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Showing papers on "Mathematical model published in 1992"


Journal ArticleDOI
TL;DR: In this paper, a suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry, which exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth.

829 citations


Journal ArticleDOI
TL;DR: In this article, a mathematical model of a lead-acid battery is presented, which takes into account self-discharge, battery storage capacity, internal resistance, overvoltage, and environmental temperature.
Abstract: A mathematical model of a lead-acid battery is presented. This model takes into account self-discharge, battery storage capacity, internal resistance, overvoltage, and environmental temperature. Nonlinear components are used to represent the behavior of the different battery parameters thereby simplifying the model design. The model components are found by using manufacturers specifications and experimental tests. A comparison between the model and experimental results obtained from a battery evaluation test system was used for verification. This model can be used to accurately evaluate battery performance in electrical systems. >

637 citations


Book
14 Sep 1992
TL;DR: A light projector for providing uniform surface area illumination of the type utilized in motion picture studios or the like, employs a housing having a reflector arranged at one end and a Fresnel lens arranged at the other end.
Abstract: A light projector for providing uniform surface area illumination of the type utilized in motion picture studios or the like, employs a housing having a reflector arranged at one end and a Fresnel lens arranged at the other end. At least two linear light sources are located in the interior of the projector at right angles to the optical axis and are electrically connected to a three-phase energization circuit. The lamps are arranged in a star-shaped pattern, relative one to another, and each is a single, self-operating, interchangeable unit, such that by replacing only one of the lamps in the light projector the color temperature of the illumination may be maintained approximately at the desired value.

419 citations


Journal ArticleDOI
TL;DR: The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data?
Abstract: The gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data. The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H/sub infinity // mu framework models. A necessary condition for such a model to describe an experimental datum is obtained. For a large class of models in the robust control framework, this condition is computable as the solution of a quadratic optimization problem. >

368 citations


Journal ArticleDOI
TL;DR: A simulated annealing algorithm is proposed for the equilibrium network design problem and the ability of this algorithm to determine a globally optimal solution for two different networks is demonstrated.
Abstract: The equilibrium network design problem can be formulated as a mathematical program with variational inequality constraints. We know this problem is nonconvex; hence, it is difficult to solve for a globally optimal solution. In this paper we propose a simulated annealing algorithm for the equilibrium network design problem. We demonstrate the ability of this algorithm to determine a globally optimal solution for two different networks. One of these describes an actual city in the midwestern United States.

294 citations


Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate that a new mixing rule allows cubic equations of state to be used for a broad range of nonideal mixtures which previously could only be described by activity coefficient models.
Abstract: In this paper, the authors demonstrate that a new mixing rule allows cubic equations of state to be used for a broad range of nonideal mixtures which previously could only be described by activity coefficient models. Further, the authors show that there is no need to recorrelate phase equilibrium data to do this; activity coefficient model parameters currently reported, for example in the DECHEMA Data Series, can be used directly in our model. Perhaps most important is that the authors also find that the authors can use the parameters in our model obtained from one low pressure-low temperature isotherm to make accurate predictions at conditions which are hundreds of degrees and hundreds of bars above the experimental data used to obtain those parameters. Consequently, this new model provides a way of being able, with confidence, to use data for nonideal mixtures obtained at moderate laboratory conditions for design at harsh processing conditions.

172 citations


Proceedings ArticleDOI
TL;DR: In this paper, the authors presented simplified mathematical representations of four gas turbines covering the horsepower range from 26,000 HP to 108, 000 HP, and incorporated both the control and fuel system characteristics as well as those of the turbomachinery.
Abstract: There have been several recent applications of large single shaft, heavy duty gas turbines in mechanical drive service, powering high horsepower, multi-casing compressors. This variable speed application of a traditional constant speed driver, with a more limited operating speed range, has created a need for simplified but accurate mathematical representations that can be incorporated into overall process simulations to allow interactive dynamic evaluation of the complete system.This paper presents simplified mathematical representations of four gas turbines covering the horsepower range from 26,000 HP to 108,000 HP. The models incorporate both the control and fuel system characteristics as well as those of the turbomachinery. Although gas fuel is assumed, listed references can be used to accomodate liquid fuel. The models are suitable for a wide range of ambient temperatures, and the influence of axial flow compressor variable inlet guide vanes is included in the models as appropriate to the actual machinery configuration.Copyright © 1992 by ASME

156 citations


Journal ArticleDOI
TL;DR: In this paper, an elementary time-dependent global convection model is presented, where convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection.
Abstract: Consideration is given to the solar wind-magnetosphere interaction within the framework of deterministic nonlinear dynamics. An earlier dripping faucet analog model of the low-dimensional solar wind-magnetosphere system is reviewed, and a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is characterized as an elementary time-dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The model's behavior under steady loading and also some elementary forms of time-dependent loading is discussed.

