Numerical Method

We develop a multiscale simulation method for dense granular drainage, based on the recently proposed spot model, where the particle packing flows by local collective displacements in response to diffusing "spots" of interstitial free volume. By comparing with discrete-element method (DEM) simulations of 55,000 spheres in a rectangular silo, we show that the spot simulation is able to approximately capture many features of drainage, such as packing statistics, particle mixing, and flow profiles. The spot simulation runs two to three orders of magnitude faster than DEM, making it an appropriate method for real-time control or optimization. We demonstrate extensions for modeling particle heaping and avalanching at the free surface, and for simulating the boundary layers of slower flow near walls. We show that the spot simulations are robust and flexible, by demonstrating that they can be used in both event-driven and fixed timestep approaches, and showing that the elastic relaxation step used in the model can be applied much less frequently and still create good results.

The majority of concrete dams worldwide have behaved relatively well during seismic events. However, there are several cases where global failure or substantial damages have occurred. The need for new dam construction and retrofitting of existing dams necessitates the use of advanced design approaches that can take realistically into account the potential dam-reservoir-foundation interaction. Seismic design of concrete dams is associated with difficulties to estimate the dynamic distress of the dam as well as the response of the damreservoir-foundation system and to assess the impact of the various parameters involved. In this chapter, after an extensive literature review on the dynamic interaction of concrete dams with retained water and underlying soil, results from numerical simulations are presented. Initially, analytical closed-form solutions that have been widely used for the calculation of dam distress are outlined. Subsequently, the numerical methods based on the finite element method (FEM) which is unavoidably used for complicated geometries of the reservoir and/or the dam, are reviewed. Emphasis is given on FEM-based procedures and especially the boundary conditions and interactions involved. Numerical results are presented to illustrate the impact of various key parameters on the distress and response of concrete dams considering dam-foundation interaction phenomena. In general, a good agreement is observed between the results of analytical and numerical approaches for the examined characteristic dam configuration.

Survey Modelling Simulation a b s t r a c t Computer simulation has become a required tool in the design phase of vapor compression systems; however with relatively few exceptions most simulations focus on the basic four component systems. With an increasing focus being placed on energy efficiency, the simulation of multi-component vapor compression systems (having multiple evaporators, condenser or compressors) will become essential to assist in the design of these more complicated systems. The implementation of a component-based framework will facilitate the simulation of multi-component systems. This paper describes three algorithms used to simulate a component-based vapor compression system. A test matrix of 6174 sample runs covering a wide range of operating conditions was constructed to determine the robustness and speed of each method when using three different types of nonlinear equation solvers. Each method was tested by simulating a basic four component cycle and a more advanced multiple evaporator system. The results are presented in such a format as to describe the reasons that contribute to any instability of the solvers and the computational efficiency of each method is discussed. ª 2007 Elsevier Ltd and IIR. All rights reserved.

This paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability of a folding multi-layered truss. Both analyses are based on bifurcation theory and include geometrical nonlinearity. The dynamic analysis includes an allowance for contact between nodes. Comparisons are made between published experimental folding patterns and the patterns obtained from both numerical methods in which bifurcations are demonstrated as elastic unstable snap-through behaviour. Several folding patterns are identified during the elastic instability where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading. The authors suggest that the understanding of the behaviour will be very useful for the development of light weight structures subject to dynamic loading based on the bifurcation static analysis and dynamic analysis (using both the displacement control method and the load control method). (I. Ario), [email protected] (A. Watson).

The purpose of the paper is to develop a formalism for solving the problem of scattering of electromagnetic waves by a tilted, in"nite, multilayered cylinder. The approach allows us to obtain the Mie scattering coe$cients without involving matrix calculations. This method provides the basis for constructing an e$cient algorithm for the case of a multilayered cylinder, extending the procedure developed for a multilayered sphere. For the case of a cylinder, such a procedure does not follow directly from the boundary conditions, but requires a special mathematical justi"cation. The proof is presented in this study.

