Search results for: Differential Calculus

Authors: Sherif. S. Nafee, Ameer. K. Al-Ramady, Salem. A. Shaheen

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The analytical prediction of the decay heat results from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team from King Abdulaziz University (KAU), Saudi Arabia, and supervised by Argonne National Laboratory (ANL) has collaborated with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic comparisons with the measurements reported by the University of Tokyo, in YAYOI reactor.

Keywords: Decay heat, fast neutron fission, and Numerical Solution of Linear Differential Equations.

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Authors: Viet-Hoang Vu, Nhan Le-Thanh

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Recently the usefulness of Concept Abduction, a novel non-monotonic inference service for Description Logics (DLs), has been argued in the context of ontology-based applications such as semantic matchmaking and resource retrieval. Based on tableau calculus, a method has been proposed to realize this reasoning task in ALN, a description logic that supports simple cardinality restrictions as well as other basic constructors. However, in many ontology-based systems, the representation of ontology would require expressive formalisms for capturing domain-specific constraints, this language is not sufficient. In order to increase the applicability of the abductive reasoning method in such contexts, we would like to present in the scope of this paper an extension of the tableaux-based algorithm for dealing with concepts represented inALCQ, the description logic that extends ALN with full concept negation and quantified number restrictions.

Keywords: Abductive reasoning, description logics, semantic matchmaking, non-monotonic inference, tableaux-based method.

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Authors: T. Ganesan, M. S. Aris, I. Elamvazuthi, Momen Kamal Tageldeen

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Terms set in power purchase agreements (PPA) challenge power utility companies in balancing between the returns (from maximizing power production) and securing long term supply contracts at capped production. The production limitation set in the PPA has driven efforts to maximize profits through efficient and economic power production. In this paper, a combined industrial-scale gas turbine (GT) - absorption chiller (AC) system is considered to cool the GT air intake for reducing the plant’s heat rate (HR). This GT-AC system is optimized while considering power output limitations imposed by the PPA. In addition, the proposed formulation accounts for uncertainties in the ambient temperature using Type-2 fuzzy programming. Using the enhanced chaotic differential evolution (CEDE), the Pareto frontier was constructed and the optimization results are analyzed in detail.

Keywords: Absorption chillers, turbine inlet air cooling, power purchase agreement, multiobjective optimization, type-2 fuzzy programming, chaotic differential evolution.

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Authors: Adriana Souza M. Batista, Cláubia Pereira, Luiz O. Faria

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The irradiation of polymeric materials has received much attention because it can produce diverse changes in chemical structure and physical properties. Thus, studying the chemical and structural changes of polymers is important in practice to achieve optimal conditions for the modification of polymers. The effect of gamma irradiation on the crystalline structure of poly(vinylidene fluoride) (PVDF) has been investigated using differential scanning calorimetry (DSC) and X-ray diffraction techniques (XRD). Gamma irradiation was carried out in atmosphere air with doses between 100 kGy at 3,000 kGy with a Co-60 source. In the melting thermogram of the samples irradiated can be seen a bimodal melting endotherm is detected with two melting temperature. The lower melting temperature is attributed to melting of crystals originally present and the higher melting peak due to melting of crystals reorganized upon heat treatment. These results are consistent with those obtained by XRD technique showing increasing crystallinity with increasing irradiation dose, although the melting latent heat is decreasing.

Keywords: Differential scanning calorimetry, gamma irradiation, PVDF, X-ray diffraction technique.

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Authors: Saleh A. Al-Jufout

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This paper presents a procedure of forming the mathematical model of radial electric power systems for simulation of both transient and steady-state conditions. The research idea has been based on nodal voltages technique and on differentiation of Kirchhoff's current law (KCL) applied to each non-reference node of the radial system, the result of which the nodal voltages has been calculated by solving a system of algebraic equations. Currents of the electric power system components have been determined by solving their respective differential equations. Transforming the three-phase coordinate system into Cartesian coordinate system in the model decreased the overall number of equations by one third. The use of Cartesian coordinate system does not ignore the DC component during transient conditions, but restricts the model's implementation for symmetrical modes of operation only. An example of the input data for a four-bus radial electric power system has been calculated.

