Applied Mathematical Modelling

Published by Elsevier
Online ISSN: 0307-904X
Publications
Article
We describe the application of a strategy for conducting a sensitivity analysis for a complex dynamic model. The procedure involves preliminary screening of parameter sensitivities by numerical estimation of linear sensitivity coefficients, followed by generation of a response surface based on Monte Carlo simulation. Application is to a physiological model of the vegetative growth of soybean plants. The analysis provides insights as to the relative importance of certain physiological processes in controlling plant growth. Advantages and disadvantages of the strategy are discussed.
 
Article
For ARX-like systems, this paper derives a bias compensation based recursive least squares identification algorithm by means of the prefilter idea and bias compensation principle. The proposed algorithm can give the unbiased estimates of the system model parameters in the presence of colored noises, and can be on-line implemented. Finally, the advantages of the proposed bias compensation recursive least squares algorithm are shown by simulation tests.
 
Article
A coarse grid three dimensional model of the north west European Continental shelf, and a finer grid model of the region off the west coast of Scotland and the Irish Sea are used to examine flow through the North Channel of the Irish Sea. The period of the storm event of February 1994 is considered.Comparisons of computed and observed currents in the North Channel show that the shelf wide model can reproduce the main features of the flow, although the grid of the model is too coarse to resolve the detailed topography in the region. Calculations with the fine grid model alone, show that at times of strong meteorological forcing in the North Channel region (at the start of the storm) this model can accurately reproduce the flow. However at times of reduced wind forcing (later in the storm period) when shelf wide elevation gradients are important in determining flow along the west coast of Britain, the limited area fine grid model fails to reproduce the flow, to such an extent that the current is in the wrong direction.Nesting the fine grid model within the shelf wide model, using a conventional radiation condition, produces a slight improvement, although in the shelf edge region there are problems. Also, the nested model fails to reproduce the correct current direction in the North Channel to a similar extent to that found using the west coast model alone. A simple adjustment to the radiation condition to take account of the transport computed with the shelf wide model is developed. When this condition is applied to nest the west coast model to the shelf model, there is a significant improvement in the currents in the shelf edge region. Also, the flow through the North Channel is correctly reproduced.Results from the calculations show that at times of strong winds off the west coast, the North Channel flow can be explained in terms of local wind forcing. However, at times of weak winds following a strong wind period the flow is related to shelf wide elevation gradients. Including their effect in a limited area model where the open boundary crosses steep topography (namely the shelf edge) is shown to produce some problems, although these can be overcome.
 
Article
This paper reports an investigation into the performance of two commercial computational fluid dynamics (CFD) codes for pulverised coal combustion prediction. The two codes employed were FLUENT and FLOW3D 3.2 (now called CFX). The experimental case considered was a 2.5 MW Aerodynamically Air Staged Burner (AASB) fired in isolation into a rectangular furnace. Predictions were compared to velocity, temperature and species concentration experimental data. Some slight differences were noted between the two CFD codes predictions beyond one burner diameter downstream of the burner exit. Discrepancies between the predictions of the two CFD codes were concluded to be due to differences in the physical models used to describe devolatilisation and gaseous combustion. This paper therefore concludes that, for this case, the two commercial CFD codes were capable of predicting good `trend' answers.
 
Article
An existing finite-volume computational simulator for heat and mass transfer in media fully or partially filled with porous material has been adapted to predict radon-222 exhalation rates. For validation purposes, this paper numerically examines the extent of natural-convective effects on radon-222 steady-state transfer from a phosphogypsum stack into the surrounding atmosphere. The stack is approximated by a dry rectangular porous matrix having uniform porosity and isotropic permeability whereas the supposedly laminar buoyancy-driven air flow is modelled following Darcy–Brinkman–Boussinesq approach. Differential governing equations are cast in dimensionless form in order to encompass simultaneous effects from physical factors involved. Dimensionless groups related to decay and emanation processes are put forward apart from usual controlling parameters such as Prandtl, Schmidt, Darcy and Grashof numbers. Results are reported for 106 ⩽ Gr ⩽ 108 and 10−13 ⩽ Da ⩽ 10−7. Natural-convective effects on typical low-permeability phosphogypsum stacks proved to be of minor importance, as radon-222 transfer becomes diffusive dominant as expected.
 