150 citations


Journal ArticleDOI
TL;DR: In this article, a mathematical model for the non-equilibrium compaction of clay rocks in sedimentary basins is formulated, and it is shown that solutions depend on one significant dimensionless parameter A, which is the ratio of the Darcy flow rate and the sedimentation rate.
Abstract: SUMMARY A mathematical model for the non-equilibrium compaction of clay rocks in sedimentary basins is formulated. The model generalizes those of earlier authors. The simplest assumptions are made concerning the rheology, and diagenesis is neglected. In this case, we show that the model reduces to a generalized consolidation equation, which for the classical Darcy flow is a non-linear diffusion equation for the porosity, with a free boundary. The model is non-dimensionalized, and it is shown that solutions depend on one significant dimensionless parameter A, which is the ratio of the Darcy flow rate and the sedimentation rate. The model is solved numerically, and asymptotic descriptions of the solutions are given for the cases of large and small A.

133 citations


Journal ArticleDOI
TL;DR: The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, is discussed in this article. But the focus of this paper is on the mathematical models and definitions associated with chaos.
Abstract: The study of chaotic behavior has received substantial attention in many disciplines. Although often based on deterministic models, chaos is associated with complex, "random" behavior and forms of unpredictability. Mathematical models and definitions associated with chaos are reviewed. The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, are emphasized. Popular data analytic methods appearing in the literature are discussed. A major goal of this article is to present some indications of how probability modelers and statisticians can contribute to analyses involving chaos.

126 citations



Journal ArticleDOI
TL;DR: In this article, an auxiliary mass damper using an ER device is found to be capable of reducing the steady-state response of a system by an additional 30% when compared to an optimal linear viscous damper.
Abstract: Electrorheological (ER) materials consisting of alumino-silicate in fluorinated liquids are experimentally studied with the objective of developing mathematical models of the observed dynamic behaviour. Experiments investigating the oscillatory behaviour of ER materials in shear are carried out over a frequency range of 1-45 Hz. Mathematical models are developed by three approaches: first, a global equivalent linear system approach; second, a parametric identification in which a mechanical model is developed; and third, a non-parametric method which approximates the experimentally measured non-linear restoring force. Models of ER material behaviour would greatly aid designers to better evaluate the appropriateness of these materials for a specific application. One such practical application of interest explored is in the area of vibration control. An auxiliary mass damper using an ER device is found to be capable of reducing the steady-state response of a system by an additional 30% when compared to an optimal linear viscous damper.

Journal ArticleDOI
TL;DR: In this article, the ampere-hour capacity of a lead-acid battery using a mathematical modeling technique is evaluated, and the battery model is used to simulate a battery cycle at different temperatures, at different rates of charge and discharge, and at different end voltages.
Abstract: The evaluation of the ampere-hour capacity of a lead-acid battery using a mathematical modeling technique is presented. The battery model was used to simulate a battery cycle at different temperatures, at different rates of charge and discharge, and at different end voltages to determine how the battery parameter of ampere-hour capacity was affected. The parameter obtained from the model simulation was compared with experimental results for verification. It is shown that the mathematical model accurately depicts ampere-hour capacity under various operating conditions. >

Journal ArticleDOI
TL;DR: In this article, the authors developed a set of equations which govern the space and time averaged energy density in plates, and a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions.
Abstract: The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.

Journal ArticleDOI
TL;DR: In this article, the mathematical models for predicting microstructural evolution and mechanical properties of hot strips have been reviewed, and the fundamental idea of their modelling is introduced, as well as the future work and prospective of the mathematical model in hot strip rolling.
Abstract: Mathematical models for predicting microstructural evolution and mechanical properties of hot strips have been reviewed. The metallurgical features of the hot strip rolling are discussed and the fundamental idea of their modelling is introduced.As applications of the mathematical models, the on-line prediction of the microstructure and strength, the resistance to hot deformation and the cooling curves affected by the heat evolution due to transformation are given.Finally, the future work and prospective of the mathematical model in hot strip rolling is also presented.

