مجله بین المللی محاسبات و مدل سازی ریاضی
سال چهارم شماره 3 (Summer 2014)

This paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. The aquifer is in contact with a constant water level at one end. The other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. Moreover, the aquifer is replenished by a constant downward recharge. The linearized Boussinesq equation is solved analytically using Laplace transform technique to obtain the closed form expression for hydraulic head and flow rate at the stream-aquifer interface. The expressions derived in this study can also handle the cases of upward sloping, horizontal bed conditions and sudden rise in stream water. The validity of linearization method adopted in this study is examined by solving the nonlinear equation by an explicit numerical scheme. Response of an aquifer to the variations in bed slope, recharge rate and rise rate of the stream water is illustrated with a numerical example. Sensitivity of the flow rate with various parameters is analyzed.

The methods of assessing the individuals’ performance usually applied in practice are based on principles of the bivalent logic (yes-no). However, fuzzy logic, due to its nature of including multiple values, offers a wider and richer field of resources for this purpose. In this paper we use principles of fuzzy logic in developing a new method for assessing the performance of groups of individuals participating in any human activity. For this, we represent each of the groups under assessment as a fuzzy subset of a set U of linguistic labels characterizing their members’ performance and we use the centre of gravity defuzzification technique in converting the fuzzy data collected from the corresponding activity to a crisp number. The resulting structure provides a weighted assessment, in which the higher is an individual’s performance the more its “contribution” to the corresponding group’s performance. Thus, in contrast to the mean of the scores (i.e. numerical values of the performance) of all the group’s members, which is connected to the mean group’s performance, our method is connected somehow to the group’s quality performance. Two real applications are also presented, related to the bridge players’ performance and the students’ problem solving skills respectively, illustrating the importance of our assessment method in practice.

This paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. In fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. Thepower output of each hydro unit varies with the rate of water dischargedthrough the turbines. It is assumed that hydro plants alone are not sufficientto supply all the load demands during the scheduling horizon. In hydroscheduling, the specified total volume of water should be optimally dischargedthroughout the scheduling period. A novel mathematical approach has been developedto determine the optimal hydro and thermal power generation so as to minimizethe fuel cost of thermal units. The performance of the proposed method isdemonstrated with three test systems. The test results reveal that the proposedmethod provides optimal solution which satisfies the various system constraintsof fixed head hydrothermal scheduling problem.

A gas permeation model (Coupling Model) has been developed which has the flexibility to be used for different membrane module configurations. The aim of this work is to predict the performance of a single stage gas separation process using membranes and provide a comprehensive description of process parameters like flow rates, composition, stage cut and stream pressure. The significant feature of this work is the development of computational technique which combines the counter-current flow mode with co-current flow mode. In contrary to other counter-current models (reported in literature), the model reported in this work (Coupling Model) does not require initial conditions to start and also it is independent of any adjustment technique like shooting method. This model is based on real membrane operation and works by the coupling of co-current and counter-current methods. After each iteration, output values of co-current mode become the input values for counter-current mode. This model has the capability to take upto nine components, whereas model reported in literature can handle 4-5 components in a gas mixture to be separated. The results obtained are validated with the published data and will be discussed to elaborate the operation of a gas separation membrane.

In this paper, the effect of applied electric field on the damage due to partial discharges activity into the surroundings dielectrics of a narrow channel encapsulated within the volume of a dielectric material is evaluated using a kinetic model based on Particle in Cell - Monte Carlo Collision (PIC-MCC) model. After application of an electric field across a dielectric material which contains a narrow channel, repeated ionization process starts in the gaseous medium of narrow channel. Charged particles, especially electrons, gain energy from the electric field across narrow channel and cause damage into dielectric surfaces of narrow channel on impact. The dependence of the electron energy distribution function (EEDF) on the applied electric field is studied. It is seen that, during PD activity within narrow channel, the damage to the surrounding dielectrics and consequently the surface conductivity increases. These estimations are performed based on the number of C-H bond-scissions produced by the impacting electrons of a single PD pulse. Based on this technique, the consequent damage into the solid dielectric and the time required to increase surface conductivity is computed. The formation of acid molecules due to interaction of PD pulse with polymer surface in presence of air and humidity causes changes in the surface conductivity of the surrounding dielectrics of the narrow channels.

A sigmoid function is necessary for creation a chaotic neural network (CNN). In this paper, a new function for CNN is proposed that it can increase the speed of convergence. In the proposed method, we use a novel signal for controlling chaos. Both the theory analysis and computer simulation results show that the performance of CNN can be improved remarkably by using our method. By means of this control method, the outputs of the controlled CNN converge to the stored patterns and they are dependent on the initial patterns. We observed that the controlled CNN can distinguish two initial patterns even if they are slightly different. These characteristics imply that the controlled CNN can be used for pattern recognition.

It is attempted to extend a two-step without memory method to it''s with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative step applying only information from the current and the previous iteration, defining a with memory class.Although these improvements are achieved without any additional function evaluations, the $ R $-order of convergence are boosted from 4 to 5.24 and 6, respectively, and it is demonstrated that the proposed with memory classes provide a very high computational efficiency.Numerical examples are put forward and the performances are compared with the basic two-step without memory methods.

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. Numerical results are given to illustrate the efficiency of the proposed method which shows that our method can be applied for large values of N. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.