Search results for: numerical validation

Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: J. Mohammadpour, G. E. Lau, S. Cheng, A. Lee

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Numerical study was conducted using two synthetic jet actuators attached underneath a micro-channel. By fixing the oscillating frequency and diaphragm amplitude, the effects on the heat transfer within the micro-channel were investigated with two synthetic jets being in-phase and 180° out-of-phase at different orifice spacing. There was a significant benefit identified with two jets being 180° out-of-phase with each other at the orifice spacing of 2 mm. By having this configuration, there was a distinct pattern of vortex forming which disrupts the main channel flow as well as promoting thermal mixing at high velocity within the channel. Therefore, this configuration achieved higher cooling performance compared to the other cases studied in terms of the reduction in the maximum temperature and cooling uniformity in the silicon wafer.

Keywords: Synthetic jets, microchannel, electronic cooling, computational fluid dynamics.

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Authors: W. R. Li, J. K. Xia, R. Q. Peng, Z. Y. Guo, L. Jiang

Abstract:

According to 3D magnetic circuit of the transverse flux PM linear machine, distribution law is presented, and analytical expression of axial end flux leakage is derived using numerical method. Maxwell stress tensor is used to solve detent force of mover. A 3D finite element model of the transverse flux PM machine is built to analyze the flux distribution and detent force. Experimental results of the prototype verified the validity of axial end flux leakage and detent force theoretical derivation, the research on axial end flux leakage and detent force provides a valuable reference to other types of linear machine.

Keywords: Transverse flux PM linear machine, flux distribution, axial end flux leakage, detent force.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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Authors: Abeer Samy, Oliver C. Saavedra Valeriano, Abdelazim Negm

Abstract:

The Blue Nile Basin is the most important tributary of the Nile River. Egypt and Sudan are almost dependent on water originated from the Blue Nile. This multi-dependency creates conflicts among the three countries Egypt, Sudan, and Ethiopia making the management of these conflicts as an international issue. Good assessment of the water resources of the Blue Nile is an important to help in managing such conflicts. Hydrological models are good tool for such assessment. This paper presents a critical review of the nature and variability of the climate and hydrology of the Blue Nile Basin as a first step of using hydrological modeling to assess the water resources of the Blue Nile. Many several attempts are done to develop basin-scale hydrological modeling on the Blue Nile. Lumped and semi distributed models used averages of meteorological inputs and watershed characteristics in hydrological simulation, to analyze runoff for flood control and water resource management. Distributed models include the temporal and spatial variability of catchment conditions and meteorological inputs to allow better representation of the hydrological process. The main challenge of all used models was to assess the water resources of the basin is the shortage of the data needed for models calibration and validation. It is recommended to use distributed model for their higher accuracy to cope with the great variability and complexity of the Blue Nile basin and to collect sufficient data to have more sophisticated and accurate hydrological modeling.

Keywords: Blue Nile Basin, Climate Change, Hydrological Modeling, Watershed.

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Authors: Victor Bodell, Lukas Ekstrom, Somayeh Aghanavesi

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Fuel consumption (FC) is one of the key factors in determining expenses of operating a heavy-duty vehicle. A customer may therefore request an estimate of the FC of a desired vehicle. The modular design of heavy-duty vehicles allows their construction by specifying the building blocks, such as gear box, engine and chassis type. If the combination of building blocks is unprecedented, it is unfeasible to measure the FC, since this would first r equire the construction of the vehicle. This paper proposes a machine learning approach to predict FC. This study uses around 40,000 vehicles specific and o perational e nvironmental c onditions i nformation, such as road slopes and driver profiles. A ll v ehicles h ave d iesel engines and a mileage of more than 20,000 km. The data is used to investigate the accuracy of machine learning algorithms Linear regression (LR), K-nearest neighbor (KNN) and Artificial n eural n etworks (ANN) in predicting fuel consumption for heavy-duty vehicles. Performance of the algorithms is evaluated by reporting the prediction error on both simulated data and operational measurements. The performance of the algorithms is compared using nested cross-validation and statistical hypothesis testing. The statistical evaluation procedure finds that ANNs have the lowest prediction error compared to LR and KNN in estimating fuel consumption on both simulated and operational data. The models have a mean relative prediction error of 0.3% on simulated data, and 4.2% on operational data.

Keywords: Artificial neural networks, fuel consumption, machine learning, regression, statistical tests.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: Explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula.

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Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

Abstract:

This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: Expert evaluations, investment decision making, OWA operator, possibility uncertainty.

