Search results for: boundary layer thickness
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2018

Search results for: boundary layer thickness

1028 Comparison of Eurocodes EN310 and EN789 in Determining the Bending Strength and Modulus of Elasticity of Red Seraya Plywood Panel

Authors: S.F. Tsen, M. Zamin Jumaat

Abstract:

The characteristic bending strength (MOR) and mean modulus of elasticity (MOE) of tropical hardwood red seraya (Shorea spp.) plywood were determined using European Standard EN310 and EN789. The thickness of the test specimen was 4.0mm, 7.0mm, 9.0mm, 12.0mm and 15.0mm. The experiment found that the MOR of red seraya plywood in EN310 is about 12% to 20% and 7% to 24% higher than EN789 whereas MOE were about 28% to 41% and 30% to 36% lower than those obtained from EN 789 for test specimens parallel and perpendicular to the grain direction. The linear regression shows that MOR and MOE for EN789 is about 0.8 times less and 1.5 times more than EN310. The experiment also found that the MOR and MOE of EN310 and EN789 also depend on the wood species that used in the experiment.

Keywords: Bending strength, Modulus of elasticity, EN310, EN789

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1027 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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1026 Study of a Fabry-Perot Resonator

Authors: F. Hadjaj, A. Belghachi, A. Halmaoui, M. Belhadj, H. Mazouz

Abstract:

A laser is essentially an optical oscillator consisting of a resonant cavity, an amplifying medium and a pumping source. In semiconductor diode lasers, the cavity is created by the boundary between the cleaved face of the semiconductor crystal and air, and has reflective properties as a result of the differing refractive indices of the two media. For a GaAs-air interface a reflectance of 0.3 is typical and therefore the length of the semiconductor junction forms the resonant cavity. To prevent light being emitted in unwanted directions from the junction, sides perpendicular to the required direction are roughened. The objective of this work is to simulate the optical resonator Fabry-Perot and explore its main characteristics, such as FSR, finesse, linewidth, transmission and so on, that describe the performance of resonator.

Keywords: Fabry-Perot Resonator, laser diode.

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1025 Investigation of Tearing in Hydroforming Process with Analytical Equations and Finite Element Method

Authors: H.Seidi, M.Jalali Azizpour, S.A.Zahedi

Abstract:

Today, Hydroforming technology provides an attractive alternative to conventional matched die forming, especially for cost-sensitive, lower volume production, and for parts with irregular contours. In this study the critical fluid pressures which lead to rupture in the workpiece has been investigated by theoretical and finite element methods. The axisymmetric analysis was developed to investigate the tearing phenomenon in cylindrical Hydroforming Deep Drawing (HDD). By use of obtained equations the effect of anisotropy, drawing ratio, sheet thickness and strain hardening exponent on tearing diagram were investigated.

Keywords: Hydroforming deep drawing, Pressure path, Axisymmetric analysis, Finite element simulation.

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1024 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions

Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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1023 Definition and Implementation of a Simulation Model for the Physical Layer and the Radio Channel in Dedicated Short Range Communication Systems

Authors: Mounir Frikha, Michael Meincke, Semia Barouni

Abstract:

This paper proposes a vehicle-to-vehicle propagation model implemented with SDL. To estimate the channel characteristics for Inter-Vehicle communication, we first define a predicted propagation pathloss between the moving vehicles under three typical scenarios. A Ray-tracing method is used for the simple gamma model performance.

Keywords: Inter-vehicle communication (IVC), propagationmodel, road traffic, road vicinity, pathloss.

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1022 New SUZ-4 Zeolite Membrane from Sol-Gel Technique

Authors: P. Worathanakul, P. Kongkachuichay

Abstract:

A new SUZ-4 zeolite membrane with tetraethlyammonium hydroxide as the template was fabricated on mullite tube via hydrothermal sol-gel synthesis in a rotating autoclave reactor. The suitable synthesis condition was SiO2:Al2O3 ratio of 21.2 for 4 days at 155 °C crystallization under autogenous pressure. The obtained SUZ-4 possessed a high BET surface area of 396.4 m2/g, total pore volume at 2.611 cm3/g, and narrow pore size distribution with 97 nm mean diameter and 760 nm long of needle crystal shape. The SUZ-4 layer obtained from seeding crystallization was thicker than that of without seeds or in situ crystallization.

Keywords: Membrane, seeding, sol-gel, SUZ-4 Zeolite.