Article
A coupled system by the 3D rotating Navier–Stokes equations with a mixed boundary condition and a 2D biharmonic problem with two obstacles and the gradient restriction is investigated in this paper. Using the Schauder’s fixed point theorem, we show the existence of a strong solution for a sufficiently large viscosity ν and sufficiently small data.
 
Article
The present mainstream realizes that non-Fourier phenomena in heat transfer are arisen from the time-delay in heat diffusion; however, in this paper we mathematically prove this realization an untruth. The analysis is based on the construction of 2D transfer function for the parabolic equation with time-delayed Laplacian that governs the assumed non-Fourier heat transfer. There, functional representation of this spatio-temporal dynamics is performed by the composite of Laplace transform and Galerkin projection. With 2D transfer function, the heat-transfer dynamics is further represented by feedback interconnection of thermal capacitance and time-delayed diffusion, which makes it possible for Nyquist to perform stability and bifurcation analyses on this spatio-temporal dynamics. It comes out that the heat-transfer dynamics under investigation is unstable no matter how small the time-delay in heat diffusion is. That is, time-delayed heat diffusion contradicts the first law of thermodynamics and thus cannot be observed. This paper continues to show that the realization of thermal inertia by thermal inductance is supported by the principle of electro-thermal analogy and compatible with experimental observations.
 
Article
Buoyancy driven mixing of two fluids in a 2D closed cavity is simulated with a two-fluid model. The predictions are compared with a set of experimental data. The experiment involves flow visualization of the mixing process and application of the image processing technique to determine the mixing characteristics. The measurements and predictions include the interface evolution, interface elongation, and mixing width. Two Grashof numbers based on the initial density gradient, Gr=3.7×105,3.7×103 and two valve speeds, 0 and 5 cm/s are considered. The predictions are generally in good agreement with the experimental data.
 
Article
This paper presents new dynamical behavior, i.e., the coexistence of 2N domains of attraction of N-dimensional nonautonomous neural networks with time-varying delays. By imposing some new assumptions on activation functions and system parameters, we construct 2N invariant basins for neural system and derive some criteria on the boundedness and exponential attractivity for each invariant basin. Particularly, when neural system degenerates into periodic case, we not only attain the coexistence of 2N periodic orbits in bounded invariant basins but also give their domains of attraction. Moreover, our results are suitable for autonomous neural systems. Our new results improve and generalize former ones. Finally, computer simulation is performed to illustrate the feasibility of our results.
 
Article
Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers a type of project scheduling problem with fuzzy activity duration times. According to some management goals, three types of fuzzy models are built to solve the project scheduling problem. Moreover, the technique of fuzzy simulation and genetic algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy models. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.
 
Article
In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.
 
Article
Fluidized bed systems have the potential to be widely used in the power generation, mineral processing and chemical industries. One factor limiting their increased use is the lack of adequate design techniques for scaling such systems. A model has been developed for simulating gas–solid fluidized bed plant. The model uses a multiphase Eulerian–Eulerian technique to predict the transient behaviour of fluidized bed systems. The commercial CFD code CFX is used as the computational framework for solving the discretized equations. To overcome the problem of accurate geometrical representation experienced in previous models a body fitted grid system is employed. The model is used to predict isothermal flow in a three-dimensional bubbling fluidized bed. Predictions of the three-dimensional model show bubble formation with gas bubbles or voids preferentially moving along the centre of the bed. Predicted behaviour is qualitatively consistent with experimental observations.
 
Article
Numerical simulation is a common approach to understand many phenomena, usually yielding a computationally intensive problem. To overcome insufficient computer capacity and computational speed, a grid computing environment is a suitable approach. In this paper we focus on the development of parallel algorithms to solve a 3D transport model in such a context. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Algorithms are implemented using JACE, a grid-enabled Java Asynchronous Computing Environment. This programming environment allows users to design synchronous and asynchronous parallel iterative algorithms as well. Experiments are carried out on a heterogeneous grid environment in which the behaviour of both parallel iterative algorithms is analysed. The results allow us to draw some conclusions about the use of the programming library JACE and the design of parallel iterative algorithms in a grid computing environment.
 