Keywords: Mathematical Modelling, Radial Power System, Steady-State, Transients

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Authors: Ramya Dorai, M. Rajaram

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A Mobile Adhoc Network (MANET) is a collection of mobile nodes that communicate with each other with wireless links and without pre-existing communication infrastructure. Routing is an important issue which impacts network performance. As MANETs lack central administration and prior organization, their security concerns are different from those of conventional networks. Wireless links make MANETs susceptible to attacks. This study proposes a new trust mechanism to mitigate wormhole attack in MANETs. Different optimization techniques find available optimal path from source to destination. This study extends trust and reputation to an improved link quality and channel utilization based Adhoc Ondemand Multipath Distance Vector (AOMDV). Differential Evolution (DE) is used for optimization.

Keywords: Mobile Adhoc Network (MANET), Adhoc Ondemand Multi-Path Distance Vector (AOMDV), Trust and Reputation, Differential Evolution (DE), Link Quality, Channel Utilization.

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Authors: M. P. Nanda Kumar, K. Dheeraj

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The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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Authors: Tulika Bhattacharjee, A. K.Chakraborty

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Due to the deregulation of the Electric Supply Industry and the resulting emergence of electricity market, the volumes of power purchases are on the rise all over the world. In a bid to meet the customer-s demand in a reliable and yet economic manner, utilities purchase power from the energy market over and above its own production. This paper aims at developing an optimal power purchase model with two objectives viz economy and environment ,taking various functional operating constraints such as branch flow limits, load bus voltage magnitudes limits, unit capacity constraints and security constraints into consideration.The price of purchased power being an uncertain variable is modeled using fuzzy logic. DEMO (Differential Evolution For Multi-objective Optimization) is used to obtain the pareto-optimal solution set of the multi-objective problem formulated. Fuzzy set theory has been employed to extract the best compromise non-dominated solution. The results obtained on IEEE 30 bus system are presented and compared with that of NSGAII.

Keywords: Deregulation, Differential Evolution, Multi objective Optimization, Pareto Optimal Set, Optimal Power Flow

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Authors: Hanan Rizk

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Heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques, and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed the proportional–integral–derivative (PID) controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: H. Dardour, S. Mazouz, A. Bellagi

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For many industrial applications plate heat exchangers are demonstrating a large superiority over the other types of heat exchangers. The efficiency of such a device depends on numerous factors the effect of which needs to be analysed and accurately evaluated. In this paper we present a theoretical analysis of a cocurrent plate heat exchanger and the results of its numerical simulation. Knowing the hot and the cold fluid streams inlet temperatures, the respective heat capacities mCp and the value of the overall heat transfer coefficient, a 1-D mathematical model based on the steady flow energy balance for a differential length of the device is developed resulting in a set of N first order differential equations with boundary conditions where N is the number of channels.For specific heat exchanger geometry and operational parameters, the problem is numerically solved using the shooting method. The simulation allows the prediction of the temperature map in the heat exchanger and hence, the evaluation of its performances. A parametric analysis is performed to evaluate the influence of the R-parameter on the e-NTU values. For practical purposes effectiveness-NTU graphs are elaborated for specific heat exchanger geometry and different operating conditions.

Keywords: Plate heat exchanger, thermal performance, NTU, effectiveness.

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Authors: S. S. Nafee, A. K. Al-Ramady, S. A. Shaheen

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The mixed oxide nuclear fuel (MOX) of U and Pu contains several percent of fission products and minor actinides, such as neptunium, americium and curium. It is important to determine accurately the decay heat from Curium isotopes as they contribute significantly in the MOX fuel. This heat generation can cause samples to melt very quickly if excessive quantities of curium are present. In the present paper, we introduce a new approach that can predict the decay heat from curium isotopes. This work is a part of the project funded by King Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, and take place in King Abdulaziz University (KAU), Saudi Arabia. The approach is based on the numerical solution of coupled linear differential equations that describe decays and buildups of many nuclides to calculate the decay heat produced after shutdown. Results show the consistency and reliability of the approach applied.

