Showing papers on "Mathematical model published in 1973"

Man-Made Noise in Urban Environments and Transportation Systems: Models and Measurements

Abstract: Analytically tractable statistical-physical models of man-made noise environments have been constructed [1]-[3]. These permit quantitative description of the various types of electromagnetic interference appearing in typical radio receivers and, in particular here, for the communication links employed in mobile transportation systems and urban environments generally. This paper presents a summary of some of the principal analytical results obtained to date [1], [4], and includes some suggested next steps for joint theoretical and experimental study of these increasingly important phenomena. First-order probability density functions (pdf's) and probability distributions (pd's) are obtained explicitly; (higher order pdf's and pd's may also be found by similar methods) [2]. These models are based on a Poisson distribution of sources in space. The approach is canonical, in that the results are, in form, independent of particular emitted waveforms, propagation conditions, source distributions, beam patterns, and specific system parameters, as long as the interference is narrow-band following (at least) the aperture and/or the RF stages of a typical receiver. Considered here only are the cases of communication interference, where source and receiver bandwidths are comparable. The paper concludes with a short discussion of some features of suggested future interaction between theory and experiment.

Mathematical modeling of spinning elastic bodies for modal analysis.

Abstract: The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

A weighting function approach to modeling of irregular surfaces

Abstract: A novel approach is presented for efficient mathematical modeling of discretely measured irregular surfaces. The technique is applicable to modeling of arbitrary surfaces; it is shown to be especially well suited for modeling of fine-structure topographic surfaces. The macroscopic features of the method are as follows. (1) Given a set of discrete coordinate measurements, an average least squares mathematical model for the surface geometry is determined. (2) The model consists of an arbitrarily large family of locally valid surface functions that join smoothly; nth-order continuity is satisfied everywhere. (3) Each locally valid surface function can typically be reduced to a low-degree polynomial of two variables; thus an efficient and consistent mathematical model for local surface calculations is provided. (4) The method sequentially operates on a moderate to small subset of the measured data; it is therefore applicable to an arbitrarily large set of observed data. These features and associated computational devices are discussed in the light of numerical results obtained by using actual geodetic data sets. These results demonstrate that the method is a versatile, accurate, and efficient means for obtaining general-purpose mathematical models of irregular surfaces.

Integrated System Identification and Optimization

Abstract: Publisher Summary The modern systems approach in handling large scale problems includes the concepts of system identification and optimization. The coupling relationship between these concepts is inherent in the nature of the desired “optimal solution.” Any mathematical model consists of unknown variables and “known” parameters characterizing the system. These parameters are not known, but are estimated or determined under non-optimal conditions. The solution that is generated from such system models might be non-optimal. The identification of the system's parameters, referred to as system modeling, is essential to obtain an optimal control policy. This chapter discusses the coupling relationship between these concepts and describes the analytical tools and methods for tackling the joint problem. Mathematical models, which aim at representing real physical systems in quantitative form, have become important tools in the design, synthesis, analysis, operation, and control of complex systems.

Finite element analysis of acoustically radiating structures with applications to sonar transducers

Abstract: A numerical technique for mathematically modeling the vibrational response of a complex structure immersed in an infinite acoustic medium is presented. The elastic response of the structure is modeled using the finite element method, and the acoustic radiation loading on the structure is modeled by approximating the surface Helmholtz integral equation formulation of the acoustic radiation problem. Arbitrary (and distinct) nodal point distributions and interpolation functions can be used in the finite element and acoustic radiation models. A technique defined in terms of these nodes and interpolation functions is presented for combining the results of these models into a combined equation of motion for the acoustically damped structure. The application of this technique to sonar transducers is discussed, including the modeling of piezoelectric material. The problem of obtaining reliable piezoelectric material parameters is discussed. Mathematical models are given for a piezoelectric sphere, a piezoelectric...

Gaps between Logical Theory and Mathematical Practice

Abstract: Mathematical practice seems to presuppose what Church has called an underlying logic. Mathematical logic proceeds in strict analogy with mathematical physics where mathematical models of physical systems are constructed and studied. Mathematical logic constructs models of underlying logics. This paper focuses on mismatches between currently accepted models and the underlying logics.