Article
A three-dimensional (3D) model based on the first principles of mass, momentum and energy was developed that numerically simulates the processes of static and forward smoldering in a porous packed bed of plant materials. The packed bed contains cellulose material or tobacco (cigarette) wrapped in a porous paper and surrounded by an ambient air. Other major characteristics of the model are including the effects of buoyancy forces in the flow field, separate treatment of solid and gas in a thermally non-equilibrium environment, and use of multi-precursor kinetic models for the pyrolysis of staring material and oxidation of char. The changes in porosity due to pyrolysis and char oxidation and the effect of porosity on the bed permeability and gas diffusivity are included. The mass, momentum, energy, and species transport equations are solved in a discretized computational domain using a commercially available computational fluid dynamics (CFD) code. The simulation results show that the model reasonably reproduces the major features of a burning cigarette during smoldering and puffing and are in a good agreement with the existing experimental results for cigarettes. Results include the velocity profiles, gas and solid temperatures, coal shape, burn rates, profile and transport of gas and vapor species throughout the packed bed, dilution through the wrapper paper and ventilation in the filter section, and the mass fraction of some pyrolysis and oxidation products in the mainstream and sidestream flows.
 
Article
While the discrete element method (DEM) is attracting increasing interest for the simulation of industrial granular flow, much of the previous DEM modelling has considered two-dimensional (2D) flows and used circular particles. The inclusion of particle shape into DEM models is very important and allows many flow features, particularly in hoppers, to be more accurately reproduced than was possible when using only circular particles. Elongated particles are shown here to produce flow rates up to 30% lower than for circular particles and give flow patterns that are quite different. The yielding of the particle microstructure resembles more the tearing of a continuum solid, with large-scale quasi-stable voids being formed and large groups of particles moving together. The flow becomes increasingly concentrated in a relatively narrow funnel above the hopper opening. This encourages the hope that DEM may be able to predict important problems such as bridging and rat-holing. Increasing the blockiness or angularity of the particles is also shown to increase resistance to flow and reduces the flow rates by up to 28%, but without having perceptible effect on the nature of the flow. We also describe our methodology for constructing and modelling geometrically complex industrial applications in three dimensions and present a series of industrially important three-dimensional (3D) case studies. The charge motion in a 5 m diameter ball mill and in a Hicom nutating mill, discharge from single- and four-port cylindrical hoppers, and particle size separation by a vibrating screen are demonstrated. For each case, plausible particle size distributions (PSDs) have been used. The results obtained indicate that DEM modelling is now sufficiently advanced that it can make useful contributions to process optimisation and equipment design. Finally the parallelisation of such a DEM code is described and benchmark performance results for a large-scale 2D hopper flow are presented.
 
Article
This paper is concerned with the prediction of three-dimensional turbulent flows around bodies of arbitrary shape, with particular emphasis on a ship's hull. Two solution methods are compared employing a non-orthogonal coordinate system, in which the surface of the body is arranged to coincide with a coordinate surface. The velocity components are solved for the axial, radial and circumferential components in the cylindrical-polar system from which the non-orthogonal coordinates are derived.The partial-differential equations governing the flows under consideration are solved by two finite-difference methods for three-dimensional, parabolic1and partially-parabolic2flows. Turbulence is accounted for through a two-equation model of turbulence developed by Harlow and Nakayama3and modelled by Launder and Spalding.4Solutions are presented for flow around a ship's hull which demonstrate the potential of the present methods.
 
Article
This study aimed to evaluate continuous and simultaneous variations of dental implant diameter and length, and to identify their relatively optimal ranges in the posterior mandible under biomechanical consideration. A 3D finite element model of a posterior mandibular segment with dental implant was created. Implant diameter ranged from 3.0 to 5.0 mm, and implant length ranged from 6.0 to 16.0 mm. The results showed that under axial load, the maximum Von Mises stresses in cortical and cancellous bones decreased by 76.53% and 72.93% respectively, with the increasing of implant diameter and length; and under buccolingual load, by 83.97% and 84.93%, respectively. Under both loads, the maximum displacements of implant-abutment complex decreased by 58.09% and 75.53%, respectively. The results indicate that in the posterior mandible, implant diameter plays more significant roles than length in reducing cortical bone stress and enhancing implant stability under both loads. Meanwhile, implant length is more effective than diameter in reducing cancellous bone stress under both loads. Moreover, biomechanically, implant diameter exceeding 4.0 mm and implant length exceeding 12.0 mm is a relatively optimal combination for a screwed implant in the posterior mandible with poor bone quality.
 