Keywords: Decay heat, Mixed oxide nuclear fuel, Numerical Solution of Linear Differential Equations, and Curium isotopes

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Authors: L. Vítek

Abstract:

The Czech Republic has over the past decade carried out two waves of tax and benefit reforms. The first one took place in 2005–2006 during the left-wing government and the second one has been carried out in 2008 by the right-wing government. Using EUSILC data for selected types of households, the paper assesses changes in the distribution of gross incomes and effects of the changes in taxes and benefits on the distribution of incomes after taxes and a provision of social benefits. The analysis is carried out on four types of households with and without children. The analysis is performed using Lorenz curves and Gini coefficients. The results show that the tax system changes the distribution of incomes less significantly than benefits. The 2006 reform reduced the differential between the Gini coefficient for the gross income and the Gini coefficient after taxes and benefits for households with active parents and one child. Reform in 2008 supported families with children and an reduced the differential between the gross income and income after taxes and benefits for different types of families.

Keywords: Czech Republic, redistribution, tax reforms.

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Authors: Feras Al-Obeidat, Nabil Belacel, Juan A. Carretero, Prabhat Mahanti,

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In this paper, a new learning algorithm based on a hybrid metaheuristic integrating Differential Evolution (DE) and Reduced Variable Neighborhood Search (RVNS) is introduced to train the classification method PROAFTN. To apply PROAFTN, values of several parameters need to be determined prior to classification. These parameters include boundaries of intervals and relative weights for each attribute. Based on these requirements, the hybrid approach, named DEPRO-RVNS, is presented in this study. In some cases, the major problem when applying DE to some classification problems was the premature convergence of some individuals to local optima. To eliminate this shortcoming and to improve the exploration and exploitation capabilities of DE, such individuals were set to iteratively re-explored using RVNS. Based on the generated results on both training and testing data, it is shown that the performance of PROAFTN is significantly improved. Furthermore, the experimental study shows that DEPRO-RVNS outperforms well-known machine learning classifiers in a variety of problems.

Keywords: Knowledge Discovery, Differential Evolution, Reduced Variable Neighborhood Search, Multiple criteria classification, PROAFTN, Supervised Learning.

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Authors: Thanh Nguyen, Andrei Doncescu, Pierre Siegel

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Classification is an important data mining technique and could be used as data filtering in artificial intelligence. The broad application of classification for all kind of data leads to be used in nearly every field of our modern life. Classification helps us to put together different items according to the feature items decided as interesting and useful. In this paper, we compare two classification methods Naïve Bayes and ADTree use to detect spam e-mail. This choice is motivated by the fact that Naive Bayes algorithm is based on probability calculus while ADTree algorithm is based on decision tree. The parameter settings of the above classifiers use the maximization of true positive rate and minimization of false positive rate. The experiment results present classification accuracy and cost analysis in view of optimal classifier choice for Spam Detection. It is point out the number of attributes to obtain a tradeoff between number of them and the classification accuracy.

Keywords: Classification, data mining, spam filtering, naive Bayes, decision tree.

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Authors: G.Ashwini, A.T.Eswara

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This paper examines the forced convection flow of incompressible, electrically conducting viscous fluid past a sharp wedge in the presence of heat generation or absorption with an applied magnetic field. The system of partial differential equations governing Falkner - Skan wedge flow and heat transfer is first transformed into a system of ordinary differential equations using similarity transformations which is later solved using an implicit finite - difference scheme, along with quasilinearization technique. Numerical computations are performed for air (Pr = 0.7) and displayed graphically to illustrate the influence of pertinent physical parameters on local skin friction and heat transfer coefficients and, also on, velocity and temperature fields. It is observed that the magnetic field increases both the coefficients of skin friction and heat transfer. The effect of heat generation or absorption is found to be very significant on heat transfer, but its effect on the skin friction is negligible. Indeed, the occurrence of overshoot is noticed in the temperature profiles during heat generation process, causing the reversal in the direction of heat transfer.