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1021 Plasmonic Absorption Enhancement in Au/CdS Nanocomposite

Authors: K. Easawi, M. Nabil, T. Abdallah, S. Negm, H. Talaat

Abstract:

Composite nanostructures of metal core/semiconductor shell (Au/CdS) configuration were prepared using organometalic method. UV-Vis spectra for the Au/CdS colloids show initially two well separated bands, corresponding to surface plasmon of the Au core, and the exciton of CdS shell. The absorption of CdS shell is enhanced, while the Au plasmon band is suppressed as the shell thickness increases. The shell sizes were estimated from the optical spectra using the effective mass approximation model (EMA), and compared to the sizes of the Au core and CdS shell measured by high resolution transmission electron microscope (HRTEM). The changes in the absorption features are discussed in terms of gradual increase in the coupling strength of the Au core surface plasmon and the exciton in the CdS. leading to charge transfer and modification of electron oscillation in Au core.

Keywords: Nanocomposites, Plasmonics.

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1020 Evaluation of Optimal Residence Time in a Hot Rolled Reheating Furnace

Authors: Dong-Eun Lee

Abstract:

To calculate the temperature distribution of the slab in a hot rolled reheating furnace a mathematical model has been developed by considering the thermal radiation in the furnace and transient conduction in the slab. The furnace is modeled as radiating medium with spatially varying temperature. Radiative heat flux within the furnace including the effect of furnace walls, combustion gases, skid beams and buttons is calculated using the FVM and is applied as the boundary condition of the transient conduction equation of the slab. After determining the slab emissivity by comparison between simulation and experimental work, variation of heating characteristics in the slab is investigated in the case of changing furnace temperature with various time and the slab residence time is optimized with this evaluation.

Keywords: Reheating Furnace, Thermal Radiation, ResidenceTime, FVM for Radiation

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1019 Analytical Study and Modeling of Free Vibrations of Functionally Graded Plates Using a Higher Shear Deformation Theory

Authors: A. Meftah, D. Zarga, M. Yahiaoui

Abstract:

In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.

Keywords: FGM plates, Navier method, vibratory behavior.

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1018 The Effects of a Thin Liquid Layer on the Hydrodynamic Machine Rotor

Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

Abstract:

A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.

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1017 Phosphorus Reduction in Plain and Fully Formulated Oils Using Fluorinated Additives

Authors: Gabi N. Nehme

Abstract:

The reduction of phosphorus and sulfur in engine oil are the main topics of this paper. Very reproducible boundary lubrication tests were conducted as part of Design of Experiment software (DOE) to study the behavior of fluorinated catalyst iron fluoride (FeF3), and polutetrafluoroethylene or Teflon (PTFE) in developing environmentally friendly (reduced P and S) anti-wear additives for future engine oil formulations. Multi-component Chevron fully formulated oil (GF3) and Chevron plain oil were used with the addition of PTFE and catalyst to characterize and analyze their performance. Lower phosphorus blends were the goal of the model solution. Experiments indicated that new sub-micron FeF3 catalyst played an important role in preventing breakdown of the tribofilm.

Keywords: Wear, SEM, EDS, friction, lubricants.

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1016 Vehicle Detection Method using Haar-like Feature on Real Time System

Authors: Sungji Han, Youngjoon Han, Hernsoo Hahn

Abstract:

This paper presents a robust vehicle detection approach using Haar-like feature. It is possible to get a strong edge feature from this Haar-like feature. Therefore it is very effective to remove the shadow of a vehicle on the road. And we can detect the boundary of vehicles accurately. In the paper, the vehicle detection algorithm can be divided into two main steps. One is hypothesis generation, and the other is hypothesis verification. In the first step, it determines vehicle candidates using features such as a shadow, intensity, and vertical edge. And in the second step, it determines whether the candidate is a vehicle or not by using the symmetry of vehicle edge features. In this research, we can get the detection rate over 15 frames per second on our embedded system.

Keywords: vehicle detection, haar-like feauture, single camera, real time

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1015 Feature Level Fusion of Multimodal Images Using Haar Lifting Wavelet Transform

Authors: Sudipta Majumdar, Jayant Bharadwaj

Abstract:

This paper presents feature level image fusion using Haar lifting wavelet transform. Feature fused is edge and boundary information, which is obtained using wavelet transform modulus maxima criteria. Simulation results show the superiority of the result as entropy, gradient, standard deviation are increased for fused image as compared to input images. The proposed methods have the advantages of simplicity of implementation, fast algorithm, perfect reconstruction, and reduced computational complexity. (Computational cost of Haar wavelet is very small as compared to other lifting wavelets.)