Article
The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three-dimensional fluid flow with significant free surface fragmentation and splashing. A Lagrangian simulation technique that is particularly well suited to modelling HPDC is smoothed particle hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling the accurate prediction of fluid flows involving complex free surface motion.Validation of isothermal SPH flow predictions for the casting of a servo piston head using water analogue experiments is presented. Comparison with MAGMAsoft predictions provides information of the relative strengths of these two approaches. The SPH simulations were better able to capture the key details of the fluid motion and splashing, particularly the relative rates of flow around sharp bends and through thin sections. Validation of flow predictions coupled to temperature and solidification using short shots are also presented. The bulk features of the final solid castings are in good agreement with the predictions.Several automotive examples of SPH simulated HPDC flows are presented, ranging from simple cases such as a servo piston to steering column components and a full engine rocker cover. These show unprecedented detail in the fluid free surfaces, particularly in the extent of fragmentation and void formation.These results together combine to demonstrate that SPH modelling of HPDC has now reached a level where both isothermal and thermal simulations can be performed in reasonable computation times for large scale automotive castings and provide a high degree of predictive accuracy.
 
Article
The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.
 
Article
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly coupled time-dependent diffusion-reaction partial differential equations with convection terms describing the principal electrical, thermal and chemical phenomena that determine the macroscopic electrical response of the device under the action of externally applied electrical and thermal forces. The system is supplied with suitable initial, boundary and interface conditions that account for the interaction occurring among the various regions of the device with the surrounding environment. Temporal semi-discretization of the problem is carried out with the Backward Euler Method while a fixed-point iteration of Gummel type is used for system decoupling. Numerical approximation of the linearized subproblems is carried out using an exponentially fitted stabilized Finite Element Method on unstructured tetrahedral grids. Several computational experiments are included to validate the physical accuracy of the proposed computational algorithm in the study of realistic device structures.
 
Article
This work presents a time-domain hypersingular integral equation (TD-HIE) method for modeling 3D crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) under extended incremental loads rate through intricate theoretical analysis and numerical simulations. Using Green’s functions, the extended general incremental displacement rate solutions are obtained by time-domain boundary element method. Three-dimensional arbitrary crack growth problem in EMTE-CVP-MCs is reduced to solving a set of TD-HIEs coupled with boundary integral equations, in which the unknown functions are the extended incremental displacement discontinuities gradient. Then, the behavior of the extended incremental displacement discontinuities gradient around the crack front terminating at the interface is analyzed by the time-domain main-part analysis method of TD-HIE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral near the crack fronts in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HIE for a 3D crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of time-domain basic density functions and polynomials. Finally, examples are presented to demonstrate the application of the proposed method.
 
Article
In this paper the combined integral method is applied to a simple one-dimensional ablation problem. One of the drawbacks of heat balance integral methods is how to choose the approximating function. It is common to use a polynomial form but even then it is not clear what the power of the highest order term should be. Previous studies have determined exponents either from exact solutions or from expansions valid over short time scales; neither approach is satisfactory nor very accurate for larger times. We combine the heat balance and refined integral methods to determine this exponent as part of the solution process, and conclude that it is in fact time-dependent in the ablation stage. From comparing the approximate solutions with numerical and exact analytical solutions whenever possible, we show that this new method greatly improves the accuracy on standard methods, without overcomplicating the method.
 
Article
A unified method is presented for the analysis of vibration and stability of axially loaded non-uniform beams with abrupt changes of cross-section. The beam may also be supported on Winkler elastic foundation, and both the axial force and the foundation stiffness can be varied arbitrarily. The method is based on the Euler–Lagrangian approach using a family of C1 admissible functions as the assumed modes. The assumed modes comprise essentially the vibration modes of a single span hypothetical prismatic beam with the same end supports but without the intermediate supports, modified by piecewise C1 cubic polynomials. The chosen admissible functions therefore possess both the advantages of fast convergence of the eigenfunctions and the appropriate order of continuity at the location of abrupt change of cross-section. The method allows extensive use of matrix notations and programming is rather straightforward. Numerical results also show that the method is versatile, efficient and accurate.
 
