Showing papers on "Mathematical model published in 1993"

On Explicit Algebraic Stress Models for Complex Turbulent Flows

Abstract: Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers

Abstract: This paper presents an approach for generating weighted-sum-of-gray gases (WSGG) models directly from the line-by-line spectra of H[sub 2]O. Emphasis is placed on obtaining detailed spectral division among the gray gases. Thus, for a given model spectrum, the gray gas weights are determined as blackbody fractional functions for specific subline spectral regions at all temperatures. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance, etc., and can be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). A single absorption cross section spectrum is assumed over the entire spatial domain in order to fix the subline spectral regions associated with a single spectral calculation. The error associated with this assumption is evaluated by comparison with line-by-line benchmarks for problems of nonisothermal and nonhomogeneous media. 28 refs., 7 figs.

Models in biology : mathematics, statistics and computing

Abstract: MODELS FOR SINGLE POPULATIONS AND PROCESSES Deterministic Models of Growth and Decline Deterministic Genetic Models Stochastic Models of Genetic, Environmental and Sampling Variation Structured Stochastic Models: Models with Both Deterministic and Stochastic Elements Fitting Models: Constants, Straight Lines, Polynomials and Non-Linear Models BIOLOGICAL COMPARISONS AND DESIGN ISSUES Statistical Methods for Comparing Biological Populations and Processes Sampling, Controlling and Measuring the Random and Systematic Variation: Design of Experiments and Surveys BIOLOGICAL INTERACTIONS The Mathematics of Interaction Biochemistry and Physiology Ecology and Epidemiology Advanced Model Fitting ADVANCED TOPICS Transport and Diffusion Statistical Analysis of Pattern and Sequence: Temporal and Spatial Series and DNA Sequences Descriptive Models of Complex Relationships: Multiple Regression and Response Surface Models Models of the Brain: Neural Networks GLOSSARY, TABLES, REFERENCES AND INDEX Mathematical Glossary Statistical Tables References Index.

Three-dimensional magnetotelluric modeling using difference equations­ Theory and comparisons to integral equation solutions

Abstract: We have developed an algorithm for computing the magnetotelluric response of three‐dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of Maxwell’s equations rather than the differential forms. This formulation does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second‐order vector diffusion equation. Rather, one must determine how averages are to be computed. Side boundary values for the H fields are obtained from putting two‐dimensional (2-D) slices of the model into a larger‐scale 2-D model and solving for the fields at the 3-D boundary positions. To solve the 3-D system of equations, we propagate an impedance matrix, which relates all the horizontal E fields in a layer to all the horizontal H fields in that same layer, up through the earth model. Applying a plane‐wave source condition and the side boundary H field values allows us to solve for the unknown fields within the model. The r...

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Abstract: Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.

Matrices and Graphs Stability Problems in Mathematical Ecology

Abstract: Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.

Modelling of Driver/Vehicle Directional Control System

Abstract: Different driver models and driver/vehicle/road closed-loop directional control systems are reviewed and compared. Evaluation methods of vehicle handling quality based on closed-loop system dynamics, stability of the closed-loop system, and optimization of vehicle design are discussed.

Interface motion in models with stochastic dynamics

Abstract: We derive the phenomenological dynamics of interfaces from stochastic “microscopic” models. The main emphasis is on models with a nonconserved order parameter. A slowly varying interface has then a local normal velocity proportional to the local mean curvature. We study bulk models and effective interface models and obtain Green-Kubo-like expressions for the mobility. Also discussed are interface motion in the case of a conserved order parameter, pure surface diffusion, and interface fluctuations. For the two-dimensional Ising model at zero temperature, motion by mean curvature is established rigorously.

Nonlinear aerodynamic modeling using multivariate orthogonal functions

Abstract: A technique was developed for global modeling of nonlinear aerodynamic coefficients using multivariate orthogonal functions based on the data. Each orthogonal function retained in the model was decomposed into an expansion of ordinary polynomials in the independent variables, so that the final model could be interpreted as selectively retained terms from a multivariable power series expansion. A predicted squared-error metric was used to determine the orthogonal functions to be retained in the model; analytical derivatives were easily computed. The approach was demonstrated on the Z-body axis aerodynamic force coefficient (Cz) wind tunnel data for an F-18 research vehicle which came from a tabular wind tunnel and covered the entire subsonic flight envelope. For a realistic case, the analytical model predicted experimental values of Cz very well. The modeling technique is shown to be capable of generating a compact, global analytical representation of nonlinear aerodynamics. The polynomial model has good predictive capability, global validity, and analytical differentiability.