Ahatract-We investigate the existence and uniqueness of robust time-optimal control solutions of flexible structures for rest-torest motion. We show that several robust time-optimal control designs for flexible systems are equivalent to traditional nonrobust time-optimal controls for difirent systems. This equivalence implies that the robust time-optimal controllers must then have all the properties that are known about traditional timeoptimal controllers. Further, many of the numerical methods developed for generating time-optimal commands are directly applicable to designing robust time-optimal commands. 0

A new nonlinear integral-equation model is derived in terms of hodograph variables for free-surface flow past an arbitrary bottom obstruction. A numerical method, carefully chosen to solve the resulting nonlinear algebraic equations and a simple, yet effective radiation condition have led to some very encouraging results. In this paper, results are presented for a semi-circular obstruction and are compared with

A blade element momentum (BEM), vortex lattice (VL) and a Reynolds-averaged thin-layer Navier-Stokes method (RaNS) were evaluated for their ability to predict the aerodynamic performance of the Combined Experiment Phase II Horizontal Axis Wind Turbine. To evaluate blade stall modeling, the BEM and VL methods utilized the Du-Selig stall delay model along with experimental and computationally derived airfoil characteristics. To validate the methods, experimental data from the IEA Annex XIV database were used. Additional data reduction was applied to sort the experimental data into steady wind speed bins with known error and to make it suitable for validation of numerical methods. All three methods produce good power and sectional normal force predictions at pre-stall wind conditions. The RaNS method fails to capture the correct aerodynamic performance once the blade begins to stall. The VL and BEM methods show better capability in predicting post stall behavior, however to obtain more accurate power and load predictions they need improved stall delay models and adequate airfoil properties. Predicting the correct inboard stall delay is still a challenge to these methods.

Fatigue Pro®le, a new numerical method for characterising fatigue in isokinetic cycle ergometry is presented and compared with the conventional fatigue index (FI). The new method describes the temporal development of muscle fatigue based on the decline of peak power output throughout a whole trial. The advantage of this method is demonstrated by the analysis of two 25 s maximum trials, separated by 90 s recovery, performed by a well-trained athlete at a pedal frequency of 120 revolutions per minute. A fourth degree polynomial was ®tted to model the peak power data. Using the polynomial model coecients the ®rst derivative represented the rate of changing peak power which represented the Fatigue Pro®le. The conventional FI was calculated as A35 Ws A1 and A32 Ws A1 for trials 1 and 2 respectively, indicating minor dierences in fatigue between trials. In contrast the Fatigue Pro®le revealed important numeric and temporal dierences between the trials. For trial 1 a maximum rate of peak power decline of A65 Ws A1 was reached at approximately 6 s into the trial. In marked contrast, in trial 2, maximum rate of peak power decline (A146 Ws A1) occurred immediately. The Fatigue Pro®le approach allows the characterisation of the temporal development of fatigue under dierent experimental conditions and in combination with other techniques may yield further insight into the underlying mechanisms of fatigue.

We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method [1] could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods-one originally proposed by Lewis, and Black-Scholes-wise method are considered that seem to work fine for any value of the VG parameters. Test examples are given to demonstrate efficiency of these methods. Convergency of all methods is also discussed.

Based on the two-dimensional (2-D) least squares method, this paper presents a novel numerical method to calculate the magnetic characteristics for switched reluctance motor drives. In this method, the 2-D orthogonal polynomials are used to model the magnetic characteristics. The coefficients in these polynomials are determined by the 2-D least squares method. These coefficients can be computed off line and can also be trained on line. The computed results agree well with the experimental results. In addition, the effect of the order number of the polynomials on the computation errors is discussed. The proposed method is very helpful in torque prediction, simulation studies and development of sensorless control of switched reluctance motor drives.

A numerical method, based on the integral equation formulation of Symm, is described for computing approximations to the mapping functions which accomplish the following conformal maps: (a) the mapping of a domain interior to a closed Jordan curve onto the interior of the unit disc, (b) the mapping of a domain exterior to a closed Jordan curve onto the exterior of the unit disc, (c) the mapping of a doubly-connected domain bounded by two closed Jordan curves onto a circular annulus. The numerical method is based on approximating the unknown source density by cubic splines and "singular" functions, and is particularly suited for the mapping of difficult domains having sharp corners.

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601×601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.