Article
Recently, the generalized fractional reaction–diffusion equation subject to an external linear force field has been proposed to describe the transport processes in disordered systems. The solution of this generalized model can be formally expressed in closed form through the Fox function. For the sack of completeness, we dedicate this work to construct a neatly derivation of the generalized fractional reaction–diffusion equation. Remarkably, such derivation could in general offer some novel and inspiring inspection to the phenomena of anomalous transport. For instance, there is a strong evidence that the fractional calculus offers some physical insight into the origin of fractional dynamics for a systems which exhibit multiple trapping.
 
Article
This paper is concerned with modelling and long-range predictive control of an absorption packed column. The absorption column is used to decrease the concentration of CO2 in a gas mixture below a desired value. A solution of Diethanolamine (DEA) is used as the absorbent. The flow rate of the absorbent and the concentration of CO2 in the gas mixture are selected, respectively, as control and controlled variables. A physically based model has been developed from considerations of mass balances, of transport phenomena, and of chemical reaction in the liquid phase. It consists of three nonlinear partial differential equations. The control design is based on a simple low-order linear discrete model with unknown and possibly time-varying parameters. The parameters of this model are estimated using the least squares algorithm taking into account the requirements for long-term adaptive control. An extended horizon control policy, based on the minimization of a quadratic criterion function of the input and output tracking errors, is used for feedback control. Several simulation studies highlight the applicability of the involved adaptive control algorithm.
 
Article
The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.
 
Article
The present analysis brings out the interaction of curvature and a weak wall absorption parameter on the dispersion process using Taylor analysis. A perturbation series solution has been obtained to find the values of the effective dispersion coefficient. The constraints imposed by the perturbation techniques have been removed using a numerical scheme based on spectral method. Results are found to be applicable for a time at which the Taylor dispersion model holds. It has been observed that in the interphase transport of reactive contaminants the effective dispersion coefficient is significantly different from that of Taylor due to the wall absorption parameter. The results corresponding to the straight tube are verified with the published results, and those obtained from the perturbation and spectral techniques are found to be comparable. The restriction of the present analysis is confined to the effect of weak wall absorption under laminar flow conditions. This restriction needs to be relaxed. For moderate or large values of the absorption parameter a generalized dispersion model has to be resorted to.
 
Article
Integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM) which uses the differential quadrature (DQ) techniques to the finite element discretization is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor–corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm.
 
Article
In this paper, we present a novel decision support system for order acceptance/rejection in a hybrid Make-to-Stock/Make-to-Order production environment. The proposed decision support system is comprised of five steps. At the first step, the customers are prioritized based on a fuzzy TOPSIS method. Rough-cut capacity and rough-cut inventory are calculated in the second step and in case of unavailability in capacity and materials, some undesirable orders are rejected. Also, proper decisions are made about non-rejected orders. At the next step, prices and delivery dates of the non-rejected orders are determined by running a mixed-integer mathematical programming model. At the fourth step, a set of guidelines are proposed to help the organization negotiate over price and due date with the customers. In the next step, if the customer accepts the offered price and delivery date, the order is accepted and later considered in the production schedule of the shop floor, otherwise the order is rejected. Finally, numerical experiments are conducted to show the tractability of the applied mathematical programming model.
 
Article
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic operations. The proposed model can serve as a deterministic alternative to existing probabilistic methods for checking balancedness in binary sequence generators. The procedure here described can be devised as a first selective criterium for acceptance/rejection of this type of generators. Comment: 16 pages, 0 figures
 
Article
In this paper, a new optimization method has been proposed for accident prediction non-linear models. This has been achieved by eliminating the Hessian matrix from the equation of optimal pace length in the gradient vector method. One advantage is that it is independent of the starting point in optimization processes and it provides convergence at the highest top as well. This method has been tested on an accident prediction model and its preference over the gradient vector method has been proven.
 
