Showing papers on "Mathematical model published in 1972"

Lectures in mathematical models of turbulence

Abstract: Lectures in mathematical models of turbulence , Lectures in mathematical models of turbulence , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Mathematical models in the social sciences

Abstract: As the need for more substantial mathematical training has increased among social science students, the lack of any adequate textbook between the very elementary and the very advanced levels has become crutial. The authors, long-time experts in this field, have answered the need with this volume, and the MIT Press has repsonded by bringing it into renewed circulation.Mathematical Models in the Social Sciences investigates and teaches the formation and analysis of mathematical models with detailed interpretations of the results. These models are self-contained, with the necessary mathematics included in each chapter. A vast range of topics in the social sciences and a wide variety of mathematical techniques are covered by the models. Ample opportunity is also provided for the students to form their own models. Republication of this book provides social science and mathematics students with a text that is the analogue of mathematical methods textbooks used in the study of the physical sciences and engineering. Prerequisites are kept to a minimum; a course in finite mathematics and a semester of calculus are all that is necessary.The chapters cover these main topics (and employ the mathematical approach parenthetically indicated): methodology; preference rankings (an axiomatic approach); ecology (two dynamic models); market stability (a dynamic model); a Markov chain model in sociology; stabilization of money flow (an application of discrete potential theory); branching processes; organization theory (applications of graph theory); and optimal scheduling (a problem in dynamic programming).

LISREL: A General Computer Program for Estimating a Linear Structural Equation System Involving Multiple Indicators of Unmeasured Variables.

Abstract: ABSTRACT A,,general computer program for estimating the 'unknown coefficients in a set of linear structural equations is described. In its most general form, the variables in the equation system may he. Unmeasured hypdthetical constructs or latent variables, and there may 4' be several measured variables or multiple indicators for each 'unmeasured variable. Also, the method allows for both errors in equations (residuals, disturbances) and errors.in the observed variables (errors of measurement, observational errors) and yields estimates of the disturbance variance-covariance matrix and the measurement error variances, as well as estimates of the unknown coefficients in the.structual equations, provided that all these parameters are identified. The method is so general and flexible that it is possible to handle a wide range of models. The model considered here 4s a generalization of the model considered by Joreskog (1973).' (Author/DB)

Aircraft performance optimization.

Abstract: Using the calculus of variations, the solutions to various fixed end point flight-path optimization problems are developed These include the minimum fuel-fixed range problem, the minimum time-fixed range problem, and the minimum fuel-fixed range-fixed time problem Altitude profiles and throttle control laws are presented A variety of aircraft mathematical models is initially examined, and the existence of a classically optimal controller is verified for a simple model For this model, the first integral condition is used to eliminate the requirement of integrating the Euler Lagrange adjoint differential equations The resulting computational algorithms are attractive for both laboratory investigations and airborne implementations

Large Deflection Analysis of Prestressed Networks

Abstract: A finite element computer procedure is developed, based on the matrix displacement method, for the analysis of large prestressed networks. The mathematical theory including the effect of the nonlinear contribution of the so-called geometrical stiffness are first reviewed on a novel basis. The iterative attainment of the equilibrium is considered in detail, both as far as theory and practice are concerned. The important question of the determination of an initial trial geometry of the network surface in which the equilibrium is only satisfied approximately is considered next. Attention is also paid to the layout of the initial net on the mathematical surface. The last main section reviews the practical organization of a network analysis in a computer. Following the assembly of the initial data, the measures are enumerated which are necessary for ensuring a given prestress condition. Finally practical steps for accelerating convergence and the selection of a simplified net are presented.

Comparison of some approximations for isotropic turbulence

Abstract: Study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments. The approximations considered include the direct-interaction equations (Kraichnan, 1964), Herring's (1966) self-consistent-field theory, a generalization of Edwards' (1964) theory, the abridged Lagrangian-history, direct-interaction approximation (Kraichnan, 1966), the test-field model (Kraichnan, 1971), and an approximation, not previously described, in which one velocity field passively suffers convection by another. Most of the cited approximations are representable by stochastic model equations for the velocity amplitude. Explicit constructions are given for the stochastic models, in a form that can be approximated on a digital computer. These constructions are used to discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.-

Mathematical models for landform evolution

Abstract: The equation ht = −f(hx, hy, h) is solved by characteristics. The results are interpreted geometrically for erosion problems, and several graphical examples are given. Shock development is examined, as well as the connection with the theory of kinematic waves. Certain effects of fluid flow are then introduced into the model, and an example is given.