Numerical computation of the electric field strength and ionic space charge density in electrode systems consisting of ionizing wire and non-ionizing cylinder, connected to the same DC high-voltage supply and facing a grounded plate, is a difficult problem, which is of interest to several electrostatic processes applications. In a previous study a simple numerical method has been proposed to calculate the spatial distributions of electric field and ionic space charge in a case of a continuum and uniform corona discharge originating at the surface of the wire. The aim of the present paper is to improve the physical model of the corona discharge in this particular electrode configuration, by assuming a more realistic law of charge injection on the wire circumference. The computations were carried out for an ionizing wire of radius r ¼ 0.1 mm, located at different distances h from a metallic tubular support of radius R ¼ 13.4 mm.The initial conditions of the corona discharge took into account the non-uniformity of the charge injection around the ionizing wire electrode. The computational results were compared with those obtained under the assumption of uniform corona discharge. The comparison pointed out that neither the non-uniformity of the electric field nor that of the charge injection can be neglected. They depend on the geometry of the electrode system and affect the distribution of the electric field and of the space charge density in the inter-electrode gap.

and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Linearconstitutiveequationsofa thermopiezomagneticmedium involving mechanical, electrical, magnetic, and thermal e elds are presented with the aid of a thermodynamic potential. A thermopiezomagnetic medium can be formed by bonding together a piezoelectric and magnetostrictive composite. Two energy functionals are dee ned. It is shown via Hamilton’ s principle that these functionals yield the equations of motion for the mechanical e eld, Maxwell’ s equilibrium equations for the electrical and magnetic e elds, and the generalized heat equation for the thermal e eld. Finite element equations for the thermopiezomagnetic media are obtained by using the linear constitutive equations in Hamilton’ s principle together with the e nite element approximations. The e nite element equations are utilized on an example two-layer smartstructure, which consistsof a piezoceramic (barium titanate ) layer at the bottom and a magnetoceramic (cobalt ferrite ) layer at the top. An electrostatic e eld appl...

The horizontal electric field both at points above and below ground in the vicinity of lightning return strokes were evaluated by numerical solution of Sommerfeld's integrals. Results are presented for ground conductivities in the range of 0.01 and 0.0001 S/m. The results are compared with the following approximate procedures used in the literature to calculate horizontal electric fields: (a) the surface impedance approximation, (b) the quasi static approximation frequently used in lightning protection standards and (c) Cooray's simplified formula for the computation of underground electric field. Based on this comparison the distance range in which these approximations are valid is obtained. The results obtained show that: (1) The surface impedance approximation can generate correct horizontal electric field when the distance to the point of observation is larger than about 50 m, 100 m, and 500 m for ground conductivities of 0.01, 0.001 and 0.0001 S/m respectively.

This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential ψ = 1/(1 + ξ), which provides a good model for many astrophysical systems, including elliptical galaxies (with an R 1/4 law), dark matter halos (where N-body simulations indicate a nearly universal density profile), and young embedded star clusters (with gas density ρ ∼ ξ −1 ). For a given potential, one can readily calculate orbital solutions as a function of energy and angular momentum using numerical methods. In contrast, this paper presents a number of analytic results for the Hernquist potential and proves a series of general constraints showing that orbits have similar properties for any extended mass distribution (including, e.g., the NFW profile). We discuss circular orbits, radial orbits, zero energy orbits, different definitions of eccentricity, analogs of Kepler's law, the definition of orbital elements, and the relation of these orbits to spirograph patterns (epicycloids). Over a large portion of parameter space, the orbits can be adequately described (with accuracy better than 10%) using the parametric equations of epicycloids, thereby providing an analytic description of the orbits. As an application of this formal development, we find a solution for the orbit of the Large Magellanic Cloud in the potential of our Galaxy.

This paper describes a new formulation, based on linear ÿnite elements and non-linear programming, for computing rigorous lower bounds in 1, 2 and 3 dimensions. The resulting optimization problem is typically very large and highly sparse and is solved using a fast quasi-Newton method whose iteration count is largely independent of the mesh reÿnement. For two-dimensional applications, the new formulation is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming. Although it has been developed primarily for geotechnical applications, the method can be used for a wide range of plasticity problems including those with inhomogeneous materials, complex loading, and complicated geometry.

Many numerical methods produce sequences of vectors converging to the solution of a problem. When the convergence is slow, the sequence can be transformed into a new vector sequence which, under some assumptions, converges faster to the same limit. The construction of a sequence transformation is based on its kernel, that is the set of sequences which are transformed into a constant sequence. In this paper, new vector sequence transformations are built from kernels which extent those of the most general transformations known so far.

