Showing papers on "Mathematical model published in 1977"
TL;DR: In this paper, a mathematical model of the stream flow in border irrigation is presented in the context of negligible accelerations everywhere in the stream, where numerical solution of the governing equations is achieved on an oblique grid in the x-t plane.
Abstract: A mathematical model of the stream flow in border irrigation is presented in the context of negligible accelerations everywhere in the stream. During the advance phase, numerical solution of the governing equations is achieved on an oblique grid in the x-t plane. The equations of motion are integrated over each oblique cell formed by joining the node points at constant times and distances by diagonals. The resulting nonlinear algebraic equations for depth and discharge at the upper corners of a cell (on the unknown time lines) are linearized with respect to the known values at the lower corners. The resultant set of linear algebraic equations in the incremental changes of depth and discharge that occur over the time interval are solved by a double-sweep technique. During runoff and recession, the grid is changed to a rectangular net. Solutions for advance recession and runoff volume compare very favorably with the results of models based on the complete hydrodynamic equations and with field tests, at but a fraction of the expense.
175 citations
123 citations
TL;DR: In this paper, a random-matrix model is used to describe the transformation of kinetic energy of relative motion into intrinsic excitation energy typical of a deeply inelastic heavy-ion collision.
118 citations
TL;DR: In this article, mathematical models of the control behavior of human drivers while following another vehicle in single lane traffic are presented. But the focus is on the representation of the individual driver, rather than on such abstract parameters of multi-lane traffic as average density or average velocity.
Abstract: This paper is concerned with mathematical models of the control behavior of human drivers while following another vehicle in single lane traffic The emphasis is on the representation of the individual driver, rather than on such abstract parameters of multi-lane traffic as average density or average velocity Three basic types of approaches to representing the driver's control strategy are reviewed First is a classical control structure in which assumptions concerning the stimulus-response characteristics of the driver are included, and a form for his control strategy algorithm is assumed The second class of models is based on optimal control theory The major feature of this class of models is that an assumed performance index is explicitly included in the formulation, so that the driver's control strategy arises as a result of his attempts to minimize this index or criterion The third class of models reviewed in the paper are heuristic models, which arise from control theory The first of these, ter
88 citations
85 citations
54 citations
TL;DR: The mathematical models as they arise in various application disciplines are arranged along a spectrum according to the relative amount of deduction and induction involved in their construction, providing an insight into the ultimate validity of simulations and to what use they can properly be put.
51 citations
Journal Article•
TL;DR: In this paper, the authors considered the short-term probabilistic description of random wave loading on offshore structures composed of members for which the Morison form of load mechanism is appropriate.
Abstract: This paper considers the short-term probabilistic description of random wave loading on offshore structures composed of members for which the Morison form of load mechanism is appropriate. Special consideration is given to dealing with the inherent nonlinearity of the drag forces. The general multivariate distribution of loading is derived from the linear Gaussian model of long-crested random seas. The application of the multivariate distribution to yield the probabilistic description of structural response variables is indicated. Probability distributions of peak loads are developed which show the general wideband behavior contrasted with the simpler distribution which results from appropriate narrow band assumptions. Comparisons of the theoretical models are made with prototype recordings from an offshore platform and laboratory scale experiments.
TL;DR: The concept of channel theory is used to locate spatial regions that are important in contributing to a shielding response, and sample problems are given to exhibit and verify properties predicted by the mathematical equations.
Abstract: The concept of channel theory is used to locate spatial regions that are important in contributing to a shielding response. The method is analogous to the channel-theory method developed for ascertaining important energy channels in cross-section analysis. The mathematical basis for the theory is shown to be the generalized reciprocity relation, and sample problems are given to exhibit and verify properties predicted by the mathematical equations. A practical example is cited from the shielding analysis of the Fast Flux Test Facility performed at Oak Ridge National Laboratory, in which a perspective plot of channel-theory results was found useful in locating streaming paths around the reactor cavity shield.
TL;DR: In this article, the analytical basis for the formulation of a distributed catchment model within the flexible framework of the finite element method is described, and the constitutive equations for the mathematical model are obtained by assuming overland flow conditions in the main drainage paths and through flow conditions elsewhere in the catchment.
TL;DR: In this article, the exp(S) equations of Coester and Kummel are rederived from the Schrodinger equations for n-body subsystems which are specified by the amplitudes of n fermions being at certain positions in r-space and the rest moving in shell model states.