Parametric resonance of stiffened rectangular plates

Abstract: Stiffened rectangular plates parametric instability under in-plane sinusoidal dynamic forces, using mathematical model with stiffeners as discrete elements

Shock‐Wave Structure using Nonlinear Model Boltzmann Equations

Abstract: The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity‐independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss‐Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods. Extensive comparisons were made of the model results with Monte Carlo solutions, and significant aspects of the comparisons are discussed.

Stochastic Models for the Distribution of Particles in Space

Abstract: This paper is an elementary introduction to mathematical models of particles distributed in space. It covers the laws of probability, the definitions of a Poisson process, and the relationship between Markov fields and Gibbsian ensembles. RANDOM PARTICLES; POISSON PROCESS; MARKOV FIELD; GIBBS ENSEMBLE; LATTICE STATISTICS

A Mathematical Model for Physical Theories. Nota I and II

Abstract: : Many physical theories exhibit a common mathematical structure that is independent of the physical contents of the theory and is common to discrete and continuum theories, be they of classic, relativistic or quantum nature. The starting point of this structure is the possibility of decomposing the fundamental equation of many physical theories in three equations, known in classical fields of the macrocosm as definition, balance and constitutive equations, whose operators enjoy peculiar properties. The properties are as follows: the operator of balance equation is the adjoint, with respect to an opportune bilinear functional, of the operator of definition equation (if the last is linear) or of its Gateaux derivative (if it is nonlinear). Moreover, the operator of constitutive equation is symmetric (when it is linear) or has symmetric Gateaux derivative (when it is nonlinear). Such a peculiar decomposition permits us to obtain a profound introspection into the mathematical structure of a theory. The fact that this decomposition can be achieved in a large number of physical theories and the fact that when it exists we can deduce easily a large number of mathematical properties, suggest constructing a mathematical model for physical theories.

Optimal synchronization of traffic signal networks by dynamic programming

Abstract: THIS PAPER PRESENTS A SYNCHRONIZATION METHOD FOR DETERMINATION OF OPTIMAL OFFSETS IN ROAD TRAFFIC NETWORKS CONTROLLED BY FIXED-TIME SIGNALS. THE METHOD IS BASED ON DYNAMIC PROGRAMMING AND PROVIDES AN OPTIMAL SOLUTION, INDEPENDENT OF NETWORK LAYOUT, IN A FINITE NUMBER OF COMPUTATION STEPS. THE MATHEMATICAL MODEL OF THE SYNCHRONIZATION PROBLEM IS INTRODUCED FIRST. DEFINITIONS OF THE SYSTEM'S INDEPENDENT VARIABLES ARE GIVEN AND THE EQUATIONS CHARACTERIZING THE CONSTRAINTS IMPOSED ON THE OFFSET ACROSS-VARIABLES ARE FORMULATED. THE DEPENDENT VARIABLES OF THE SYSTEM ARE THE COST FUNCTIONS ASSOCIATED WITH EACH LINK OF THE TRAFFIC NETWORK. THE OPTIMIZATION TARGET IS A MINIMIZED ECONOMIC OBJECTIVE FUNCTION COMPRISING THE INDIVIDUAL LINK FUNCTIONS AND POSSIBLY IN- CLUDING DELAY TIMES AS WELL AS STOPS. THE PROBLEM IS NONLIN- EAR (OWING TO THE CHARACTER OF THE LINK COST FUNCTIONS) AND CONTAINS INTEGER VARIABLES IN THE CIRCUIT CONSTRAINT EQUA- TIONS. THE ALGORITHM FOR ITS SOLUTION IS BASED ON PARTIAL MINIMIZATIONS CONCLUDED BY DETERMINING A FUNDAMENTAL SET OF OPTIMAL OFFSETS AS WELL AS THE OPTIMAL VALUE OF THE OBJECT- IVE FUNCTION. IN ORDER TO OVERCOME THE "CURSE OF DIMENSION- ALITY" INHERENT IN MULTIVARIABLE PROBLEMS, A DECISION-TREE ALGORITHM IS EMPLOYED FOR OBTAINING A MINIMIZATION PLAN WHICH IS OPTIMAL IN TERMS OF THE COMPUTATIONAL EFFORT INVESTED. THE AIM, IN THIS CASE, IS TO MINIMIZE THE REQUIRED COMPUTER STORAGE CAPACITY AND NUMBER OF OPERATIONS.