Precooling refers to the rapid removal of field heat from freshly harvested fruits and vegetables prior to shipping, storage or processing. Hydrocooling is a form of precooling in which the product is sprayed with or immersed in an agitated bath of chilled water. The design of hydrocooling systems requires accurate estimation of the hydrocooling times of fruits and vegetables as well as the corresponding refrigeration loads. Numerous methods for predicting the hydrocooling times of fruits and vegetables have been proposed, and the designer is faced with the challenge of selecting an appropriate estimation method from those available. Therefore, this paper reviews selected estimation methods for the hydrocooling times of fruits and vegetables, and quantitatively evaluates the selected hydrocooling time estimation methods by comparing their numerical results to a comprehensive experimental hydrocooling time data set compiled from the literature.

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual (numerical) solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.

We discuss two numerical techniques, based on the path integral approach described in a previous paper, for solving the stochastic equations underlying the financial markets: the path integral Monte Carlo, and the path integral deterministic evaluation. In particular, we apply the latter to some specific financial problems: the pricing of a European option, a zero-coupon bond, a caplet, an American option, and a Bermudan swaption.

Several electrostatic technologies, such as separation of granular mixtures, flocking, printing, or biological cell manipulation, are based on the accurate control of conductive particle motion in insulating gases or liquids by means of relatively high dc electric fields. This paper aimed at characterizing the behavior of such particles by numerical modeling of two aspects: 1) particle motion under the action of electric field forces and 2) insulation breakdown triggered by mobile particles. The equations of particle motion were written by taking into account both gravitational and drag forces, as well as the rebound at particle impact with the electrodes. If the particles move in ionized air, their charge varies in time. In that case, the equation of particle charge should be added to the mathematical model. The output data of the programs for numerical simulation of particle behavior are in good agreement with the available experimental results. Particle movements were shown to be influenced by the intensity of the electric field, by the density of the space charge, by size and mass density of the particles, as well as by their coefficient of restitution at impact with the electrodes. The conclusions regarding the behavior of conductive particles in insulating fluids are useful for the development of improved electrostatic separation technologies; they are of particular interest to all manufacturers of high-voltage equipment.

The ultrasonic pulse-echo backscattered amplitude integral (BAI)-mode imaging technique [IEEE Trans. UFFC, 45:30 (1998)] has demonstrated sensitive detection of subwavelength channel defects (38-m diameter reliably and 6-m diameter occasionally) in flexible 220-m-thick food package seals (17.3 MHz, Ϸ 86 m). However, the underlying subwavelength defect detection mechanism is poorly understood. In this contribution, a theoretical modeling study was undertaken to elucidate the mechanism. The subwavelength diameter channel was fused in-between two plastic package films by applying heat from one side of the films. The sample cross-section microstructure was characterized from both optical and acoustic images. The cross-section impedance profiles along sample thickness dimension were determined. Although identical in nominal impedance properties before sealing, the two binding films showed an asymmetric impedance profile after sealing. Transient finite-element heat conduction analysis and impedance profiles of multiple-sealed package samples showed that the single-sided heating process caused an asymmetric impedance profile. A generalized impedance model was proposed based on these observations. An efficient two-dimensional simulation tool using a finite-difference time-domain method and the perfectly matched layer numerically evaluated the defect detection behavior of the radio-frequency (rf) echo waveforms. The normalized correlation coefficients between the simulated and the measured rf echo waveforms were greater than 95% for this generalized model, which suggested the validity of the proposed impedance model.

Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10. A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

We have developed a new software tool, LENSVIEW, for modelling resolved gravitational lens images. Based on the LENSMEM algorithm, the software finds the best fitting lens mass model and source brightness distribution using a maximum entropy constraint. The method can be used with any point spread function or lens model. We review the algorithm and introduce some significant improvements. We also investigate and discuss issues associated with the statistical uncertainties of models and model parameters and the issues of source plane size and source pixel size.