Keywords: Lifting wavelet transform, wavelet transform modulus maxima.

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1014 IMDC: An Image-Mapped Data Clustering Technique for Large Datasets

Authors: Faruq A. Al-Omari, Nabeel I. Al-Fayoumi

Abstract:

In this paper, we present a new algorithm for clustering data in large datasets using image processing approaches. First the dataset is mapped into a binary image plane. The synthesized image is then processed utilizing efficient image processing techniques to cluster the data in the dataset. Henceforth, the algorithm avoids exhaustive search to identify clusters. The algorithm considers only a small set of the data that contains critical boundary information sufficient to identify contained clusters. Compared to available data clustering techniques, the proposed algorithm produces similar quality results and outperforms them in execution time and storage requirements.

Keywords: Data clustering, Data mining, Image-mapping, Pattern discovery, Predictive analysis.

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1013 Two Different Solutions for Gigabit Ethernet Transmission over POF

Authors: Stefano Straullu, Silvio Abrate, Antonino Nespola, Paolo Savio, Roberto Gaudino

Abstract:

Two completely different approaches for a Gigabit Ethernet compliant stream transmission over 50m of 1mm PMMA SI-POF have been experimentally demonstrated and are compared in this paper. The first solution is based on a commercial RC-LED transmission and a careful optimization of the physical layer architecture, realized during the POF-PLUS EU Project. The second solution exploits the performance of an edge-emitting laser at the transmitter side in order to avoid any sort of electrical equalization at the receiver side.

Keywords: Gigabit Ethernet, Home Networking, Step-Index Polymer Optical Fiber (SI-POF)

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1012 Analysis of a Fluid Behavior in a Rectangular Enclosure under the Effect of Magnetic Field

Authors: Y.Bakhshan, H.Ashoori

Abstract:

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Keywords: Rectangular Cavity, magneto-hydrodynamic, free convection, simulation

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1011 3D-Printing Plates without “Support”

Authors: Yasusi Kanada

Abstract:

When printing a plate (or dish) by an FDM 3D printer, the process normally requires support material, which causes several problems. This paper proposes a method for forming thin plates without using wasteful support material. This method requires several extraordinary parameter values when slicing plates. The experiments show that the plates can, for the most part, be successfully formed using a conventional slicer and a 3D printer; however, seams between layers spoil them and the quality of printed objects strongly depends on the slicer.

Keywords: Fused deposition modeling (FDM), 3D printing, Support-less, Layer seam, Slicer.

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1010 Identification and Classification of Plastic Resins using Near Infrared Reflectance Spectroscopy

Authors: Hamed Masoumi, Seyed Mohsen Safavi, Zahra Khani

Abstract:

In this paper, an automated system is presented for identification and separation of plastic resins based on near infrared (NIR) reflectance spectroscopy. For identification and separation among resins, a "Two-Filter" identification method is proposed that is capable to distinguish among polyethylene terephthalate (PET), high density polyethylene (HDPE), polyvinyl chloride (PVC), polypropylene (PP) and polystyrene (PS). Through surveying effects of parameters such as surface contamination, sample thickness, label and cap existence, it was obvious that the "Two-Filter" method has a high efficiency in identification of resins. It is shown that accurate identification and separation of five major resins can be obtained through calculating the relative reflectance at two wavelengths in the NIR region.

Keywords: Identification, Near Infrared, Plastic, Separation, Spectroscopy

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1009 Investigation of Stability of Functionally Graded Material when Encountering Periodic Loading

Authors: M. Amiri

Abstract:

In this work, functionally graded materials (FGMs), subjected to loading, which varies with time has been studied. The material properties of FGM are changing through the thickness of material as power law distribution. The conical shells have been chosen for this study so in the first step capability equations for FGM have been obtained. With Galerkin method, these equations have been replaced with time dependant differential equations with variable coefficient. These equations have solved for different initial conditions with variation methods. Important parameters in loading conditions are semi-vertex angle, external pressure and material properties. Results validation has been done by comparison between with those in previous studies of other researchers.

Keywords: Impulsive semi-vertex angle, loading, functionally graded materials, composite material.

