Showing papers on "Mathematical model published in 1978"

Axial currents in nuclei

Abstract: It is shown that the time component of axial currents in nuclei can be given a simple description in terms of a one-pion exchange diagram with its structure constrained by a soft-pion theorem. We suggest the directional correlation mesurements in nuclear ..beta.. decay as a possible means to test the theory.

Numerical methods in water-wave diffraction and radiation

Abstract: The subject of diffraction and radiation of water wave s by natural boundarie s or man-made structure s i s of con siderable im portance in ocean engineering. A s a re sult of the ra pid growth of ocean e xploration and tran sportation, detailed knowledge of wave effect s i s now a virtual nece ssity for the safe de sign of co stly pro ject s such a s tanker s and their mooring s, off shore terminal s and drilling rig s, etc. Predicting the re spon se s to po ssible incident waves i s essential for the safe and economical o peration of exi sting and new harbor s. Effect s of t sunami s along a coa st line mu st be under stood in order to devi se mea sure s for protecting live s and pro pertie s. In di scu ssing wave effect s it i s im portant to di stingui sh between small and large bodie s (of ty pical dimen sion a) in com pari son with the characteri stic wave­ length (2n/k) and the wave am plitude (A). For small ka and large A/a [�0( 1)], vortex shedding and flow se paration are dominant, but diffraction i s in significant, i.e. while the body i s affected by the wave field near by, it doe s not materially alter the wave field at large. For small A/a and ka � 0(1 ), se paration become s in signi ficant while diffraction become s crucial. It i s to the latter category that thi s review i s addre ssed. In the conte xt of linearized theory, some analytical solution s are available for sim ple geometrie s by em ploying either re sult s that are known in cla ssical phy sic s (a circular vertical cylinder, a semi-in finite long breakwater, etc) or other exact technique s ( e.g., Dean 1945, Ur sell 1947, 1948, John 1948, Hein s 1948, Lewin 196 3, Mei 1966). A sym ptot ic theorie s for short or long wave s have al so been deve lo ped. Thi s review cover s numerical methods f or arbitrary geometrie s and frequencie s for which exten sive u se of the com puter i s nece ssary. It i s further re stricted to sim ple harmonic wave s. The more general ca se s of tran sient or random wave s can in princi ple be obtained by Fou rier integral s from the single-frequency re spon se calculated for all frequencie s (0 < W < CfJ). Direct calculation of tran sient problem s u sing tran sient Green function s ha s ju st begun ( see Shaw 197 5, Harten 197 5).

A three-dimensional model of corotating streams in the solar wind. 1: Theoretical foundations

Abstract: The paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single-fluid, polytropic magnetohydrodynamic or hydrodynamic equations. Efficient numerical techniques are outlined for solving this complex system of coupled, hyperbolic partial differential equations. The present formulation is inviscid and nonmagnetic, but the methods used allow for the potential inclusion of both features with only modest modifications. A simple, highly idealized hydrodynamic model stream is examined to illustrate the fundamental processes involved in the three-dimensional dynamics of stream evolution. It is found that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics.

A class of mathematical models for sorption of swelling solvents in glassy polymers

Abstract: A class of mathematical models for sorption of swelling solvents in glassy polymers is analyzed. The essential features of these models are the explicit consideration of the kinetics of swelling and of the driving force for swelling. It is shown that, even when all other elementary phenomena are modeled in the simplest possible way, all the experimentally observed features of the processes considered are correctly predicted.

Predictive Model for Design of Fixed-Bed Adsorbers: Parameter Estimation and Model Development

Abstract: A predictive mathematical model for fixed-bed adsorber design which incorporates both liquid and solid phase resistances to mass transfer is formulated; numeric solutions are described and checked for accuracy. Laboratory bench scale studies used to estimate model parameters independently from adsorber break-through profiles are described, and experimental results presented. The bench scale tests involve both adsorption rate and isotherm measurements that are used to determine isotherm equation parameters and surface diffusion coefficients for model calibration. Liquid-phase mass transfer coefficients for fixed-bed operation are obtained from literature correlations; parameter values used for model calibration are presented. This paper sets the stage for single- and multi-component model verifications to be presented in two subsequent papers.

On the mathematical model of manoeuvring motion of ships

Abstract: Considering a wide variety of existing mathematical models for describing the maneuvering motion of ships and the needs to rationalize them, a new mathematical model is proposed. The model consists of the individual open-water characteristics of hull, propeller, and rudder, and the interaction effect between them.

Continuum modeling of three-dimensional truss-like space structures

Abstract: A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

Paradigm Development in the Social Sciences: A Proposed Research Strategy

Abstract: A paradigm development strategy of research consists of: fitting data into a theoretical framework with general laws to explain the data; deducing hypotheses from the general laws; and subjecting these hypotheses to empirical test. Deductive-nomological reasoning, crucial experiments, and typology of experimental control strategies are presented. Methods of strong inference are discussed, followed by a description of paradigm development research. Examples illustrate the strategy of paradigm research.