Article
An offshoot of an existing general model of road traffic accidents (MRTA) is presented. The general MRTA contains an unwieldy number of terms for practical purposes. A reduction in the number of terms becomes necessary to render the model suitable for numerical computations. The method used to achieve this through grouping primary causes is shown. Some potential applications of the model are also outlined. Computations performed using this model yielded results which compared favourably with available results from other practical sources.
 
Article
Heavy metals like cadmium and arsenic have serious health consequences and ecosystem impacts. Due to various factors including the disposal of municipal and industrial wastes, application of fertilizers, atmospheric deposition and discharge of wastewater on land, has resulted in increase in the concentration of heavy metals in the soil. Crops and vegetables grown on such soil accumulate heavy metals, which leads to phyto-toxicity. For understanding and managing precious natural resources, mathematical models are increasingly being used. This paper describes a dynamic macroscopic numerical model for heavy metal transport and its uptake by vegetables in the root zone. The model is applied for simulating cadmium uptake by radish (Raphanus sativus), carrot (Daucos carota), spinach (Spinacia oleracea) and cabbage (Brassica oleracea) by using measured field data. The governing non-linear partial differential equations are solved numerically by an implicit finite difference method using Picard’s iterative technique and the source code is written in MATLAB.
 
Article
A two dimensional tidal model of the northwest European shelf is used to examine the influence of sampling rate, number of harmonic constituents analysed for, and length of data upon the accuracy of tidal constituents. Calculations show that in shallow water, where non-linear interactions give rise to higher harmonics, an accurate analysis can be obtained from a short span of data provided the higher harmonics are included in the analysis. In very shallow water where the tidal range is comparable to the water depth, asymmetry in the tidal signal due to substantial differences in friction at times of high and low water produces a number of semi-diurnal constituents in particular ν2 and L2 that must be included in the harmonic analysis. When these constituents together with the “classical” shallow water constituents are used in the harmonic analysis then an accurate analysis can be performed on a short span of data. The significant saving in computer time, particularly for a fine grid three dimensional model of using frequent sampling and analysing for a full set of constituents is stressed.
 
Article
Comparisons are made between various finite difference algorithms used for the numerical solution of two-dimensional viscous flow. Central difference algorithms recently developed by the authors are compared with the well established upwind difference algorithms. Some analytical solutions to the Navier-Stokes equations have been produced in order for meaningful comparisons to be made. On the basis of the results, the new central difference algorithms are recommended as being more accurate whilst requiring little additional computational effort. There is an upper limit on the grid Reynolds number for which these new methods will converge, but this will usually be when the flow would in practice be turbulent.
 
Article
This paper explains significant differences in truncation error between finite-difference and finite-volume convection-diffusion schemes. Specifically, the order of accuracy of the QUICK scheme for steady-state convection and diffusion is discussed in detail. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a -factor multiplying the “curvature” term) is indeed a third-order representation of the finite-volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a -factor) is a third-order representation of the finite-difference single-point formulation; this can be written in a pseudo-flux-difference form. These are both third-order convection schemes; however, the QUICK finite-volume convection operator is 33% more accurate than the single-point implementation of SPUDS. Another finite-volume scheme, writing convective fluxes in terms of cell-average values, requires a -factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages and then express this in pseudo-flux-difference form; for third-order accuracy, this requires a curvature factor of . Diffusion operators are also considered in both finite-difference and finite-volume formulations. Finite-volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite-volume formulation as it is in a finite-difference formulation.
 
Article
The symplectic geometry approach is introduced for accurate bending analysis of rectangular thin plates with two adjacent edges free and the others clamped or simply supported. The basic equations for rectangular plates are first transferred into Hamilton canonical equations. Using the symplectic approach, the analytic solution of rectangular thin plate with two adjacent edges simply supported and the others slidingly supported is derived. Accurate bending solutions of title problems are then obtained using the superposition method. The approach used in this paper eliminates the need to pre-determine the deformation function and is hence more reasonable than conventional methods. Numerical results are presented to demonstrate the validity and efficiency of the approach as compared with those reported in other literatures.
 
