasmas.

Mathematical Modeling of Biofilms

Abstract: A set of mathematical equations constitutes a mathematical model if it aims to represent a real system and is based on some theory of that system's operation. On this definition, mathematical models, some very simple, are everywhere in science. A complex system like a biofilm requires modeling by numerical methods and, because of inevitable uncertainties in its theoretical basis, may not be able to make precise predictions. Nevertheless, such models almost always give new insight into the mechanisms involved, and stimulate further investigation. The way in which diffusion coefficients are measured for use in a model, particularly whether they include effects of reversible reaction, is a key element in the modeling. Reasons are given for separating diffusion from reversible reaction effects and dealing with them in a separate subroutine of the model.

A Comparative Analysis of Neural Networks and Statistical Methods for Predicting Consumer Choice

Abstract: This paper presents a definitive description of neural network methodology and provides an evaluation of its advantages and disadvantages relative to statistical procedures. The development of this rich class of models was inspired by the neural architecture of the human brain. These models mathematically emulate the neurophysical structure and decision making of the human brain, and, from a statistical perspective, are closely related to generalized linear models. Artificial neural networks are, however, nonlinear and use a different estimation procedure feed forward and back propagation than is used in traditional statistical models least squares or maximum likelihood. Additionally, neural network models do not require the same restrictive assumptions about the relationship between the independent variables and dependent variables. Consequently, these models have already been very successfully applied in many diverse disciplines, including biology, psychology, statistics, mathematics, business, insurance, and computer science. We propose that neural networks will prove to be a valuable tool for marketers concerned with predicting consumer choice. We will demonstrate that neural networks provide superior predictions regarding consumer decision processes. In the context of modeling consumer judgment and decision making, for example, neural network models can offer significant improvement over traditional statistical methods because of their ability to capture nonlinear relationships associated with the use of noncompensatory decision rules. Our analysis reveals that neural networks have great potential for improving model predictions in nonlinear decision contexts without sacrificing performance in linear decision contexts. This paper provides a detailed introduction to neural networks that is understandable to both the academic researcher and the practitioner. This exposition is intended to provide both the intuition and the rigorous mathematical models needed for successful applications. In particular, a step-by-step outline of how to use the models is provided along with a discussion of the strengths and weaknesses of the model. We also address the robustness of the neural network models and discuss how far wrong you might go using neural network models versus traditional statistical methods. Herein we report the results of two studies. The first is a numerical simulation comparing the ability of neural networks with discriminant analysis and logistic regression at predicting choices made by decision rules that vary in complexity. This includes simulations involving two noncompensatory decision rules and one compensatory decision rule that involves attribute thresholds. In particular, we test a variant of the satisficing rule used by Johnson et al. Johnson, Eric J., Robert J. Meyer, Sanjoy Ghose. 1989. When choice models fail: Compensatory models in negatively correlated environments. J. Marketing Res.26August 255--270. that sets a lower bound threshold on all attribute values and a “latitude of acceptance” model that sets both a lower threshold and an upper threshold on attribute values, mimicking an “ideal point” model Coombs and Avrunin [Coombs, Clyde H., George S. Avrunin. 1977. Single peaked functions and the theory of preference. Psych. Rev.84 216--230.]. We also test a compensatory rule that equally weights attributes and judges the acceptability of an alternative based on the sum of its attribute values. Thus, the simulations include both a linear environment, in which traditional statistical models might be deemed appropriate, as well as a nonlinear environment where statistical models might not be appropriate. The complexity of the decision rules was varied to test for any potential degradation in model performance. For these simulated data it is shown that, in general, the neural network model outperforms the commonly used statistical procedures in terms of explained variance and out-of-sample predictive accuracy. An empirical study bridging the behavioral and statistical lines of research was also conducted. Here we examine the predictive relationship between retail store image variables and consumer patronage behavior. A direct comparison between a neural network model and the more commonly encountered techniques of discriminant analysis and factor analysis followed by logistic regression is presented. Again the results reveal that the neural network model outperformed the statistical procedures in terms of explained variance and out-of-sample predictive accuracy. We conclude that neural network models offer superior predictive capabilities over traditional statistical methods in predicting consumer choice in nonlinear and linear settings.

Introduction to Adjoint Techniques and the MM5 Adjoint Modeling System.