Spreading of excitation in 3-d models of the anisotropic cardiac tissue. I. validation of the eikonal model

Abstract: In this work we investigate, by means of numerical simulations, the performance of two mathematical models describing the spread of excitation in a three dimensional block representing anisotropic cardiac tissue. The first model is characterized by a reaction-diffusion system in the transmembrane and extracellular potentials v and u. The second model is derived from the first by means of a perturbation technique. It is characterized by an eikonal equation, nonlinear and elliptic in the activation time psi(x). The level surfaces psi(x) = t represent the wave-front positions. The numerical procedures based on the two models were applied to test functions and to excitation processes elicited by local stimulations in a relatively small block. The results are in excellent agreement, and for the same problem the computation time required by the eikonal equation is a small fraction of that needed for the reaction-diffusion system. Thus we have strong evidence that the eikonal equation provides a reliable and numerically efficient model of the excitation process. Moreover, numerical simulations have been performed to validate an approximate model for the extracellular potential based on knowledge of the excitation sequence. The features of the extracellular potential distribution affected by the anisotropic conductivity of the medium were investigated.

Problematics in Formulation of Wind‐Force Models for Bridge Decks

Abstract: The present paper concentrates on two-dimensional static and dynamic fluid-structure force effects. Forces acting on elongated bluff bodies like long-span bridge decks have been described by theories and analytical formats strongly influenced by analogous expressions found in two-dimensional airfoil theory. These theories are first reviewed. The resulting formats are seen to contain some formalisms that may overly constrain the force descriptions when applied to bluff bodies. The particular circumstances where this is evident are pointed out. An important point of the present paper is to emphasize the need to employ a format that can be applied directly to design studies of real bridges and that can be reinforced by experiment. The nature of experiments needed to support design calculations for bridge decks is briefly discussed. In sum, the paper offers an integrated version of aeroelastic theory applicable to long, flexible, bluff bodies such as suspended-span bridges. Emphasis is placed upon origins and legacies of aeronautical theory and upon identification of the key parameters that must be measured experimentally in the present contest.

Determination of optimal cutting conditions using design of experiments and optimization techniques

Abstract: In process planning or NC part programming, optimal cutting conditions are to be determined using reliable mathematical models representing the machining conditions of a particular work-tool combination. The development of such mathematical models requires detailed planning and proper analysis of experiments. In this paper, the mathematical models for TiN-coated carbide tools and Rochling T4 medium carbon steel were developed based on the design and analysis of machining experiments. The models developed were then used in the formulation of objective and constraint functions for the optimization of a multipass turning operation with such work-tool combinations.

Impairment by Suspended Solids Invasion: Testing and Prediction

Abstract: A new model was developed to predict wellbore impairment by internal filter-cake formation during water injection. In the model, formation damage is approached semiempirically; no assumptions were made with respect to the specific mechanism underlying impairment. Model constants, derived from linear core-flow experiments, were used to calculate radial flow damage. Radial core-flow experiments subsequently were carried out to validate the proposed model. Theory and experiment were in good agreement. This paper shows that the model can obtain realistic performance and half-life estimates for water injectors. During the experiments, a pronounced velocity effect on impairment rate was found. The extent of impairment increased by several orders of magnitude when injection dropped below a critical inflow velocity of 2 cm/min. The generally accepted 1/3:1/7 rule' (the particle/pore ratio for internal cake formation) is confirmed for inflow velocities exceeding 10 cm/min. At low injection velocities (<2 cm/min), even smaller particles were found to cause increased damage: a 1/3:1/14 rule' may be more applicable for such low inflow velocities.

A trajectory sensitivity method for the identification of nonlinear excitation system models

Abstract: A sensitivity method for identifying parameters of nonlinear synchronous generator models is proposed and applied to the identification of the parameters of IEEE type ST3 and DC1 models. The method generates the sensitivities directly from the nonlinear model and does not require linearization. The use of singular values and singular vectors to detect the identifiability of parameters is discussed. The identification of the parameters requires, in general, very few iterations. The presence of noise in data reduces the identifiability of the parameters. However, reasonable approximations can be obtained if the parameters to be identified are chosen carefully. >

A review of nonsteady flow models for compressor stability

Abstract: This paper presents a review of the different approaches to modeling the nonsteady fluid dynamics associated with two-dimensional compressor flow fields. These models are used to predict the time development of flow field disturbances and have been found useful in both the study of rotating stall and the development of active control. The opportunity to digest the earlier investigations has now made it possible to express the modeling ideas using only a very simple mathematical treatment. Here, the emphasis is on the underlying physical processes that the models simulate and how the assumptions within the models affect predictions

Fitting Microphysical Observations of Nonsteady Convective Clouds to a Numerical Model: An Application of the Adjoint Technique of Data Assimilation to a Kinematic Model

Abstract: Rapid advances in the quality and quantity of atmospheric observations have placed a demand for the development of techniques to assimilate these data sources into numerical forecasting models. Four-dimensional variational assimilation is a promising technique that has been applied to atmospheric and oceanic dynamical models, and to the retrieval of three-dimensional wind fields from single-Doppler radar observations. This study investigates the feasibility of using space–time variational assimilation for a complex discontinuous numerical model including cloud physics. Two test models were developed: a one-dimensional and a two-dimensional liquid physics kinematic microphysical model. These models were used in identical-twin experiments, with observations taken intermittently. Small random errors were introduced into the observations. The retrieval runs were initialized with a large perturbation of the observation run initial conditions. The models were able to retrieve the original initial condi...