Article
Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. Because the information of inter-urban traffic presents a challenging situation, the traffic flow forecasting involves a rather complex nonlinear data pattern. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a short-term traffic forecasting model which combines the support vector regression model with continuous ant colony optimization algorithms (SVRCACO) to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed SVRCACO model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA) time series model. Therefore, the SVRCACO model is a promising alternative for forecasting traffic flow.
 
Article
This study proposes an effective numerical model based on the Computational Fluid Dynamics (CFD) approach to obtain the flow structure around a passenger car with wing type rear spoiler. The topology of the test vehicle and grid system is constructed by a commercial package, ICEM/CFD. FLUENT is the CFD solver employed in this study. After numerical iterations are completed, the aerodynamic data and detailed complicated flow structure are visualized using commercial packages, Field View and Tecplot. The wind effect on the aerodynamic behavior of a passenger car with and without a rear spoiler and endplate is numerically investigated in the present study. It is found that the installation of a spoiler with an appropriate angle of attack can reduce the aerodynamic lift coefficient. Furthermore, the installation of an endplate can reduce the noise behind the car. It is clear that the vertical stability of a passenger car and its noise elimination can be improved. Finally, the aerodynamics and aero-acoustics of the most suitable design of spoiler is introduced and analyzed.
 
Article
A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS.It is shown that the reduced order model decreases the simulation time by at least one order of magnitude, while maintaining the desired accuracy of the state variables under investigation. The method could prove as a valuable tool to analyze complex coupled structural–acoustic systems, and their subsequent optimization or sensitivity analysis, where, in addition to fast analysis, a fine frequency resolution is often required.
 
Article
A detailed study is undertaken to analyze the non-steady interaction of plane progressive pressure pulses with an isotropic, homogeneous, fluid-filled and submerged spherical elastic shell of arbitrary wall thickness within the scope of linear acoustics. The formulation is based on the general three dimensional equations of linear elasticity and the wave equation for the internal and external acoustic domains. The Laplace transform with respect to the time coordinate is invoked, and the classical method of separation of variables is used to obtain the transformed solutions in the form of partial-wave expansions in terms of Legendre polynomials. The inversion of Laplace transforms have been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations (Gibbs’ phenomenon), and obtain uniformly convergent solutions. Detailed numerical results for the transient and vibratory responses of water-submerged steel shells of selected wall thickness parameters with various internal fluid loadings under an exponential wave excitation are presented. Many of the interesting dynamic features in the transient shell–shock interaction such as shock transparency, shell-radiated negative pressure waves, formation of triple points, and focusing of the reflected waves are examined using appropriate 2D images of the internal pressure field. Also, the temporal behavior of the specularly-reflected, the lowest symmetric S0- and antisymmetric A0-Lamb waves, as well as appearance of the Franz’s creeping waves are discussed through proper visualization of the external scattered field. Likelihood of cavitation is addressed and regions proned to cavitation are identified. Moreover, the effects of internal fluid impedance in addition to shell wall thickness on the dynamic stress concentrations induced within the shell are analyzed. Limiting cases are considered and fair agreements with well-known solutions are established.
 
Article
Infinite element computations are very efficient for predicting the vibro-acoustic response and sensitivities of a vibrating structure for an exterior acoustic domain. In addition, domain decomposition methods are very powerful algorithms for solving large linear systems in parallel. In this paper, an infinite element method is proposed and analyzed for parallel computations purpose. An original formulation of this method with Lagrange multipliers defined on (semi-)infinite space is presented. The implementation aspects of this method in an industrial acoustic software (SYSNOISE) are discussed. New numerical results illustrate the efficiency of the proposed method for realistic acoustical radiation problems.
 
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The indirect boundary element method naturally allows the simultaneous modelling of acoustic domains on both sides of thin vibrating structures. To fully utilize the potential of this technique a formulation that permits the application of separate impedance on the surface of acoustic domains on each side of the vibrating structure is developed. The resulting integral equations are solved by using a variational approach. The formulation and the numerical implementation are validated by comparing the results from the present development to analytical solutions. The applicability of this procedure to the solution of a realistic engineering problem is also demonstrated.
 