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Authors: P. Pongsumpun

Abstract:

The Swine flu outbreak in humans is due to a new strain of influenza A virus subtype H1N1 that derives in part from human influenza, avian influenza, and two separated strains of swine influenza. It can be transmitted from human to human. A mathematical model for the transmission of Swine flu is developed in which the human populations are divided into two classes, the risk and non-risk human classes. Each class is separated into susceptible, exposed, infectious, quarantine and recovered sub-classes. In this paper, we formulate the dynamical model of Swine flu transmission and the repetitive contacts between the people are also considered. We analyze the behavior for the transmission of this disease. The Threshold condition of this disease is found and numerical results are shown to confirm our theoretical predictions.

Keywords: Mathematical model, Steady state, Swine flu, threshold condition.

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Authors: R. Borghol, T. Aguili

Abstract:

In this paper, we investigate theoretically the waves propagation in a lossless double-negative grounded slab (DNG). This study is performed by the Transverse Resonance Method (TRM). The proper or improper nature of real and complex modes is observed. They are highly dependent on metamaterial parameters, i.e. ɛ_r-negative, µ_r-negative, or both. Numerical results provided that only the proper complex modes (i.e., leaky modes) exist in DNG slab, and only the improper complex modes exist in single-negative grounded slab.

Keywords: Double-negative grounded slab, real and complex modes, single-negative grounded slab, transverse resonance method.

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Authors: C. Slim

Abstract:

Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary non-seasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Keywords: Stationarity, unit root tests, economic time series.

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Authors: A. Omran, G. El-Bayiumi, M. Bayoumi, A. Kassem

Abstract:

Applicability of tuning the controller gains for Stewart manipulator using genetic algorithm as an efficient search technique is investigated. Kinematics and dynamics models were introduced in detail for simulation purpose. A PD task space control scheme was used. For demonstrating technique feasibility, a Stewart manipulator numerical-model was built. A genetic algorithm was then employed to search for optimal controller gains. The controller was tested onsite a generic circular mission. The simulation results show that the technique is highly convergent with superior performance operating for different payloads.

Keywords: Stewart kinematics, Stewart dynamics, task space control, genetic algorithm.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

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In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: E. Kaygan, A. Gatto

Abstract:

A numerical study of a design concept for actively controlling wing twist is described in this paper. The concept consists of morphing elements which were designed to provide a rigid and seamless skin while maintaining structural rigidity. The wing structure is first modeled in CATIA V5 then imported into ANSYS for structural analysis. Athena Vortex Lattice method (AVL) is used to estimate aerodynamic response as well as aerodynamic loads of morphing wings, afterwards a structural optimization performed via ANSYS Static. Overall, the results presented in this paper show that the concept provides efficient wing twist while preserving an aerodynamically smooth and compliant surface. Sufficient structural rigidity in bending is also obtained. This concept is suggested as a possible alternative for morphing skin applications. 

Keywords: Aircraft, morphing, skin, twist.

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Authors: L. Dzierzbicka-Głowacka, M. Janecki

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Seasonal variability of nutrients concentration in the Baltic Sea using the 3D ecosystem numerical model 3D-CEMBS has been investigated. Additionally this study shows horizontal and vertical distribution of nutrients in the Baltic Sea. Model domain is an extended Baltic Sea area divided into 600x640 horizontal grid cells. Aside from standard hydrodynamic parameters 3D-CEMBS produces modeled ecological variables such as: three types of phytoplankton, two detrital classes, dissolved oxygen and the nutrients (nitrate, ammonium, phosphate and silicate). The presented model allows prediction of parameters that describe distribution of nutrients concentration and phytoplankton biomass. 3D-CEMBS can be used to study the effect of different hydrodynamic and biogeochemical processes on distributions of these variables in a larger scale.

Keywords: ecosystem model, nutrients, Baltic Sea

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Authors: Sule Yucelbas, Gulay Tezel, Cuneyt Yucelbas, Seral Ozsen

Abstract:

In this study, it was tried to identify some heart rhythm disorders by electrocardiography (ECG) data that is taken from MIT-BIH arrhythmia database by subtracting the required features, presenting to artificial neural networks (ANN), artificial immune systems (AIS), artificial neural network based on artificial immune system (AIS-ANN) and particle swarm optimization based artificial neural network (PSO-NN) classifier systems. The main purpose of this study is to evaluate the performance of hybrid AIS-ANN and PSO-ANN classifiers with regard to the ANN and AIS. For this purpose, the normal sinus rhythm (NSR), atrial premature contraction (APC), sinus arrhythmia (SA), ventricular trigeminy (VTI), ventricular tachycardia (VTK) and atrial fibrillation (AF) data for each of the RR intervals were found. Then these data in the form of pairs (NSR-APC, NSR-SA, NSR-VTI, NSR-VTK and NSR-AF) is created by combining discrete wavelet transform which is applied to each of these two groups of data and two different data sets with 9 and 27 features were obtained from each of them after data reduction. Afterwards, the data randomly was firstly mixed within themselves, and then 4-fold cross validation method was applied to create the training and testing data. The training and testing accuracy rates and training time are compared with each other.