We present some examples of detailed analysis of intrinsic localized modes in lattices, using the accurate numerical methods derived from the proof of existence of MacKay-Aubry. We report on some improvements on the methods, which are then used to the fullest to obtain the Floquet analysis of the breather solutions. Such calculations are possible taking into account the whole lattice,

The research in this paper deals with the simulation of continuous machine systems that can be described in a discrete manner (discrete-event systems), using qualitative simulation techniques. In order to represent discrete-time descriptions of machine systems and processes in an efficient way, this approach uses a combination of both qualitative modelling techniques and numerical methods. An objectoriented qualitative modelling and simulation toolbox, called QMTOOL, was extended and applied into modelling specific machine processes. Experiments carried out using this qualitative modelling and simulation toolbox, provided performance metrics and assisted the design and real-time control of specific industrial machines and processes. The results obtained have shown that qualitative modelling can provide less complex computational models for describing and simulating discrete-event machine systems, and that these models could be applied in cases where traditional mathematical models are difficult to manage.

The design of an idle speed controller for automotive engines is considered. A hybrid nonlinear model of the engine is presented. Based on suitable (nonlinear) change of variables, the idle speed control design problem can satisfactorily be addressed via LTI techniques. Specifically, the design problem has been formalized as a finite dimensional discrete-time ℓ ∞ optimal control problem, whereby the fuel consumption has to be minimized. Polynomial techniques have been used to convert the control design formulation to a linear "least absolute data fitting" problem, for which solution very efficient and stable numerical methods exist. Experimental results on a commercial car have been finally reported.

We consider the problem of regular refraction (where regular implies all waves meet at a single point) of a shock at an oblique planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic (MHD) simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180 • rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the types of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180 • rotational discontinuities, each followed by a slowmode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading-order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively.

In this paper, a numerical method for the evaluation of topological derivatives is proposed. The integral shape functional is considered for the Signorini type variational inequality in nonsmooth geometrical domain with a cut. The so-called smooth domain method is used for the purposes of numerical analysis for the variational inequality. The topological derivative of the integral shape functional is defined and computed using the mixed finite elements. Results of computations are presented. The shape topological derivatives can be used for numerical solution of some shape optimization as well as inverse problems.

Summary form only given. The purpose of this paper is to determine the radial distribution of the emission coefficient from the measured intensity distribution emitted by an extended source of radiation, particularly a plasma source. The source is assumed to be optically thin and axially symmetrical. This problem is solved by inverting Abel's integral equation. A smoothing procedure is made

In this paper a novel approach based on Asymptotic Iteration Method (AIM) is presented to solve analytically the light propagation through one-dimensional inhomogeneous slab waveguide. Practically implemented optical slab waveguides based on traditional techniques are usually inhomogeneous and numerical methods are used to obtain guided wave characteristics. In this work, we develop analytical method for modal analysis includes Eigen modes

The main goal of this paper is to present a numerical model describing the major physical phenomena involved in electromagnetic casting industrial processes as precisely as possible. Under suitable physical assumptions, we derive the set of equations in the two-dimensional case; we describe in detail the numerical methods used to solve such equations and derive an iterative algorithm. Numerical results describing the case of an aluminium ingot are presented in order to show the efliciency of the method. lc'

Kinetics of solidification of phase change materials (PCM) was analyzed for combined heat conduction in the PCM and container wall, and convection in the cold fluid. Stable and convergent numerical methods were derived after transformation to normalized size scale, and corresponding immobilization of the moving boundary. The accuracy was confirmed by comparing numerical solutions and corresponding analytical solutions for control by heat conduction in solidifying layers. The proposed method was used to assess when solidification is controlled solely by conduction in solidified layer, and to analyze relative roles of conduction through the container and convection in the cold fluid.

Context awareness has been a vital field of ubiquitous computing research. Numerous methods for capturing, interring external context and providing necessary service have been developed and relevant projects have been performed. However, user's internal context is more valuable than the external one. Thus, more searches on internal context are needed. This paper confines its research domain to the internet based information system (IS) in order to infer the internal context of user. For inferring internal context in this IS domain, one of the computer network techniques, packet sniffing technique, is utilized. This is effective and efficient in acquiring the information of the user's demand. Also, inference algorithm which is integrated with the acquired user's information is proposed. Furthermore, this paper demonstrates that the prototype system adopts the suggested technique and algorithm in order to prove its validity. The proposed prototype system is the basis of providing IS user with ubiquitous services and enhances the convenience and efficiency during business hour of IS user. In this fashion, this paper presents a new pattern of context acquisition and inference in implementing the ubiquitous computing based-IS along with the direction of internal context awareness research.