A comparison among eight different techniques to achieve an optimum estimation of electrical grounding parameters in two-layered earth

Abstract: This paper intends to compare the performance of eight techniques, based on five different methods, used to find the electrical grounding parameters of a two-layered earth (resistivities and thickness) corresponding to a specific mathematical model. Parameter estimation is carried out in such a way as to obtain an optimum fitting between the set of resistivity values measured in the field by means of Wenner's Method, and those calculated from the mathematical model using such parameters. Firstly, the paper presents a review of the mathematical basis of five optimization methods used for the implementation of the different techniques subject to comparison. Secondly, the paper defines the implementation of the algorithms for the eight techniques. Three of them are of first order gradient type, one more of second order (Newton-method), the fifth one is based on the Levenberg-Marquardt method, the sixth one on the generalized inverse method, the seventh one on a quasi-Newton method and the last one on a mixed Newton-generalized inverse method. Algorithms are applied to six test cases and comparison of the results is shown. Furthermore, new algorithms to improve existing procedures are presented. >

Predicting Flow in Curved Open Channels by Depth‐Averaged Method

Abstract: A depth‐averaged model formulated in the Cartesian coordinate system is introduced for simulating the velocity distribution in curved open channels. The finite element method is used to simplify the geometry problems in practical cases such as irregular cross sections and channels of varying plan curvature. The mathematical model consists of the depth‐averaged continuity equation, the momentum equations, and two moment‐of‐momentum equations for closure purposes. The numerical analysis predicts satisfactory depth‐averaged longitudinal and transverse velocities as well as reasonable secondary flows. The comparison of the numerical predication and the experimental results is included. The mathematical model discussed here can be applied to other channel flow problems where secondary flow and its effects are important.

Air traffic collision risk modelling

Abstract: In view of the high safety standards required from air traffic management (ATM), the validation of an advanced ATM design can only be done with the help of mathematical models for the collision risk of controlled air traffic in route networks, that allow for numerical evaluation. Hence, we need a model for collision risk between controlled aircraft in an arbitrary route network, the numerical evaluation of which compares with the well known Reich model for uncontrolled aircraft. We first consider the well-known theory on the (first) hitting of an absorbing boundary by a Markov process. Since the characterization of (first) hitting reads in terms of a partial differential equation with boundary conditions, its numerical evaluation is too complex for a situation of many aircraft in a network. In view of this finding, we next consider the in-crossing of a transient boundary, to develop an extended version of the Reich model which is general enough to model air traffic in arbitrary route networks. >

Fundamental Mass Transfer Model for Indoor Air Emissions from Surface Coatings

Abstract: The paper discusses the work of researchers at the U.S. EPA's Air and Energy Engineering Research Laboratory (Indoor Air Branch) who are evaluating mass transfer models based on fundamental principles to determine their effectiveness in predicting emissions from indoor architectural coatings. As a first step, a simple model based on Fick's Law of Diffusion has been developed. In the model, the mass transfer rate is assumed to be controlled by the boundary layer mass transfer coefficient, the saturation vapor pressure of the material being emitted, and the mass of volatile material remaining in the source at any point in time. Both static and dynamic chamber tests were conducted to obtain model validation data. Further validation experiments were conducted in a test house. Results of these tests are presented.

An improved hydrodynamic transport model for silicon

Abstract: A closed set of hydrodynamic equations for silicon device analysis is obtained with the aid of self-consistent Monte Carlo device simulation data. This set of macroscopic equations is derived without invoking any phenomenological relations such as the Fourier law for heat flow and the Wiedemann-Franz law for thermal conductivity. The model is developed by taking the first four moments of the Boltzmann transport equation (BTE). This model taken into account the difference between the moments of the collision terms of the BTE both for bulk and inhomogeneous systems. The cause of the spurious velocity overshoot sometimes predicted by other models is identified. By introducing different levels of approximation, this system of hydrodynamic equations can be reduced to the conventional hydrodynamic or energy transport equations. The improved model appears to be more accurate than any existing approach for modeling silicon devices. >

Animal Dispersal Patterns: A Reassessment of Simple Mathematical Models

Abstract: Attempts to fit simple mathematical models of animal movement to observed distributions of movements have been extremely successful. However, the extent to which these results were influenced by use of potentially distance—weighted sampling methods has not been evaluated. Of the 15 field studies used to test model fits, 13 used methods that sample unevenly over distance. We use a simple Monte—Carlo simulation model to evaluate the effects of unequal sampling over distance on results obtained from simple mathematical models of animal movement. For three data sets that provide detailed maps of observation sites, the effects of unequal sampling are profound. Prior to sampling, data simulated by our model follow a uniform distribution, but a geometric model adequately fits the "sampled" simulated data. Following corrections to the field data to mitigate the effects of distance—weighted sampling, in only one of five studies do simple mathematical models adequately fit the observed distribution of movements.