As a result, performances of the hybrid classification systems, AIS-ANN and PSO-ANN were seen to be close to the performance of the ANN system. Also, the results of the hybrid systems were much better than AIS, too. However, ANN had much shorter period of training time than other systems. In terms of training times, ANN was followed by PSO-ANN, AIS-ANN and AIS systems respectively. Also, the features that extracted from the data affected the classification results significantly.

Keywords: AIS, ANN, ECG, hybrid classifiers, PSO.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Exponential stability, LMI approach, Time-varying delays.

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Authors: Murat Ayyıldız, Oya Kalıpsız, Sırma Yavuz

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Software project effort estimation is frequently seen as complex and expensive for individual software engineers. Software production is in a crisis. It suffers from excessive costs. Software production is often out of control. It has been suggested that software production is out of control because we do not measure. You cannot control what you cannot measure. During last decade, a number of researches on cost estimation have been conducted. The metric-set selection has a vital role in software cost estimation studies; its importance has been ignored especially in neural network based studies. In this study we have explored the reasons of those disappointing results and implemented different neural network models using augmented new metrics. The results obtained are compared with previous studies using traditional metrics. To be able to make comparisons, two types of data have been used. The first part of the data is taken from the Constructive Cost Model (COCOMO'81) which is commonly used in previous studies and the second part is collected according to new metrics in a leading international company in Turkey. The accuracy of the selected metrics and the data samples are verified using statistical techniques. The model presented here is based on Multi-Layer Perceptron (MLP). Another difficulty associated with the cost estimation studies is the fact that the data collection requires time and care. To make a more thorough use of the samples collected, k-fold, cross validation method is also implemented. It is concluded that, as long as an accurate and quantifiable set of metrics are defined and measured correctly, neural networks can be applied in software cost estimation studies with success

Keywords: Software Metrics, Software Cost Estimation, Neural Network.

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Authors: Wookuen Shin, Gregory R. Miller, Pedro Arduino, Peter Mackenzie-Helnwein

Abstract:

This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.

Keywords: Numerical Analysis, Material Point Method, Large Deformations, Moving Boundaries.

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Authors: Adel A. Ghoneim

Abstract:

In most existing buildings in hot climate, cooling loads lead to high primary energy consumption and consequently high CO2 emissions. These can be substantially decreased with integrated renewable energy systems. Kuwait is characterized by its dry hot long summer and short warm winter. Kuwait receives annual total radiation more than 5280 MJ/m2 with approximately 3347 h of sunshine. Solar energy systems consist of PV modules and parabolic trough collectors are considered to satisfy electricity consumption, domestic water heating, and cooling loads of an existing building. This paper presents the results of an extensive program of energy conservation and energy generation using integrated photovoltaic (PV) modules and Parabolic Trough Collectors (PTC). The program conducted on an existing institutional building intending to convert it into a Net-Zero Energy Building (NZEB) or near net Zero Energy Building (nNZEB). The program consists of two phases; the first phase is concerned with energy auditing and energy conservation measures at minimum cost and the second phase considers the installation of photovoltaic modules and parabolic trough collectors. The 2-storey building under consideration is the Applied Sciences Department at the College of Technological Studies, Kuwait. Single effect lithium bromide water absorption chillers are implemented to provide air conditioning load to the building. A numerical model is developed to evaluate the performance of parabolic trough collectors in Kuwait climate. Transient simulation program (TRNSYS) is adapted to simulate the performance of different solar system components. In addition, a numerical model is developed to assess the environmental impacts of building integrated renewable energy systems. Results indicate that efficient energy conservation can play an important role in converting the existing buildings into NZEBs as it saves a significant portion of annual energy consumption of the building. The first phase results in an energy conservation of about 28% of the building consumption. In the second phase, the integrated PV completely covers the lighting and equipment loads of the building. On the other hand, parabolic trough collectors of optimum area of 765 m2 can satisfy a significant portion of the cooling load, i.e about73% of the total building cooling load. The annual avoided CO2 emission is evaluated at the optimum conditions to assess the environmental impacts of renewable energy systems. The total annual avoided CO2 emission is about 680 metric ton/year which confirms the environmental impacts of these systems in Kuwait.