Mathematical approach to estimating highway impact on air quality

Abstract: THIS MANUAL IS THE FOURTH IN A SERIES OF SIX INTENDED AS GUIDES IN THE GATHERING OF FIELD DATA, ANALYSIS OF RESULTS, AND WRITING OF THE REPORT FOR AN ENVIRONMENTAL IMPACT STATEMENT. THE MATHEMATICAL ANALYSIS PRESENTED HERE CONSISTS OF TWO ANALYSES, NAMELY, THE CORRIDOR ANALYSIS AND THE MESOSCALE ANALYSIS. IN THE FORMER,SPECIAL CONSIDERATION IS GIVEN TO ESTIMATING THE CO POLLUTANT CONCENTRATIONS FROM THE HIGHWAY TO THE POINT DOWNWIND WHERE AMBIENT LEVELS ARE AGAIN APPROACHED. THE MESOSCALE ANALYSIS EMPHASIZES THE "AIR BASIN CONCEPT". THIS ANALYSIS EVALUATES THE EFFECTS OF THE PROPOSED HIGHWAY ON GENERAL COMMUNITY AIR QUALITY. CONSIDERATION IS LIMITED TO TWO PRIMARY GASEOUS POLLUTANTS (CO AND HC) EMITTED FROM MOTOR VEHICLES. GENERALIZED FLOW CHARTS ILLUSTRATE THE CORRIDOR AND MESOSCALE ANALYSES ALONG WITH THE REQUIRED INPUTS. IN THE CORRIDOR ANALYSIS, THE MATHEMATICAL MODEL PRESENTED IS BASED ON THE GAUSSIAN DIFFUSION EQUATION. OTHER BASIC ASSUMPTIONS THAT WERE MADE CONCERNING CONTINUOUS EMISSION SOURCES, SURFACE STABILITY CLASSES OF THE ATMOSPHERE, THE CONCENTRATION OF POLLUTANTS ON HIGHWAYS WITHIN THE MECHANICAL MIXING CELL, UNIFORM WIND FLOW FIELD, AND AERODYNAMIC EFFECTS ARE LISTED. THE REQUIRED INPUTS TO THE MODEL TO ESTIMATE HOURLY POLLUTION CONCENTRATIONS ARE: TRAFFIC VOLUME IN NUMBER OF VEHICLES PER HOUR; AND EMISSION FACTORS OF VEHICLES USING THE HIGHWAY AS A FUNCTION OF HEAVY DUTY VEHICLE MIX AND AVERAGE ROUTE SPEED. OUTPUT FROM MATHEMATICAL ANALYSIS AND CALCULATIONS FOR CROSSWINDS AND PARALLEL WINDS ARE DISCUSSED. THE ANALYSIS PRESENTED HERE HAS NOT BEEN VALIDATED BY FIELD MEASUREMENTS. THE REASONS WHY THE MODEL WILL GIVE LESS RELIABLE ESTIMATES ARE LISTED. THE MESOSCALE ANALYSIS IS DISCUSSED. THE CALCULATION OF POLLUTANT BURDEN FOR THE MESOSCALE ANALYSIS DEPENDS ON TRAFFIC VOLUMES, DAILY VEHICLE MILES TRAVELED, VEHICLE MIX, AND EMISSION FACTORS. MORE EXTENSIVE WORK WITH ACTUAL FIELD MEASUREMENT OF POLLUTANT CONCENTRATIONS WLL BE MADE IN THE FUTURE TO DEVELOP AND STATISTICALLY VALIDATE REGIONAL MODELS TO SUPPLEMENT THE PRESENT MESOSCALE ANALYSIS.