A nonlinear mathematical model of motions of a planing boat in regular waves

Abstract: : A nonlinear mathematical model has been formulated of a craft having a constant deadrise angle, planing in regular waves, using a modified low- aspect-ratio or strip theory. It was assumed that the wavelengths would be large in comparison to the craft length and that the wave slopes would be small. The coefficients in the equations of motion were determined by a combination of theoretical and empirical relationships. A simplified version for the case of a craft or model being towed at constant speed was programmed for computations on a digital computer, and the results were compared with existing experimental data. Comparison of computed pitch and heave motions and phase angles with corresponding experimental data was remarkably good. Comparison of bow and center of gravity vertical accelerations was fair to good.

A model for the behaviour of overconsolidated soil

Abstract: A mathematical model is formulated to represent the stress-strain behaviour of overconsolidated soil. The full range of behaviour from lightly to heavily over-consolidated states is covered. The basis of the model is the utilization of a constitutive equation for a work-hardening plastic material. The model fits into the general framework provided by the critical state view of soil behaviour. As with the other critical state models four parameters characterize a particular soil. These are determined from routine laboratory tests. The object of the model is to enable good qualitative predictions of a wide range of soil behaviour to be made using only four easily measureable parameters. The Paper is confined to modelling behaviour under the stress conditions imposed in the conventional triaxial apparatus and oedometer, but extension to more general stress systems is possible. In Part I, the model is developed for material with a spherical past stress history; in Part II, it is extended so that loading from ...

An Introduction to Mathematical Models in the Social and Life Sciences

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Supersymmetry at high temperatures

Abstract: We investigate the properties of Green's functions in a spontaneously broken supersymmetric model at high temperatures. We show that, even at high temperatures, we do not get restoration of supersymmetry, at least in the one-loop approximation.

Numerical modeling of liquid geothermal systems

Abstract: A mathematical model describing the physical behavior of hot-water geothermal systems is presented. The model consists of a set of coupled partial differential equations for heat and mass transfer in porous media and an equation of state relating fluid density to temperature and pressure. The equations are solved numerically using an integrated finite difference method which can treat arbitrary nodal configurations in one, two, or three dimensions. The model is used to analyze cellular convection in permeable rock layers heated from below. Results for cases with constant fluid and rock properties are in good agreement with numerical and experimental results from other authors.

Modeling methods in physical and spectral space

Abstract: A model of turbulence including a Reynolds‐stress‐mean velocity relation is developed. The functional nature of this relationship is presented and expressions are given for the unknown terms that can be derived from spectral information. With some modifications, inhomogeneous turbulent fields in which shear effects prevail can be pretty well predicted.

Mathematical Simulation of Dam-Break Flow

Abstract: A one-dimensional mathematical model for the simulation of this flow is described, especially the boundary conditions and the application of numerical schemes to highly nonprismatic channels. To analyze the applicability and the accuracy of the mathematical model, four physical models were used. The conclusions are: (1)In relatively nonprismatic rivers the order of accuracy of the mathematical model described is 15% to 20%, and the model becomes unreliable in some extreme cases; (2)the main part of the error is due to the imperfection of the St. Venant equations used and only a smaller part to the inaccuracy of numerical methods; and (3)two explicit numerical schemes are investigated, the diffusive and the Lax-Wendroff scheme, the latter being more accurate. For the calculation of flow in highly nonprismatic channels, both schemes require completion of the St. Venant equations by a dissipative term in order to prevent instability and to achieve better simulation of the flow.

Variational theory of drift and tearing eigenmodes in slab geometry

Abstract: A variational formulation of the radial eigenmode equations describing kink‐tearing modes, drift‐tearing modes, and drift modes, in slab geometry, is derived. The formalism is shown to provide accurate dispersion relations for a wide range of problems, with fewer approxmimations and less analytical effort than conventional methods require. Furthermore, derivation from a unified framework illuminates the relationships between different instabilities. The variational method is particularly well suited to the approximate solution of physically realistic problems, heretofore considered tractable only by numerical methods.

An analysis of the multiple model adaptive control algorithm. Ph.D. Thesis

Abstract: An analysis of the Multiple Model Adaptive Control algorithm is presented based on the analysis of a canonical problem simulations of which are similar to those obtained in applications. These results allow the prediction of stability and the characterization of the behaviors observed in the system.

Control Strategies for Transport Systems with Nonlinear Waiting Costs

Abstract: The interaction between a transport company and its passengers is modeled as a cooperative game in which the company, subject to an economic constraint, uses the vehicle dispatch strategy under which a time-related cast function for passengers is minimized. A rudimentary transport system is studied in detail, and the joint optimal strategy for passengers and the transport company is obtained.

Simulation of Multibody Systems Using the Vector-Network Model

Abstract: This paper describes the “vector-network” method for creating mathematical models of dynamic mechanical systems. The vector-network method is a combination of vector dynamics and some concepts of graph theory; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description. The vector-network method also permits us to observe a useful but little-known “principle of orthogonality” which is an extension of Tellegen’s theorem for electrical networks, discovered in 1952. Many basic dynamic concepts, such as the principle of virtual work and the instantaneous balance of power, are special cases of this principle.