Keywords: Building integrated renewable systems, Net-Zero Energy Building, solar fraction, avoided CO2 emission.

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Authors: Tao Zhao, Xin Wang

Abstract:

With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, L. Addar, H. Kebir

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This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems.

Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: Aluminium alloys, plate, crack, failure.

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Authors: Tanuj Kumar, Rakesh Kumar Bajaj

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In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

Keywords: Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

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Authors: Salah Al-Enezi, Rashed Al-Zufairi, Naseer Ahmad

Abstract:

A Thermo-mechanical technique was developed to determine softening point temperature/glass transition temperature (Tg) of polystyrene exposed to high pressures. The design utilizes the ability of carbon dioxide to lower the glass transition temperature of polymers and acts as plasticizer. In this apparatus, the sorption of carbon dioxide to induce softening of polymers as a function of temperature/pressure is performed and the extent of softening is measured in three-point-flexural-bending mode. The polymer strip was placed in the cell in contact with the linear variable differential transformer (LVDT). CO₂ was pumped into the cell from a supply cylinder to reach high pressure. The results clearly showed that full softening point of the samples, accompanied by a large deformation on the polymer strip. The deflection curves are initially relatively flat and then undergo a dramatic increase as the temperature is elevated. It was found that increasing the pressure of CO₂ causes the temperature curves to shift from higher to lower by increment of about 45 K, over the pressure range of 0-120 bars. The obtained experimental Tg values were validated with the values reported in the literature. Finally, it is concluded that the defection model fits consistently to the generated experimental results, which attempts to describe in more detail how the central deflection of a thin polymer strip affected by the CO₂ diffusions in the polymeric samples.

Keywords: Softening, high-pressure, polystyrene, CO2 diffusions.

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Authors: Donepudi Jagadish, Ravi Kumar Puli, K. Madhu Murthy

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A zero dimensional model has been used to investigate the combustion performance of a single cylinder direct injection diesel engine fueled by biofuels with options like supercharging and exhaust gas recirculation. The numerical simulation was performed at constant speed. The indicated pressure, temperature diagrams are plotted and compared for different fuels. The emissions of soot and nitrous oxide are computed with phenomenological models. The experimental work was also carried out with biodiesel (palm stearin methyl ester) diesel blends, ethanol diesel blends to validate simulation results with experimental results, and observed that the present model is successful in predicting the engine performance with biofuels.

Keywords: Biofuels Zero Dimensional Modeling, EnginePerformance, Engine Emissions

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Authors: Reza Nadimi, Fariborz Jolai

Abstract:

This article combines two techniques: data envelopment analysis (DEA) and Factor analysis (FA) to data reduction in decision making units (DMU). Data envelopment analysis (DEA), a popular linear programming technique is useful to rate comparatively operational efficiency of decision making units (DMU) based on their deterministic (not necessarily stochastic) input–output data and factor analysis techniques, have been proposed as data reduction and classification technique, which can be applied in data envelopment analysis (DEA) technique for reduction input – output data. Numerical results reveal that the new approach shows a good consistency in ranking with DEA.

Keywords: Effectiveness, Decision Making, Data EnvelopmentAnalysis, Factor Analysis

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Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

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Heat transfer from flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube which is varied in range of 100 to 300. In these range of Reynolds number flow is considered to be laminar, unsteady, and incompressible. Equations are solved by using finite volume method. Results show that increasing l/D from 1 to 2 has insignificant effect on heat transfer and Nusselt number of flat tube is slightly lower than circular tube. However, thermal-hydraulic performance of flat tube is up to 2.7 times greater than circular tube.

Keywords: Laminar flow, flat tube, convective heat transfer, heat exchanger.

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Authors: T. Tchawe Moukam, N. Ngongang François, D. Thomas, K. Bienvenu, T. -Toko Dénis

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Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.

Keywords: Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.

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Authors: Li-Li Li, Jinghai Feng, Lixin Song

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This paper evaluates the dividend payments for general claim size distributions in the presence of a dividend barrier. The surplus of a company is modeled using the classical risk process perturbed by diffusion, and in addition, it is assumed to accrue interest at a constant rate. After presenting the integro-differential equation with initial conditions that dividend payments satisfies, the paper derives a useful expression of the dividend payments by employing the theory of Volterra equation. Furthermore, the optimal value of dividend barrier is found. Finally, numerical examples illustrate the optimality of optimal dividend barrier and the effects of parameters on dividend payments.

Keywords: Dividend payout, Integro-differential equation, Jumpdiffusion model, Volterra equation

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