01 Jun 1977
TL;DR: In this paper, an accurate mathematical model for sound propagation in axisymmetric aircraft engine ducts with compressible mean flow is reported, which is based on the usual perturbation of the basic fluid mechanics equations for small motions.
Abstract: An accurate mathematical model for sound propagation in axisymmetric aircraft engine ducts with compressible mean flow is reported. The model is based on the usual perturbation of the basic fluid mechanics equations for small motions. Mean flow parameters are derived in the absence of fluctuating quantities and are then substituted into the equations for the acoustic quantities which were linearized by eliminating higher order terms. Mean swirl is assumed to be zero from the restriction of axisymmetry. A linear rectangular serendipity element is formulated from these equations using a Galerkin procedure and assembled in a special purpose computer program in which the matrix map for a rectangular mesh was specifically coded. Representations of the fluctuating quantities, mean quantities and coordinate transformations are isoparametric. The global matrix is solved by foreward and back substitution following an L-U decomposition with pivoting restricted internally to the blocks. Results from the model were compared with results from several alternative analyses and yielded satisfactory agreement.
05 Dec 1977
TL;DR: This discussion focuses on that class of models which attempts to capture the relationship between the behavior of a measure or measures of system effectiveness and thebehavior of those variables and parameters which influence the measure(s) of effectiveness and includes simulation and mathematical models.
Abstract: Since World War II system modeling has played an increasingly important role in the analysis of complex systems in both the private and public sectors. In the broadest sense, a model may be considered to be a representation of reality without the presence of reality itself. Hence, pictures, graphs, management games, computer programs, and mathematical equations may be considered models of those systems which they represent. For the purposes of this discussion we will restrict our attention to that class of models which attempts to capture the relationship between the behavior of a measure or measures of system effectiveness and the behavior of those variables and parameters which influence the measure(s) of effectiveness and includes analog, simulation and mathematical models. The specific focus of our attention will be on simulation models.
TL;DR: The mathematical models as they arise in various application disciplines are arranged along a spectrum according to the relative amount of deduction and induction involved in their construction, providing an insight into the ultimate validity of simulations and to what use they can properly be put.
Abstract: The methodology involved in the modeling and simulation of physical, life and social science systems is viewed in perspective. A critical factor determining the validity of a model is the extent to which it can be derived from basic laws and insights into the internal structure of the system using deductive methods, rather than relying upon observations and measurements of the system input and outputs. Accordingly, the mathematical models as they arise in various application disciplines are arranged along a spectrum according to the relative amount of deduction and induction involved in their construction. This provides an insight into the ultimate validity of simulations and to what use they can properly be put.
01 Nov 1977
TL;DR: In this article, the authors developed a simple numerical model for the prediction of coastal inlet velocities, discharge, and resulting bay level fluctuations, which can be used for single or multiple inlets, bays, and seas.
Abstract: : This report discusses the development of a simple numerical model for the prediction of coastal inlet velocities, discharge, and resulting bay level fluctuations. The model is a time-marching model that simultaneously solves the area-averaged momentum equation for the inlet and the continuity equation for the bay. It is assumed that the bay surface elevation remains horizontal as it rises and falls. At each time step the geometric and hydraulic factors describing the inlet-bay system are calculated by evaluating flow conditions throughout the inlet and by spatially integrating this information to determine coefficients of the first-order differential equations. This model, which includes the important terms in the equation of motion, is flexible, easy and inexpensive to use, and gives a good estimate of the inlet-bay system hydraulics for various conditions. The model can be used for single or multiple inlets, bays, and seas. This report includes the model theory and derivation, a FORTRAN computer program for solving the model equations, and instructions for use of the program. Examples are given to illustrate how the model may be used to predict coastal inlet response to astronomical tides, seiching, tsunamis, and storm surges. (Author)
TL;DR: In this article, the sensitivity of predictions of runoff peak and its time by five linear and nonlinear surface runoff models to errors in rainfall excess was examined and it was shown that if rainfall excess errors are sufficiently large, a perfectly identified nonlinear model does not perform always as well as an optimally identified linear model in predicting runoff peak, according to an objective function based upon fitting of runoff peaks.
01 Feb 1977
TL;DR: A mathematical model for crash simulation of aircraft structures built up from beams, stringers, and skin panels is developed in the form of a finite element, large displacement elastic-plastic computer code called DYCAST as mentioned in this paper.