This paper proposes a model for the reoccupation of ants in a region of attraction, using evolutive partial differential diffusion-advection equations, in which the population dispersion and velocity in directions x and y are fuzzy parameters. The domain under study contains an attractive region, representing areas with high concentrations of palatable host plants with better nutritious qualities. The algorithm developed here uses information about the foraging behavior of a leaf-cutting ant colony of the Amazon region in northern Brazil. In the first model, we determined the numerical solution of the partial differential deterministic equation with constant dispersion and velocity, without incorporating uncertainties that may occur in this type of biological phenomenon. In the second model, we calculated the numerical solution of the partial differential equation, determining the dispersion at each iteration and for each triangular finite element. The dispersion was determined from a fuzzy rule-based system that depends on the number of individuals of the population and on the characteristics of the terrain. In this model, we also considered the velocity along the x and y directions as a fuzzy parameter that depends on the ant movement characteristics on the terrain in the y and x directions, respectively. The two models produced solutions consistent with ant behavior in response to the proximity of an attractive region, as stated in the papers by Shepherd (1982) [2] and Vasconcelos (1999) [3], but the fuzzy model incorporates uncertainties that do occur in the biological phenomenon under study.

Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter's liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agrement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.

The field and loss in the transition between a bent asymmetric and a straight symmetric slab waveguide are analyzed by the beam propagation method. The steady-state results obtained at large axial propagation distances are compared with the results of other theoretical approaches. The numerical results show how the asymmetric index distribution reduces the bending loss.

The solar water heating system functioning on a fixed temperature control (FTC) mode, rather than a differential temperature control (DTC) mode (continuous water flow rate), has appreciable advantages for saving parasitic power consumption and reducing the maintenance cost. A computer simulation model, using a numerical analysis method, has been developed to study a forced flow solar water heating system taking into account the realistic conditions of operations. It is noted that the most critical parameter in designing such types of system is the water flow rate. The results are obtained, corresponding to a solar water heating system of 40001/day capacity working at an average temperature of 60°C. Fixed temperature control Forced circulation NOMENCLATURE A c = Area of system (m 2) Cp = Specific heat (J/kg °C) hp_ c = Heat transfer coefficient between plate and cover (W/m2°C) hr,p_ ¢ = Radiative heat transfer coefficient between plate and cover (W/m2°C) hw = Heat transfer coefficient for water (W/m2°C) h ..... = Radiative heat transfer coefficient between cover and sky (W/m2°C) Ht = Global solar radiation at tilt (W/m 2) K = Thermal conductivity of insulation (W/m°C) L = Thickness of insulation (m) U L = Overall heat loss coefficient (W/m2°C) Ub = Bottom heat loss coefficient of collector (W/m2°C) U t = Top heat loss coefficient of collector (W/m2°C) Tp = Temperature of plate (°C) T,n = Temperature at inlet of system (°C) T O = Temperature of outlet of system (°C) T a = Ambient temperature (°C) ct = Absorptivity of black paint z = Transmittivity of cover E = Emissivity of absorber plate 6 = Control function, value 0 or 1.

The inverse dynamic model of a multibody system is used for many applications in engineering. A very interesting property of these models is that they can be written in a linear form with respect to the inertial parameters of the solids, provided that some conditions hold. This property is very helpful in fields like dynamic parameter identification, design optimization, model reduction and others.

Simulation of wear evolution during abrasive processes is a very difficult task compared to that of machining processes because of the degree of randomness of geometry and disposition of cutting teeth. Superfinishing is a specific case of abrasive process, where the temperature is not consistently involved. A wear model and a numerical method of simulating the process, involving data collected in a testing experiment that resulted in determining an abrasive function, are presented for the specific case of the superfinishing the ball track of an inner bearing ring. Four types of stones were tested while abrading a cylindrical sample of M50 steel, using a high fluidity oil as a lubricant. The abrasive function characteristic to the materials involved in the process was determined. The wear volume of stone, that resulted in simulation and superfinishing experiments, is compared for three of the stones, and a good agreement between them was obtained, endorsing the viability of the simulation. The stability of the results with mesh refinement was analyzed. Three other output parameters of the simulated process and their dependency on the stone type were discussed.