Obtaining Overland Flow Resistance by Optimization

Abstract: A mathematical model simulates and predicts overland flow hydrographs. The kinematic form of the nonlinear partial differential equations of unsteady, spatially varied, shallow-water flow are solved simultaneously by numerical integration. The mathematical model is verified by laboratory data obtained from a rainfall generator and a physical model. Parameter optimization provides a set of representative, synthetic, resistance-parameter values. The synthetic data and a dimensional analysis yield predictive resistance-parameter relationships. Power equations relate the resistance parameter to the precipitation number (precipitation rate divided by the product of unit discharge and downstream depth) during rainfall and to the Weber number after rainfall. Satisfactory results are obtained using a constant resistance-parameter value during rainfall and another smaller constant value during recession. This suggests that the hydrographs are fairly insensitive to changes in the precipitation number and the Weber number.

Mathematical Models of Continuous Combustion

Abstract: The Problem Considered — Economical design and operation of combustion systems can be greatly facilitated by prior predictions of performance by way of a mathematical model, incorporated into a digital-computer program. Morever, since the emission of pollutants is more sensitive to detailed design changes than is the overall heat transfer or power output of the system, the refined insight provided by predictions of concentration distributions is especially valuable nowadays. Suitable mathematical models exist for simple combustion systems and are being developed for others.

Pyritic systems: a mathematical model

Abstract: A mathematical model of an acid mine drainage system has been developed for underground mines. The model relates the rate of acid formation to the rate of pollution discharge from the system. The calculational model was developed using a digital computer to simulate an existing mine as the sum of many micro scale mines. The input to the model is a physical and chemical description of the system. Day-to-day simulation requires data on temperature, rainfall, and oxygen concentration at the exposed coal face. The output of the model is estimates of daily acid load and drainage flow. The calculational model was based on a carefully described physical model so that a predictive model can be constructed with little or no experimental data. However, methods for constructing the computational model are given which can use the field data available to increase the reliability. (GRA)

Scaled fluid-flow models with geometry differing from that of prototype

Abstract: Experiments on oil displacement from homogeneous porous media have shown that the component of flow across the layer is often negligibly small compared with that parallel to it. This result is applied in the inspectional analysis of the equations governing the macroscopic displacement processes. It is shown that in rectangular homogeneous models, the dimensionless groups l/h and alpha can usually be neglected. This finding has been proved experimentally in rectangular models of various dimensions, 2 extremes of which are described. The work has been extended to curved models. An additional requirement is that the angles of dip must be small. Comparative experiments have been conducted in 3-dimensional models of various geometrical configurations. The results of both studies indicte a greater flexibility in the use of models than has previously been assumed.

Wall turbulence studies

Abstract: Publisher Summary Turbulence studies were initiated to solve the problems of heat and mass transfer from the earth's surface. This chapter discusses the importance of the statistical approach in wall turbulence experimental studies. The existing experimental techniques are reviewed from this standpoint. Turbulence is essentially a statistical phenomenon. All the quantities involved are therefore, random variables characterized by the corresponding probability distributions. The complete solution of the turbulence problem would consist of the determination of time evolution of probability distribution of the hydrodynamic, enthalpy, and other fields starting from a known set of distribution functions at the initial moment and employing the relevant physical laws. The physical and mathematical models of the wall turbulence rely on experimental evidence. Integral prediction methods and simple differential procedures, such as the mixing length concept, are based on the experimental data on the characteristics of the mean motion, such as wall shear stress and mean velocity distributions. More elaborate models require experimental evidence of second or higher order statistical moments of the relevant quantities.

Paper 26. Stability and Control in Waves: A Survey of the Problem

Abstract: Manoeuvrability in waves is discussed from the point of view of the dangers of broaching-to when a ship is running before the sea. Conditions are assessed under which this may occur, illustrated by documented cases, including the Wahine disaster in 1968. Because of the problems involved in investigating broaching-to by means of free-running model tests, there is an urgent need for reliable mathematical models: however, theories published so far, based on two different simplifications, are shown to have limitations. It is argued that the theory must take account of pitching, surging, rolling and orbital motion of the water particles.