Journal ArticleDOI
TL;DR: In this article, a three-dimensional hydrodynamic model is applied to flows in open channels and the model incorporates a second-moment turbulence-closure model that has demonstrated considerable skill in simulating turbulent flows.
Abstract: A three-dimensional, hydrodynamic model is applied to flows in open channels The model incorporates a second-moment turbulence-closure model that has demonstrated considerable skill in simulating turbulent flows in laboratory experiments and in various geophysical and engineering boundary layers The closure model consists of differential equations for turbulence energy and turbulence length scale The remaining second-moment equations are reduced to a set of algebraic equations in which tendency, advection, and diffusion terms are omitted To account for the effect of the free surface on the bulk of the channel flow, a modification of the macroscale equation is introduced; the rest of the model equations and their attendant nondimensional constants remain unchanged The model performance is assessed using laser-Doppler anemometer measurements on the centerline of a large number of laboratory, smooth and rough, homogeneous and stratified, open-channel flows with different values of the aspect ratio Good agreement is found between the model and data in every case Because the model is based upon a self-consistent framework and is able to reproduce the many experiments provided here, the model can be used with confidence in environmental applications

Journal ArticleDOI
TL;DR: In this paper, the state-of-the-art in modeling the bidirectional reflectance of natural surfaces is reviewed, and the remaining challenges for the remote sensing community are highlighted.

Journal ArticleDOI
TL;DR: In this article, an overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques, including 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle.
Abstract: An overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques. The paper reviews 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle. Similarly treated are 3D Cartesian models with temperature-dependent viscosities, and briefly examined are models that are based on compressibility, nonlinear viscosity, or plates. Extensive illustrations are presented detailing: (1) temperature variations from models of 3D thermal convection in spherical shells; (2) thermal anomalies in equatorial cross sections; and (3) temperature variations in a spherical shell heated from within. The discussion relates the numerical results of the models with real mantle-convection events, and the simulations are shown to yield increasingly realistic representations of material behavior.

Journal ArticleDOI
TL;DR: In this paper, the authors developed models of unsaturated flow in large-scale heterogeneous soils, considering finite flow domains and nonstationarity of the soil properties and flow characteristics.
Abstract: Models of unsteady unsaturated flow in large-scale heterogeneous soils are developed considering finite flow domains and nonstationarity of the soil properties and flow characteristics. The problem is cast into a more general stochastic framework than the originally proposed stationary spectral framework (Mantoglou and Gelhar, 1987a, b, c). The methodology considers the three dimensionality of the local governing flow equation, the nonlinear dependence of the local output on the local soil properties, as well as the effect of finite flow domains and nonstationarity of the soil properties and flow characteristics. The large-scale model representation is in the form of a partial differential equation, with large-scale “effective” parameters, subject to a set of initial and boundary conditions. The effective model parameters are related to a set of fluctuation covariance equations obtained by using a linearized fluctuation equation. This set of covariance equations and the corresponding large-scale model of the system are coupled and must be solved simultaneously. Particular cases of interest where stationarity in two or three spatial dimensions occurs are investigated, and, using spectral representations, the dimensionality of the covariance equations is reduced. Simple closed-form and practical expressions for the effective parameters valid in specific situations are presented, and illustrative examples are discussed. The theory and the models presented provide a more complete view of the large-scale unsaturated flow problem and can prove useful for evaluation of unsaturated flow phenomena of paramount importance in practical applications, for example, for predicting the movement of liquid wastes in the unsaturated zone.


Journal ArticleDOI
TL;DR: A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks using a symbolic representation of the dynamics in this equation as a directed graph on an N-dimensional hypercube.
Abstract: A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle oscillations independent of network dimension. Model networks that display multiple stable limit cycles and chaotic dynamics are discussed. The results show that such equations are a useful and efficient method of investigating the behavior of neural networks.

01 Jul 1992
TL;DR: In this paper, the authors present a numerical model for the analysis of wave rotors and compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment.
Abstract: Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

Journal ArticleDOI
TL;DR: In this paper, the infinite volume limit of the dynamics of mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra.
Abstract: The infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven.


Book
01 Jan 1992
TL;DR: This text demonstrates how to formulate mathematical models of dynamic processes and how to study their behaviour analytically and numerically.
Abstract: Combining mathematics, biology, statistics and computer applications, this text applies mathematical methods to the solution of biological and related problems. It demonstrates how to formulate mathematical models of dynamic processes and how to study their behaviour analytically and numerically.