Abstract: Adjoint models are increasingly applied to many problems in meteorology and oceanography. The adjoint model of MM5 is a tool which effectively computes the gradient (or a Gateau-derivative) of any MM5 forecast aspect with respect to the model's control variables, which consist of model initial conditions, boundary conditions, and model parameters that define the physical and numerical conditions of the integration. Different applications of adjoint models in meteorology are briefly reviewed and their mathematical formulae are provided which illustrate how the adjoint model and/or tangent linear model are used in each application. Then the authors describe the mathematical and numerical formulation used in developing the adjoint version of MM5.

Motion Washout Filter Tuning: Rules and Requirements

Abstract: Current motion-drive algorithms have a number of coefficients that are selected to tune the motion of the simulator. Little attention has been given to the process of selecting the most appropriate coefficient values. Final tuning is best accomplished using experienced evaluation pilots to provide feedback to a washout filter expert who adjusts the coefficients in an attempt to satisfy the pilot. This paper presents the development of a tuning paradigm and the capturing of such within an expert system. The focus of this development is the University of Toronto classical algorithm, but the results are relevant to alternative classical and similarly structured adaptive algorithms. This paper provides the groundwork required to develop the tuning paradigm. The necessity of this subjective tuning process is defended. Motion cueing error sources within the classical algorithm are revealed, and coefficient adjustments that reduce the errors are presented.

An experimental study of nonlinear stiffness, hysteresis, and friction effects in robot joints with harmonic drives and torque sensors

Abstract: Despite widespread industrial applications of harmonic drives, the source of some elastokinetic phenomena causing internal instability has not been fully addressed thus far. This paper describes a new phenomenon named „torque-transmission paradox” related to the inability of transmitting the input motor torque to the output link. Also, we describe experiments and mathematical models related to other physical phenomena, such as nonlinear stiffness, hysteresis and soft-windup. The goal of our modeling strategy was not in developing very precise and possibly complicated model, but to distill an appropriate model that can be easily used by control engineers to improve joint behavior. To visualize the developed model, equivalent mechanical and electrical schemes of the joint are introduced. Finally, a simple and reliable estimation procedure has been established not only for obtaining the parameters, but also for justifying the integrity of the proposed model.

Seismic behaviour of confined masonry walls

Abstract: The results of tests of plain and confined masonry walls with h/l ratio equal to 1·5, made at 1:5 scale, have been used to develop a rational method for modelling the seismic behaviour of confined masonry walls. A trilinear model of lateral resistance–displacement envelope curve has been proposed, where the resistance is calculated as a combination of the shear resistance of the plain masonry wall panel and dowel effect of the tie-columns’ reinforcement. Lateral stiffness, however, is modelled as a function of the initial effective stiffness and damage, occurring to the panel at characteristic limit states. Good correlation between the predicted and experimental envelopes has been obtained in the particular case studied. The method has been also verified for the case of prototype confined masonry walls with h/l ratio equal to 1·0. Good correlation between the predicted and experimental values of lateral resistance indicates the general validity of the proposed method. © 1997 John Wiley & Sons, Ltd.

Numerical modeling in induction heating for axisymmetric geometries

Abstract: This paper deals with numerical simulation of induction heating for axisymmetric geometries. A mathematical model is presented, together with a numerical scheme based on the Finite Element Method. A numerical simulation code was implemented using the model presented in this paper. A comparison between results given by the code and experimental measurements is provided.

Evaluation of shock absorber models

Abstract: SUMMARY A non exhaustive overview of shock absorber models is presented. The ability of the models to match experimental data is emphasized. Two physical models are presented that are able to extract the internal valve parameters from data without hysteresis. In order to implement a model that copes with hysteresis, most models require the numerical solution to a set of nonlinear differential equations. The use of an alternative restoring force method can get round the time consuming iterative simulation and identification routines. The alternative nonparametric method models the force as a function of velocity and acceleration. The theoretical relevance of the model is studied.

The Expansion Method, Mathematical Modeling, and Spatial Econometrics:

Abstract: Consider the mode of enquiry that involves thinking about thinking. The expansion methodology originates within it, from an analysis of the thought processes presiding upon the construction of any mathematical models of any realities. The focal point of this paper is a discussion of the relations between the expansion methodology, mathematical modeling, and spatial econometrics.