Keywords: Heat generation / absorption, MHD Falkner- Skan flow, skin friction and heat transfer

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Authors: T. Cornelius

Abstract:

Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie-connectors in cavity walls was developed. The method takes into account constraint conditions limiting the free length of the wall tie, and the instability in case of pure compression which gives an optimal load bearing capacity. The model is illustrated with examples from praxis.

Keywords: Masonry, tie connectors, cavity wall, instability, differential movements, combined bending and compression.

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Authors: A.S.N.Murti, D.R.V.S.R.K. Sastry, P.K. Kameswaran, T. Poorna Kantha

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In this paper, the effects of radiation, chemical reaction and double dispersion on mixed convection heat and mass transfer along a semi vertical plate are considered. The plate is embedded in a Newtonian fluid saturated non - Darcy (Forchheimer flow model) porous medium. The Forchheimer extension and first order chemical reaction are considered in the flow equations. The governing sets of partial differential equations are nondimensionalized and reduced to a set of ordinary differential equations which are then solved numerically by Fourth order Runge– Kutta method. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) against various parameters are presented in graphs. The obtained results are checked against previously published work for special cases of the problem and are found to be in good agreement.

Keywords: Radiation, Chemical reaction, Double dispersion, Mixed convection, Heat and Mass transfer

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Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park

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In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.

Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: Heat Transfer, Nanofluid, Shrinking Surface, Stability Analysis, Three-Dimensional Flow.

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Authors: T. T. Manikandan, Rajeev Sukumaran

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Coral Reefs are very important for the majority of marine ecosystems. But, such vital species are under major threat due to the factors such as ocean acidification, overfishing, and coral bleaching. To conserve the coral reefs, reef restoration activities are carried out across the world. After reef restoration, various parameters have to be monitored in order to ensure the overall effectiveness of the reef restoration. Underwater Wireless Sensor Network (UWSN) based  monitoring is widely adopted for such long monitoring activities. Since monitoring of coral reef restoration activities is time sensitive, the QoS guarantee offered by the network with respect to delay is vital. So this research focuses on the analytical modeling of network layer delay using Stochastic Network Calculus (SNC). The core focus of the proposed model will be on the analysis of stochastic dependencies between the network flow and deriving the stochastic delay bounds for the flows that traverse in tandem in UWSNs. The derived analytical bounds are evaluated for their effectiveness using discrete event simulations.

Keywords: Coral Reef Restoration, SNC, SFA, PMOO, Tandem of Queues, Delay Bound.

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Authors: Amadi Ugwulo Chinyere, Lewis D. Gbarayorks, Emem N. H. Inamete

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In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.

Keywords: DC pension fund, modified constant elasticity of variance, optimal investment strategies, voluntary contribution, administrative charges.

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Authors: Kalthoum Riahi, Max T. Rietberg, Javier Perez y Perez, Corné Dijkstra, Bennie ten Haken, Lejla Alic

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Magnetic nanoparticles (MNPs) are widely used to facilitate magnetic particle imaging (MPI) which has the potential to become the leading diagnostic instrument for biomedical imaging. This comparative study assesses the effects of changing iron content and excitation frequency on point-spread function (PSF) representing the effect of magnetization reversal. PSF is quantified by features of interest for MPI: i.e., drive field amplitude and full-width-at-half-maximum (FWHM). A superparamagnetic quantifier (SPaQ) is used to assess differential magnetic susceptibility of two commercially available MNPs: Synomag®-D50 and Synomag®-D70. For both MNPs, the signal output depends on increase in drive field frequency and amount of iron-oxide, which might be hampering the sensitivity of MPI systems that perform on higher frequencies. Nevertheless, there is a clear potential of Synomag®-D for a stable MPI resolution, especially in case of 70 nm version, that is independent of either drive field frequency or amount of iron-oxide.