Solution of Highly Constrained Optimal Control Problems Using Nonlinear Programing

Abstract: HIS paper considers the solution of highly constrained optimal control problems using the nonlinear programing method of Fiacco-McCormick.1 Several authors2'3 have successfully applied the technique to constrained optimal control problems of a limited scope. The present paper expands the theory to encompass a general mathematical model for trajectory optimization capable of directly handling six types of equality and inequality constraints. The user-oriented model is designed to facilitate the rapid set up of a wide range of different simulations and provides for the simultaneous optimization of design parameters and continuous control variables. Accurate and efficient methods of unconstrained function minimization and linear search required to implement the Fiacco-McCormick method are discussed. Contents The general mathematical model presented provides a flexible skeletal framework for describing a wide spectrum of complex optimal control problems in terms of problem-oriented functions. The model is capable of incorporating two classes of independent variables which are to be chosen to extremize some objective function. Independent variables which are functions of time are termed dynamic control variables and are designated by uk(t). Independent variables which are constant with respect to time are termed design variables, dp. Trajectory sectioning is a device commonly used to provide flexibility in modeling. It is a method of subdividing the time history of a trajectory simulation into parts relevant to the description of the simulation. A section is defined as any portion of the trajectory in which the mathematical model is of a given form and the state variables xt(t) are continuous functions of time. Section endpoints are chosen to coincide with points at which the differential equations of motion, the control model, or the trajectory constraints change form ; or at which the state variables experience a discontinuity. If the subscript) denotes the trajectory section, then the general optimal control problem is to

Regular meander path models

Abstract: Existing mathematical models for regular meander paths are shown to be members of a general family of differential equations in which the rate of change of curvature along the channel is an odd function of path direction and bends are symmetric. The physical assumptions of the general model and possible justifications of the particular cases are outlined. Each model is specified by one scale parameter (path or axial wavelength) and one shape parameter (maximum deviation, sinuosity, or maximum curvature). Exact analytic expressions for geometric properties of circular arcs, Fargue's spiral, Von Schelling's curve, and the sine-generated curve are presented and illustrated by dimensionless plots; the last three models are generally similar. Properties of natural meander bends show fair agreement with these three regular models, although bend size and shape vary along individual channels, possibly because of nonuniform floodplain topography and sediments.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

Abstract: A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program The structure of the mathematical model is indicated by a block diagram The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems The constraints imposed on the mathematical model are defined

Test of statistical models for gases with and without internal energy states

Abstract: The problem of nonlinear rarefied Couette flow with heat transfer has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar‐Gross‐Krook type models as the governing equation and the method of discrete ordinates as a tool. The calculated results have been compared with the existing experimental data in order to test the accuracy and the applicability of the statistical models for this one‐dimensional problem. The calculated density results are found to be in good agreement with available experimental data; the calculated heat flux solution for the linear case are found to always be lower than the experimental data of Teagan and Springer. There seems to be insufficient published experimental data available to draw rigid conclusions. However, the comparisons made here indicate that the statistical models are indeed reasonably accurate so that their use is justified in the type of problems investigated.

Nonlinear Parameter Estimation in Water Quality Modeling

Abstract: The quality of water in streams, lakes and estuaries is generally measured in terms of the dissolved oxygen concentration and biochemical oxygen demand. Mathematical models for describing the behavior of BOD and DO are briefly reviewed in this paper. Three specific models are examined and parameters in these models are estimated using a nonlinear parameter estimation technique. Statistical analysis is carried out on the results obtained by calculating the residuals and F ratios for equality of variances. The results show that a model with a nonlinear decay term for BOD fits the data better than does the frequently used model with a linear decay term.

On scaling laws for production functions

Abstract: Solutions of functional equations are used in this paper to develop laws for scaling output under proportional changes in input vectors leading to special classes of production functions, which are of significance for the question of returns to scale.

Synchronous Generator Transient Control: Part I -Theory and Evaluation of Alternative Mathematical Models

Abstract: This paper describes mathematical models of varying complexity for the digital computation of transient behaviour of generators and motors in a synchronous power system, and their application in the light of extensive studies which have been made on a model power system. The computed and measured responses to transient disturbances are compared and the representation of terms in the equations which substantially affect behaviour is discussed.