Abstract: A mathematical model for crash simulation of aircraft structures -- built up from beams, stringers, and skin panels -- is being developed in the form of a finite element, large displacement elastic-plastic computer code called DYCAST. As a preliminary exercise, the code was applied to simulate a low-speed forward impact of a skin-covered framework carrying large concentrations of nonstructural mass at its rear. The computer-generated data from the mathematical crash simulation can be extremely valuable in providing physical insight into the structural behavior in the crash event. With this insight, the structural details can be more intelligently changed by the addition, deletion, or alteration of individual or groups of members, and the consequences of these design changes on the predicted crash behavior can be quickly seen. The mathematical model internally computes the variable interactive nonlinear stiffness characteristics for each component, which greatly reduces the engineering effort required for such studies.
01 Jan 1977
TL;DR: In this article, the authors discuss the computational aspects of the finite element method and assess the results solely on the basis of the errors introduced by the numerical method, often these errors are much smaller than those caused by earlier decisions about the mathematical formulations used for modeling the given problem.
Abstract: Publisher Summary This chapter discusses the computational aspects of the finite element method. In finite element method, the aim of the computations is the analysis of a given practical problem. Thus, the user wishes to obtain results that predict, with an acceptable degree of reliability and accuracy, the actual behavior of the mechanical structure at hand. It is clearly inadequate to assess the results solely on the basis of the errors introduced by the numerical method. Often these errors are much smaller than those caused by earlier decisions about the mathematical formulations used for modeling the given problem. Therefore, the accuracy of the numerical results should be a measure of their deviation from the solution of a higher mathematical model. This is because of the fact that the computations involved are generally very extensive and highly demanding on the available computer resources. Two different mathematical models are readily available, namely, a pure plate formulation based on the Kirchhoff hypotheses or the full three-dimensional elasticity formulation. The equations for either case are well known and are certainly not mathematically equivalent.
TL;DR: In this article, the propagation of non-linear deformation waves in a dissipativc medium is described by a unified asymptotic theory, making use of wave front kinematics and the concepts of progressive waves.
Abstract: The propagation of non-linear deformation waves in a dissipativc medium is described by a unified asymptotic theory, making use of wave front kinematics and the concepts of progressive waves. The mathematical models are derived from the theories of thermoclasticity or viscoclasticity taking into account the geometric and physical non-linearities and dispersion. On the basis of eikonal equations for the associated linear problem the transport equations of the nth order are obtained. In the multidimensional case the method of matched separation of initial equations is proposed. The interaction problems which occur in head-on collisions and in reflection from boundaries or interfaces are analyzed. Conditions are also studied when the interaction of non-linear waves does not take place. The inverse problem of determining materials properties according to pulse shape changes is discussed.
01 Nov 1977
TL;DR: In this article, a finite element analog using a quadratic weighting function for the discretized spatial domain is used to solve the partial differential equation for transient heat conduction and the transient problem is solved by the Crank-Nicolson approximation.
Abstract: : The partial differential equation for transient heat conduction is solved by a finite element analog using a quadratic weighting function for the discretized spatial domain. The transient problem is solved by the Crank-Nicolson approximation. Two-dimensional and three-dimensional models incorporated in the same computer program are presented. The finite element method is reviewed, assumptions and limitations upon which the model is based are presented, and a complete derivation of the system analog is included. Certain problems can only be modeled as a three-dimensional system, e.g. thaw degradation around roadway culverts, embankment dams on permafrost where dam length is short relative to dam width, and thaw and freezeback under buildings. In most cases, however, the more economical two-dimensional model can be used. Numerical tests of both models have been accomplished but field verification has not been attempted. A user's manual and a FORTRAN IV computer listing of the program are presented. (Author)
08 Aug 1977
TL;DR: In this paper, a unified approach is developed for the model structure determination problem and is applied to test data from a submarine, a missile, and an aircraft engine, and the results of some recent research are summarized.
Abstract: The technology of system identification from input/output test data has been developed into an operational procedure for improving and validating mathematical models upon which state-of-the-art guidance and control systems are based. A wide application of this technology has focused attention on one particular phase of the system identification methodology, the model structure determination phase, as an essential step. This step consists of processing the input/output data to determine the significant linear and nonlinear equations and associated parameters that are necessary to represent an observed system response. Although the model structure determination problem has been recognized for a long time, it has been attacked systematically only recently. This paper summarizes various aspects of this problem and results of some recent research. A unified approach is developed for this problem and is applied to test data from a submarine, a missile, and an aircraft engine.