A new class of cosmological models in Lyra geometry

Abstract: FRW models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe.

Queueing at unsignalized intersections

Abstract: A general queueing theory model for traffic flow at unsignalized intersections is described and analysed which contains most of the mathematical models developed in the literature as special cases. Thus a consistent approach is presented for obtaining these models from a general viewpoint. Included are green-red models which are based on an analogy to traffic signals. Critical gaps and merging times or move-up times are allowed to be stochastically dependent. Inconsistent and consistent driver behaviour is considered. Platooning of the major road traffic with random intra-bunch headways is included. The results focus on the distributions of queue lengths and delays and, in particular, on capacities. A general capacity formula is developed and it is shown how the various capacity formulas from the literature come out as special cases. Some numerical results are presented.

Analytical model for particle migration within base soil-filter system

Abstract: This study highlights a mathematical (analytical) model simulating the filtration phenomenon applicable to a base soil-filter system, incorporating the hydraulic conditions and the relevant material properties such as porosity, density, friction angle, and the shape and distribution of particles. The model is founded on the concept of critical hydraulic gradient derived from limit equilibrium considerations, where the migration of particles is assumed to occur under applied hydraulic gradients exceeding this critical value. The rate of particle erosion, and hence, the filter effectiveness is quantified on the basis of mass and momentum conservation theories. By dividing the base soil and filter domains into discrete elements, the model is capable of predicting the time-dependent particle gradation and permeability of each element, thereby the amount of material eroded from or retained within the system. Laboratory tests conducted on a fine base material verify the validity of the model. The model predictions are also compared with the available empirical recommendations, including the conventional grading ratios.

An efficient model development strategy for bioprocesses based on neural networks in macroscopic balances: Part II.

Abstract: There is a need for efficient modeling strategies which quickly lead to reliable mathematical models that can be applied for design and optimization of (bio)-chemical processes. The serial gray box modeling strategy is potentially very efficient because no detailed knowledge is needed to construct the white box part of the model and because covenient black box modeling techniques like neural networks can be used for the black box part of the model. This paper shows for a typical biochemical conversion how the serial gray box modeling strategy can be applied efficiently to obtain a model with good frequency extrapolation properties. Models with good frequency extrapolation properties can be applied under dynamic conditions that were not present during the identification experiments. For a given application domain of a model, this property can be used to considerably reduce the number of identification experiments. The serial gray box modeling strategy is demonstrated to be successful for the modeling of the enzymatic conversion of penicillin G In the concentration range of 10–100 mM and temperature range of 298–335 K. Frequency extrapolation is shown by using only constant temperatures in the (batch) identification experiments, while the model can be used reliable with varying temperatures during the (batch) validation experiments. No reliable frequency extrapolation properties could be obtained for a black box model, and for a more knowledge-driven white box model reliable frequency extrapolation properties could only be obtained by incorporating more knowledge in the model. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 62: 666–680, 1999.

Uncertainty in the estimation of critical loads : a practical methodology.

Abstract: Critical loads of acid deposition for forest soils, ground and surface water resources are calculated utilising a variety of mathematical models. The estimation of the predictive uncertainty inherent in these models is important since the model predictions constitute the cornerstone of the development of emissions abatement policy decisions in Europe and the United Kingdom. The Generalised Likelihood Uncertainty Estimation (GLUE) approach is presented here as a tool for estimating the predictive uncertainty of PROFILE, a steady-state geochemical model that is widely applied within the critical loads community. GLUE is based on Monte Carlo simulation and explicitly recognises the possible equifinality of parameter sets. With this methodology it is possible to make an assessment of the likelihood of a parameter set being an acceptable simulator of a system when model predictions are compared to observed field data. The methodology is applied to a small catchment at Plynlimon, Mid-Wales. The results highlight that there is a large amount of predictive uncertainty associated with the model at the site: three of the six chosen field characteristics lie within the predicted distribution. The study also demonstrates that a wide range of parameter sets exist that give acceptable simulations of site characteristics as well as a broad distribution of critical load values that are consistent with the site data. Additionally, a sensitivity analysis of model parameters is presented.