Experimental validation of lane-changing hypotheses from aerial data

Abstract: LANE CHANGING IS A VERY IMPORTANT COMPONENT IN HIGHWAY TRAFFIC FLOW. MANY RESEARCHERS HAVE RECENTLY PRESENTED MATHEMATICAL MODELS TO DESCRIBE LANE-CHANGING BEHAVIOR. THIS PAPER FOCUSES ON THE LINEAR MODEL BY GAZIS, ERMAN, AND WEISS, THE NONLINEAR MODEL BY OLIVER AND LAM, AND THE STOCHASTIC MODEL BY WORRALL, BULLEN, AND GUR. OUR OBJECTIVE IS TO EVALUATE THE VALIDITY OF THESE MODELS BY USING AERIAL PHOTOGRAPHIC DATA. UNKNOWN PARAMETERS OF THE LINEAR AND NONLINEAR MODELS, AS WELL AS THE PROBABILITY TRANSITION MATRIX OF THE STOCHASTIC MODEL, ARE ESTIMATED BY USING THE EXPERIMENTAL DATA. SOME STATISTICAL ANALYSES ARE CARRIED OUT TO MEASURE THEIR VALIDITY.

A mathematical description of gas-surface interactions based on reciprocity

Abstract: The general problem of the interaction between a monatomic gas and a solid surface is investigated from a mathematical point of veiw by the use of a scattering kernel. Based upon the assumptions that any scattering kernel must be non-negative, normalized in half velocity space, and satisfy the reciprocity relation, a series of product solutions is obtained in each of three coordinate systems. The first solution in each series is obtained in closed mathematical form, while subsequent solutions can be evaluated numerically. It is shown that the first scattering kernel in rectangular coordinates adequately describe experimentally observed results of gas-surface interaction. This solution has two parameters which are shown to be related to a tangential and normal thermal accommodation coefficient. This scattering kernel is integrated with the appropriate weighting function in order to obtain mean reflected properties.

Decomposition-aggregation stability analysis

Abstract: This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab.

Mathematical models of two-party negotiations

Abstract: The present paper describes a pair of mathematical models of two-party bargaining. One model is a Markov process with inputs. The other is a two-party version of the Bush-Mosteller linear operator learning model. The adequacy of the two models is examined in a computer controlled experiment. The Markov chain model fails to predict the extinction of cooperation encountered in certain experimental groups. It does adequately predict the trial of agreement. The learning model describes the proportion of cooperative responses quite accurately in all experimental groups. It is not as accurate in predicting agreement as the Markov process.

Limiting Amplitude Analysis.

Abstract: : A research program has been conducted with the objective to develop, evaluate, and verify a model for predicting the limiting amplitude of acoustic oscillations in solid rocket motors. The mathematical model used was the nonlinear oscillator model. The results of these efforts follow: Theoretical results show nonlinear particle damping and coupling of acoustic energy between acoustic modes to be significant nonlinear damping mechanisms. Results of T-burner firings using propellant seeded with inert ZrO2 particles verified the particle damping theory in that behavior predicted by theory follows the experimental frequency and diameter dependence. Also, nonlinear analyses of T-burner data showed a definite distinction between the nonlinear combustion characteristics of two propellants (SAO-101 and A-13) in terms of the quadratic nonlinear coefficient. It was possible to qualitatively explain instability behavior of a series of test motor firings. (Modified author abstract)

Mathematical Models for Engineering Analysis and Design of Howitzer, Light, Towed; 105mm Soft Recoil, XM204

Abstract: : Mathematical models used in design of the XM204 soft recoil Howitzer (advanced and engineering development prototypes) are described. The physical basis for the mathematical representation is presented along with the derivation of the required equations. While these models have been generalized to allow their use in other weapon design situations, some modification will be necessary to include features not specifically considered. Systems of equations which will provide for the definition of required control functions as well as the prediction of recoil mechanism functioning and weapon motions are summarized.

The Linear Model in Attitude Measurement: An Example and Some Comments:

Abstract: RAMSAY and Case (1970) propose a promising method for attitude measurement based on the attitude models of Fishbein (1967) and Tucker (1960). They suggest the use of linear multiple regression analysis for predicting evaluative judgments of stimuli which have been scaled on several properties. The regression weights are interpreted as evaluations of the various properties of the stimuli. Ramsay and Case outline the advantages of the method and present some data intended to provide an example of its application. The data show that a linear combination of scaled properties of nations can successfully predict evaluative judgments of the nations. It is important to note, however, that the data do not show that the regression weights are valid measures of the evaluations of the properties. An attempt by Ramsay and Case to validate the regression weights by correlating them with direct evaluations of the properties resulted in correlations of 0.15, 0.61, 0.25, and 0.18. Since regression weights are estimated from data, it is necessary to show that their interpretation as evaluations of properties is justified. The present paper presents an example of the use of the linear model for attitude measurement emphasizing the validation