Journal ArticleDOI
TL;DR: In this paper, the use of data for identifying and characterizing uncertainties in model parameters and predictions is presented and elaborated, and applied to the analysis of the uncertainty in a predictive model for global mean sea level change.
Abstract: This paper addresses the use of data for identifying and characterizing uncertainties in model parameters and predictions. The Bayesian Monte Carlo method is formally presented and elaborated, and applied to the analysis of the uncertainty in a predictive model for global mean sea level change. The method uses observations of output variables, made with an assumed error structure, to determine a posterior distribution of model outputs. This is used to derive a posterior distribution for the model parameters. Results demonstrate the resolution of the uncertainty that is obtained as a result of the Bayesian analysis and also indicate the key contributors to the uncertainty in the sea level rise model. While the technique is illustrated with a simple, preliminary model, the analysis provides an iterative framework for model refinement. The methodology developed in this paper provides a mechanism for the incorporation of ongoing data collection and research in decision-making for problems involving uncertain environmental change.

Journal ArticleDOI
01 Apr 1992
TL;DR: The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied and a quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system.
Abstract: The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith. >

Journal ArticleDOI
TL;DR: In this paper, the feasibility of integrating multicomponent mass transport equations over geologic time spans is demonstrated for the case of pure advection in a homogeneous porous medium.
Abstract: The feasibility of integrating multicomponent mass transport equations over geologic time spans is demonstrated for the case of pure advection in a homogeneous porous medium. The mathematical formulation of the problem is based on the quasi-stationary state approximation, or multiple reaction path description, in which the time evolution of a geochemical system is represented by a sequence of stationary states or reaction paths. The method is implemented in the computer code MPATH which solves the transport equations in a single spatial dimension taking into account irreversible mineral precipitation/dissolution reactions and local equilibrium of aqueous complexing reactions. An adaptive grid enables the positions of reaction zones, with widths which vary over many orders of magnitude and which move with greatly differing velocities, to be tracked simultaneously over geologic time spans. There appears to be virtually no limitation to the number of chemical species that can be included in the code without rendering the computational effort beyond the bounds of a high-performance workstation. The numerical accuracy of the solution can be verified through global mass conservation equations and by comparing the asymptotic kinetic solution with the corresponding solution to algebraic equations representing local equilibrium conditions for pure advective transport, if such solutions exist. The code MPATH is applied to several examples including migration of redox fronts, weathering and hydrothermal alteration in a spatially varying temperature field. These examples demonstrate the absolute necessity of solving the governing transport equations for sufficiently long time spans in order to fully characterize the behavior of the system.

Journal ArticleDOI
TL;DR: The VIPRE-02 code as discussed by the authors is a thermal-hydraulic analysis code designed to model steady-state conditions and operational transients in light water reactor cores and vessels.
Abstract: This paper reports on the VIPRE-02 code which is a thermal-hydraulic analysis code designed to model steady-state conditions and operational transients in light water reactor cores and vessels. It uses a two-fluid representation of two-phase flow that solves conservation equations for mass, momentum, and energy for each phase. The code uses a subchannel formulation of the conservation equations but also contains an optional three-dimensional (r-[theta] coordinates) representation of the lower plenum for vessel modeling. The six-equation formulation is solved implicitly, by a modified Gauss-Seidel iteration procedure, and has no time step size limitation for stability. Models for phase interaction based on flow regime mapping are provided that use empirical models and correlations for heat and mass transfer at the interface and vapor generation. In addition, the code contains as an option a dynamic flow regime model, which uses an interfacial area transport equation to determine the phase interaction terms.

Journal ArticleDOI
TL;DR: In this article, Baxter's formula which relates a 2-dimensional statistical model with a 1-dimensional spin model is extended into the finite temperature case, and a combination of this extension and the theory of finite size corrections gives a systematic method to evaluate low temperature expansions of physical quantities.
Abstract: Recent developments in the theory of exactly solvable models are reviewed. Particular attention is paid to the finite size corrections to the Bethe ansatz equations. Baxter’s formula which relates a 2-dimensional statistical model with a 1-dimensional spin model is extended into the finite temperature case. A combination of this extension and the theory of finite size corrections gives a systematic method to evaluate low temperature expansions of physical quantities. Applications of the method to 1-dimensional quantum spin models are discussed. Throughout this paper, the usefulness of the soliton theory should be observed.