Keywords: Magnetic nanoparticles, MNPs, Differential magnetic susceptibility, DMS, Magnetic particle imaging, MPI, magnetic relaxation, Synomag®-D.

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Authors: Beena Sethi

Abstract:

This work involves the degradation of plastic waste in the presence of three different nanocatalysts. A thin film of LLDPE was formed with all three nanocatalysts separately in the solvent. Thermo Gravimetric Analysis (TGA) and Differential Scanning Calorimetric (DSC) analysis of polymers suggest that the presence of these catalysts lowers the degradation temperature and the change mechanism of degradation. Gas chromatographic analysis was carried out for two films. In gas chromatography (GC) analysis, it was found that degradation of pure polymer produces only 32% C3/C4 hydrocarbons and 67.6% C5/C9 hydrocarbons. In the presence of these catalysts, more than 80% of polymer by weight was converted into either liquid or gaseous hydrocarbons. Change in the mechanism of degradation of polymer was observed therefore more C3/C4 hydrocarbons along with valuable feedstock are produced. Adjustment of dose of nanocatalyst, use of nano-admixtures and recycling of catalyst can make this catalytic feedstock recycling method a good tool to get sustainable environment. The obtained products can be utilized as fuel or can be transformed into other useful products. In accordance with the principles of sustainable development, chemical recycling i.e. tertiary recycling of polymers along with the reuse (zero order recycling) of plastics can be the most appropriate and promising method in this direction. The tertiary recycling is attracting much attention from the viewpoint of the energy resource.

Keywords: Degradation, differential scanning calorimetry, feedstock recycling, gas chromatography, thermogravimetric analysis. DSC.

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Authors: A.K.Balirsingh, S.C.Swain, S. Panda

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Recently, Genetic Algorithms (GA) and Differential Evolution (DE) algorithm technique have attracted considerable attention among various modern heuristic optimization techniques. Since the two approaches are supposed to find a solution to a given objective function but employ different strategies and computational effort, it is appropriate to compare their performance. This paper presents the application and performance comparison of DE and GA optimization techniques, for flexible ac transmission system (FACTS)-based controller design. The design objective is to enhance the power system stability. The design problem of the FACTS-based controller is formulated as an optimization problem and both the PSO and GA optimization techniques are employed to search for optimal controller parameters. The performance of both optimization techniques has been compared. Further, the optimized controllers are tested on a weekly connected power system subjected to different disturbances, and their performance is compared with the conventional power system stabilizer (CPSS). The eigenvalue analysis and non-linear simulation results are presented and compared to show the effectiveness of both the techniques in designing a FACTS-based controller, to enhance power system stability.

Keywords: Differential Evolution, Flexible AC TransmissionSystems (FACTS), Genetic Algorithm, Low Frequency Oscillations, Single-machine Infinite Bus Power System.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin method.

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

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The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Vikas Tewari, K.R. Pardasani

Abstract:

Calcium is very important for communication among the neurons. It is vital in a number of cell processes such as secretion, cell movement, cell differentiation. To reduce the system of reactiondiffusion equations of [Ca2+] into a single equation, two theories have been proposed one is excess buffer approximation (EBA) other is rapid buffer approximation (RBA). The RBA is more realistic than the EBA as it considers both the mobile and stationary endogenous buffers. It is valid near the mouth of the channel. In this work we have studied the effects of different types of buffers on calcium diffusion under RBA. The novel thing studied is the effect of sodium ions on calcium diffusion. The model has been made realistic by considering factors such as variable [Ca2+], [Na+] sources, sodium-calcium exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The proposed mathematical leads to a system of partial differential equations which has been solved numerically to study the relationships between different parameters such as buffer concentration, buffer disassociation rate, calcium permeability. We have used Forward Time Centred Space (FTCS) approach to solve the system of partial differential equations.

Keywords: rapid buffer approximation, sodium-calcium exchangeprotein, Sarcolemmal Calcium ATPase pump, buffer disassociationrate, forward time centred space.

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