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1008 A Comparative Study of Electrical Transport Phenomena in Ultrathin vs. Nanoscale SOI MOSFETs Devices

Authors: A. Karsenty, A. Chelly

Abstract:

Ultrathin (UTD) and Nanoscale (NSD) SOI-MOSFET devices, sharing a similar W/L but with a channel thickness of 46nm and 1.6nm respectively, were fabricated using a selective “gate recessed” process on the same silicon wafer. The electrical transport characterization at room temperature has shown a large difference between the two kinds of devices and has been interpreted in terms of a huge unexpected series resistance. Electrical characteristics of the Nanoscale device, taken in the linear region, can be analytically derived from the ultrathin device ones. A comparison of the structure and composition of the layers, using advanced techniques such as Focused Ion Beam (FIB) and High Resolution TEM (HRTEM) coupled with Energy Dispersive X-ray Spectroscopy (EDS), contributes an explanation as to the difference of transport between the devices.

Keywords: Nanoscale Devices, SOI MOSFET, Analytical Model, Electron Transport.

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1007 Preparation of Li Ion Conductive Ceramics via Liquid Process

Authors: M. Kotobuki, M. Koishi

Abstract:

Li1.5Al0.5Ti1.5 (PO4)3(LATP) has received much attention as a solid electrolyte for lithium batteries. In this study, the LATP solid electrolyte is prepared by the co-precipitation method using Li3PO4 as a Li source. The LATP is successfully prepared and the Li ion conductivities of bulk (inner crystal) and total (inner crystal and grain boundary) are 1.1 × 10-3 and 1.1 × 10-4 S cm-1, respectively. These values are comparable to the reported values, in which Li2C2O4 is used as the Li source. It is conclude that the LATP solid electrolyte can be prepared by the co-precipitation method using Li3PO4 as the Li source and this procedure has an advantage in mass production over previous procedure using Li2C2O4 because Li3PO4 is lower price reagent compared with Li2C2O4.

Keywords: Co-precipitation method, lithium battery, NASICON-type electrolyte, solid electrolyte.

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1006 Photoluminescence Properties of β-FeSi2 on Cu- or Au-coated Si

Authors: Kensuke Akiyama, Satoru Kaneko, Takeshi Ozawa, Kazuya Yokomizo, Masaru Itakura

Abstract:

The photoluminescence (PL) at 1.55 μm from semiconducting β-FeSi2 has attracted a noticeable interest for silicon-based optoelectronic applications. Moreover, its high optical absorption coefficient (higher than 105 cm-1 above 1.0 eV) allows this semiconducting material to be used as photovoltanics devices. A clear PL spectrum for β-FeSi2 was observed by Cu or Au coating on Si(001). High-crystal-quality β-FeSi2 with a low-level nonradiative center was formed on a Cu- or Au- reated Si layer. This method of deposition can be applied to other materials requiring high crystal quality.

Keywords: iron silicide, semiconductor, epitaxial, photoluminescence.

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1005 Simulation of High Performance Nanoscale Partially Depleted SOI n-MOSFET Transistors

Authors: Fatima Zohra Rahou, A. Guen Bouazza, B. Bouazza

Abstract:

Invention of transistor is the foundation of electronics industry. Metal Oxide Semiconductor Field Effect Transistor (MOSFET) has been the key for the development of nanoelectronics technology. In the first part of this manuscript, we present a new generation of MOSFET transistors based on SOI (Silicon-On-Insulator) technology. It is a partially depleted Silicon-On-Insulator (PD SOI MOSFET) transistor simulated by using SILVACO software. This work was completed by the presentation of some results concerning the influence of parameters variation (channel length L and gate oxide thickness Tox) on our PDSOI n-MOSFET structure on its drain current and kink effect.

Keywords: SOI technology, PDSOI MOSFET, FDSOI MOSFET, Kink Effect, SILVACO TCAD.

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1004 Effects of Intake Temperature and Intake Pressure on Combustion and Exhaust Emissions of HCCI Engine

Authors: Fridhi Hadia, Soua Wadhah, Hidouri Ammar, Omri Ahmed

Abstract:

In this paper, the effect of the intake temperature (IT) and intake pressure (IP) on ignition timing and pollutants emission of Homogeneous Charge Compression Ignition (HCCI) engine is investigated. Numerical computations are performed using the CHEMKIN computer code. The numerical temperature obtained using different boundary conditions is compared to published data and a good agreement is assigned. Results show that the HCCI combustion engine is significantly improved by increasing the IT. With a value of IT lower than 390 K, combustion cannot occur. However, with an IT greater than 420 K, the cylinder pressure decreases. An optimum crank rotation angle is achieved by using IT of 420 K. So, we can conclude that the variation of the IT and IP influence notably the emission concentration.