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The electromagnetic diffusion and the electromechanical phenomena arising in a solid cylinder rotating inside a magnetic field are here analyzed. The study is developed through a time stepping Finite Element voltage-driven formulation, employing the sliding mesh technique for handling the cylinder motion. The influence on the dynamic behavior and energy dissipation of the material electric and magnetic properties, the geometrical parameters and the supply conditions is investigated considering a model problem.
 
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In this study, an extended activated sludge model was established to describe the transformation of nitrite (SNO2), nitrate (SNO3) and other components in TNCU2 process (National Central University of Taiwan No. 2) that consisted of anaerobic, oxic, anoxic, oxic zones in sequence. The significant differences between this extended model and other models were that two-stage nitrification, multi-stage denitrification, and phosphorus removal were taken into account simultaneously. The results indicated that the growth rate constants of XAOB and XNOB were 1.4 and 0.4 d−1, respectively. YAOB value was 0.14 and YNOB value was 0.04. According to model simulation, the heterotrophic microorganism (XH), phosphorus accumulating organism (XPAO), XAOB and XNOB concentrations were 1160–1322, 182–226, 21–26 and 13–17 mg l−1, respectively, in TNCU2 process. XH,XPAO,XAOB, and XNOB decreased in the anaerobic tanks because of the lysis reaction. Then XH,XPAO,XAOB, and XNOB increased in the aerobic tanks due to aerobic growth. XH,XPAO,XAOB, and XNOB increased in quantities by about 5%, 6%, 6% and 4% in the first aerobic tank and decreased in quantities by about 12%, 19%, 20% and 19% in the anoxic tank in which the step feeding influent flowed. The ratio of total nitrifying species to total active biomass was about 3% in each tank.
 
(a) Exponential stability of the state variable x 1 ðtÞ and x 2 ðtÞ for the neural network with u 1 ¼ 5; u 2 ¼ 6. (b) Convergence in finite time of the state variable x 1 ðtÞ and x 2 ðtÞ for the neural network with u 1 ¼ u 2 ¼ 0.
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This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufficient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in finite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions.
 
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In this paper, a general class of neural networks with arbitrary constant delays is studied, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. Based on the Leray–Schauder alternative principle and generalized Lyapunov approach, conditions are given under which there is a unique equilibrium of the neural network, which is globally asymptotically stable. Moreover, the existence and global asymptotic stability of periodic solutions are derived, where the neuron inputs are periodic. The obtained results extend previous works not only on delayed neural networks with Lipschitz continuous neuron activations, but also on delayed neural networks with discontinuous neuron activations.
 
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In this paper, we present a general class of BAM neural networks with discontinuous neuron activations and impulses. By using the fixed point theorem in differential inclusions theory, we investigate the existence of periodic solution for this neural network. By constructing the suitable Lyapunov function, we give a sufficient condition which ensures the uniqueness and global exponential stability of the periodic solution. The results of this paper show that the Forti’s conjecture is true for BAM neural networks with discontinuous neuron activations and impulses. Further, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.
 
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In this paper, we consider the dynamical behavior of delayed Cohen–Grossberg neural networks with discontinuous activation functions. Some sufficient conditions are derived to guarantee the existence, uniqueness and global stability of the equilibrium point of the neural network. Convergence behavior for both state and output is discussed. The constraints imposed on the interconnection matrices, which concern the theory of M-matrices, are easily verifiable and independent of the delay parameter. The obtained results improve and extend the previous results. Finally, we give an numerical example to illustrate the effectiveness of the theoretical results.
 
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In this paper, a new concept called α-inverse Lipschitz function is introduced. Based on the topological degree theory and Lyapunov functional method, we investigate global convergence for a novel class of neural networks with impulses where the neuron activations belong to the class of α-inverse Lipschitz functions. Some sufficient conditions are derived which ensure the existence, and global exponential stability of the equilibrium point of neural networks. Furthermore, we give two results which are used to check the stability of uncertain neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of results obtained in this paper.
 
Top-cited authors
Paul W. Cleary
  • The Commonwealth Scientific and Industrial Research Organisation
Ian W. Turner
  • Queensland University of Technology
F. Liu
  • Queensland University of Technology
C.A. Brebbia
  • Wessex Institute of Technology
Reza Tavakkoli-Moghaddam
  • University of Tehran