A study of the damage of subway structures during the 1995 Hanshin-Awaji earthquake

Abstract: During the 1995 Hanshin-Awaji earthquake, underground subway structures suffered significant damage, including middle column shear failure which has never been experienced in the past. The present paper describes analytical studies for damage verification and for failure mechanism investigation. Focusing on box culvert structure with middle columns at Kamisawa station, Kobe city municipal subway, the following three series of analytical studies have been conducted. In the first study, soil deposit dependent ground response are investigated using equivalent linear response analysis computer program based on multi-reflection theory. The increase of the deposit layer thickness provides less acceleration, but more displacement responses, which causes more in the way of damage in the present underground structure. In the second study, structure and ground responses are investigated with using two-dimensional soil-structure interaction computer program. As a result, the horizontal motion dependent flexural shear section force has more of an effect, but the vertical motion dependent axial force has less of an effect on the middle column damage. That section force is more affected by displacement amplification of ground dependent on deposit layer. In the third study, three-dimensional FE static nonlinear analysis is conducted to investigate failure mechanism of the damaged structure subjected to earth pressure load, which is obtained in the second study. Analytical results predict shear failure of the top story middle column prior to the flexural yielding of the slabs and walls.

Mathematical models of suspension bridges

Abstract: In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature yet. We are also trying to find particular conditions for unique solutions of some models.

Distributed Control of Laminated Beams: Timoshenko Theory vs. Euler-Bernoulli Theory:

Abstract: In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The differential equations of the continuous system are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration suppression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio...

Distributed control of laminated beams: Timoshenko theory vs. Euler-Bernoulli theory

Abstract: In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are presented. The differential equations of the continuous system are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration suppression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio...

Uncertainty and error in computational simulations

Abstract: The present paper addresses the question: ``What are the general classes of uncertainty and error sources in complex, computational simulations?`` This is the first step of a two step process to develop a general methodology for quantitatively estimating the global modeling and simulation uncertainty in computational modeling and simulation. The second step is to develop a general mathematical procedure for representing, combining and propagating all of the individual sources through the simulation. The authors develop a comprehensive view of the general phases of modeling and simulation. The phases proposed are: conceptual modeling of the physical system, mathematical modeling of the system, discretization of the mathematical model, computer programming of the discrete model, numerical solution of the model, and interpretation of the results. This new view is built upon combining phases recognized in the disciplines of operations research and numerical solution methods for partial differential equations. The characteristics and activities of each of these phases is discussed in general, but examples are given for the fields of computational fluid dynamics and heat transfer. They argue that a clear distinction should be made between uncertainty and error that can arise in each of these phases. The present definitions for uncertainty and error are inadequate and. therefore, they propose comprehensive definitions for these terms. Specific classes of uncertainty and error sources are then defined that can occur in each phase of modeling and simulation. The numerical sources of error considered apply regardless of whether the discretization procedure is based on finite elements, finite volumes, or finite differences. To better explain the broad types of sources of uncertainty and error, and the utility of their categorization, they discuss a coupled-physics example simulation.

Correcting for Measurement Error Attenuation in Structural Equation Models: Some Important Reminders:

Abstract: The increasing popularity of structural equation models that correct for attenuation due to measurement error is noted. The methods by which structural models correct for the effects of measurement error are reviewed. Next, implications of such disattenuation for interpreting the results of structural equation models are considered. Recommendations are advanced for addressing the practice of disattenuation, and caution is urged in drawing inferences based on disattenuated parameter estimates.

Nonlinear control of a high-purity distillation column using a traveling-wave model

Abstract: The trade-off between model accuracy and computation tractability for model-based control applications is well known. While nonlinear models are needed to capture the detailed behavior of many chemical processes, the resultant structures may not lead to straightforward control implementation. The current work advocates the use of low-order nonlinear models based on wave propagation that are mathematically concise and capture the essential nonlinear behavior of a process. In this work, differential geometry is invoked to achieve input-output linearization of a high-purity distillation column based on a traveling-wave model. A Kalman filter is used to recursively update the parameter values. Comparison with a linear controller based on a two-time constant model shows that the nonlinear controller outperforms the linear controller in tight control of both the overhead and the bottoms composition.

Identification of linear and nonlinear aerodynamic impulse responses using digital filter techniques

Abstract: This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.