Keywords: HCCI engine, CEMKIN, intake temperature, intake pressure.

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1003 Effect of Groove Location on the Dynamic Characteristics of Multiple Axial Groove Water Lubricated Journal Bearing

Authors: M. Vijaya Kini, R. S. Pai, D. Srikanth Rao, Satish Shenoy B, R. Pai

Abstract:

The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.

Keywords: 3-axial groove, dynamic characteristics, groovelocation, water lubricated bearings.

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1002 Identifying a Drug Addict Person Using Artificial Neural Networks

Authors: Mustafa Al Sukar, Azzam Sleit, Abdullatif Abu-Dalhoum, Bassam Al-Kasasbeh

Abstract:

Use and abuse of drugs by teens is very common and can have dangerous consequences. The drugs contribute to physical and sexual aggression such as assault or rape. Some teenagers regularly use drugs to compensate for depression, anxiety or a lack of positive social skills. Teen resort to smoking should not be minimized because it can be "gateway drugs" for other drugs (marijuana, cocaine, hallucinogens, inhalants, and heroin). The combination of teenagers' curiosity, risk taking behavior, and social pressure make it very difficult to say no. This leads most teenagers to the questions: "Will it hurt to try once?" Nowadays, technological advances are changing our lives very rapidly and adding a lot of technologies that help us to track the risk of drug abuse such as smart phones, Wireless Sensor Networks (WSNs), Internet of Things (IoT), etc. This technique may help us to early discovery of drug abuse in order to prevent an aggravation of the influence of drugs on the abuser. In this paper, we have developed a Decision Support System (DSS) for detecting the drug abuse using Artificial Neural Network (ANN); we used a Multilayer Perceptron (MLP) feed-forward neural network in developing the system. The input layer includes 50 variables while the output layer contains one neuron which indicates whether the person is a drug addict. An iterative process is used to determine the number of hidden layers and the number of neurons in each one. We used multiple experiment models that have been completed with Log-Sigmoid transfer function. Particularly, 10-fold cross validation schemes are used to access the generalization of the proposed system. The experiment results have obtained 98.42% classification accuracy for correct diagnosis in our system. The data had been taken from 184 cases in Jordan according to a set of questions compiled from Specialists, and data have been obtained through the families of drug abusers.

Keywords: Artificial Neural Network, Decision Support System, drug abuse, drug addiction, Multilayer Perceptron.

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1001 Investigation of Artificial Neural Networks Performance to Predict Net Heating Value of Crude Oil by Its Properties

Authors: Mousavian, M. Moghimi Mofrad, M. H. Vakili, D. Ashouri, R. Alizadeh

Abstract:

The aim of this research is to use artificial neural networks computing technology for estimating the net heating value (NHV) of crude oil by its Properties. The approach is based on training the neural network simulator uses back-propagation as the learning algorithm for a predefined range of analytically generated well test response. The network with 8 neurons in one hidden layer was selected and prediction of this network has been good agreement with experimental data.

Keywords: Neural Network, Net Heating Value, Crude Oil, Experimental, Modeling.

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1000 Effect of Isfahan Refinery, Power Plant and Petrochemical on Borkhar District Soil

Authors: A. Gandomkar

Abstract:

This study aimed to evaluate regional soil Borkhar of the metals Lead has been made. In this field study fires visits to the regions. The limit of this study located in the East refineries, petrochemical and power plant to 20 km was selected. The 41 soil samples from depths of 0 to 10 cm in area and were randomized. Soil samples were transported to the laboratory and by air was dry and passed through 2-mil thickness sieve. In the laboratory of physical and chemical characteristics and concentrations of total absorption was measured. The results showed that the amount of lead in soil in many parts of the range higher than the standard limit. Survey maps show that the lead spatial distribution of the region does not special pattern.

Keywords: Soil Pollution, Heavy Metals, Borkhar District, Soil Sampling.

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999 Effect of Shear Theories on Free Vibration of Functionally Graded Plates

Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

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