Search results for: agent-based simulation.
1983 Recognition of Tifinagh Characters with Missing Parts Using Neural Network
Authors: El Mahdi Barrah, Said Safi, Abdessamad Malaoui
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In this paper, we present an algorithm for reconstruction from incomplete 2D scans for tifinagh characters. This algorithm is based on using correlation between the lost block and its neighbors. This system proposed contains three main parts: pre-processing, features extraction and recognition. In the first step, we construct a database of tifinagh characters. In the second step, we will apply “shape analysis algorithm”. In classification part, we will use Neural Network. The simulation results demonstrate that the proposed method give good results.
Keywords: Tifinagh character recognition, Neural networks, Local cost computation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12861982 Numerical Flow Simulation around HSP Propeller in Open Water and behind a Vessel Wake Using RANS CFD Code
Authors: Kadda Boumediene, Mohamed Bouzit
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The prediction of the flow around marine propellers and vessel hulls propeller interaction is one of the challenges of Computational fluid dynamics (CFD). The CFD has emerged as a potential tool in recent years and has promising applications. The objective of the current study is to predict the hydrodynamic performances of HSP marine propeller in open water and behind a vessel. The unsteady 3-D flow was modeled numerically along with respectively the K-ω standard and K-ω SST turbulence models for steady and unsteady cases. The hydrodynamic performances such us a torque and thrust coefficients and efficiency show good agreement with the experiment results.
Keywords: Seiun Maru propeller, steady, unsteady, CFD, HSP.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8401981 A Simple Adaptive Algorithm for Norm-Constrained Optimization
Authors: Hyun-Chool Shin
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In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.Keywords: constrained optimization, unit-norm, LMS, principle component analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21281980 Thyroids Dose Evaluation and Calculation of Backscatter Factors for Co-60 Irradiations
Authors: D. Kısınma, A. B. Tugrul
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The aim of the study is evaluation of absorbed doses for thyroids by using neck phantoms. For this purpose, it was arranged the irradiation set with different phantoms. Three different materials were used for phantom materials as, water, parafine and wood. The phantoms were three different dimensions for simulation of different ages and human race for each material. Co-60 gammao source was used for irradiation and the experimental procedure applied rigorously with narrow beam geometry. As the results of the experiments the relative radiation doses are evaluated for therapic applications for thyroids and backscattering factors were calculated and shown that water, parafine and wood can appropriate for phantom material with the converge values of backscattering factors.
Keywords: Co-60, Dosimetry, phantom, thyroids.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16311979 Model Predictive 2DOF PID Slip Suppression Control of Electric Vehicle under Braking
Authors: Tohru Kawabe
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In this paper, a 2DOF (two degrees of freedom) PID (Proportional-Integral-Derivative) controller based on MPC (Model predictive control) algorithm fo slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method aims to improve the safety and the stability of EVs under braking by controlling the wheel slip ration. There also include numerical simulation results to demonstrate the effectiveness of the method.
Keywords: Model predictive control, PID controller, Two degrees of freedom, Electric Vehicle, Slip suppression.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18461978 A Study on the Heading of Spur Gears: Numerical Analysis and Experiments
Authors: M.Zadshakouyan, E.Abdi Sobbouhi, H.Jafarzadeh
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In this study, the precision heading process of spur gears has been investigated by means of numerical analysis. The effect of some parameters such as teeth number and module on the forming force and material flow were presented. The simulation works were performed rigid-plastic finite element method using DEFORM 3D software. In order to validate the estimated numerical results, they were compared with those obtained experimentally during heading of spur gear using lead as a model material. Results showed that the optimum number of gear teeth is between 10 to 20, that is because of being the specific pressure in its minimum value.Keywords: Heading, spur gear, numerical analysis, experiments.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19541977 Confidence Intervals for the Normal Mean with Known Coefficient of Variation
Authors: Suparat Niwitpong
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In this paper we proposed two new confidence intervals for the normal population mean with known coefficient of variation. This situation occurs normally in environment and agriculture experiments where the scientist knows the coefficient of variation of their experiments. We propose two new confidence intervals for this problem based on the recent work of Searls [5] and the new method proposed in this paper for the first time. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. Monte Carlo simulation will be used to assess the performance of these intervals based on their expected lengths.
Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16511976 Approximations to the Distribution of the Sample Correlation Coefficient
Authors: John N. Haddad, Serge B. Provost
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Given a bivariate normal sample of correlated variables, (Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation coefficient is obtained in terms of the ranges, |Xi − Yi|. An approximate confidence interval for ρX,Y is then derived, and a simulation study reveals that the resulting coverage probabilities are in close agreement with the set confidence levels. As well, a new approximant is provided for the density function of R, the sample correlation coefficient. A mixture involving the proposed approximate density of R, denoted by hR(r), and a density function determined from a known approximation due to R. A. Fisher is shown to accurately approximate the distribution of R. Finally, nearly exact density approximants are obtained on adjusting hR(r) by a 7th degree polynomial.Keywords: Sample correlation coefficient, density approximation, confidence intervals.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22701975 Nonlinear Simulation of Harmonically Coupled Two-Beam Free-Electron Laser
Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani
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A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13451974 Measurement Fractional Order Sallen-Key Filters
Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman
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This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.
Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31421973 Numerical Simulation of the Aerodynamic Loads acting on top of the SMART Centre for PV Applications
Authors: M. Raciti Castelli, S. Toniato, E. Benini
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The flow filed around a flatted-roof compound has been investigated by means of 2D and 3D numerical simulations. A constant wind velocity profile, based both on the maximum reference wind speed in the building site (peak gust speed worked out for a 50- year return period) and on the local roughness coefficient, has been simulated in order to determine the wind-induced loads on top of the roof. After determining the influence of the incoming wind directions on the induced roof loads, a 2D analysis of the most severe load condition has been performed, achieving a numerical quantification of the expected wind-induced forces on the PV panels on top of the roof.Keywords: CFD, wind-induced loads, flow around buildings, photovoltaic system
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15661972 Dynamics and Control of a Chaotic Electromagnetic System
Authors: Shun-Chang Chang
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In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15981971 Auto Regressive Tree Modeling for Parametric Optimization in Fuzzy Logic Control System
Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao
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The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13891970 Bifurcation and Chaos of the Memristor Circuit
Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi
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In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.
Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17981969 Realization of Electronically Controllable Current-mode Square-rooting Circuit Based on MO-CFTA
Authors: P. Silapan, C. Chanapromma, T. Worachak
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This article proposes a current-mode square-rooting circuit using current follower transconductance amplifier (CTFA). The amplitude of the output current can be electronically controlled via input bias current with wide input dynamic range. The proposed circuit consists of only single CFTA. Without any matching conditions and external passive elements, the circuit is then appropriate for an IC architecture. The magnitude of the output signal is temperature-insensitive. The PSpice simulation results are depicted, and the given results agree well with the theoretical anticipation. The power consumption is approximately 1.96mW at ±1.5V supply voltages.Keywords: CFTA, Current-mode, Square-rooting Circuit
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14071968 A Low-Voltage Current-Mode Wheatstone Bridge using CMOS Transistors
Authors: Ebrahim Farshidi
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This paper presents a new circuit arrangement for a current-mode Wheatstone bridge that is suitable for low-voltage integrated circuits implementation. Compared to the other proposed circuits, this circuit features severe reduction of the elements number, low supply voltage (1V) and low power consumption (<350uW). In addition, the circuit has favorable nonlinearity error (<0.35%), operate with multiple sensors and works by single supply voltage. The circuit employs MOSFET transistors, so it can be used for standard CMOS fabrication. Simulation results by HSPICE show high performance of the circuit and confirm the validity of the proposed design technique.Keywords: Wheatstone bridge, current-mode, low-voltage, MOS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30221967 A Quadcopter Stability Analysis: A Case Study Using Simulation
Authors: C. S. Bianca Sabrina, N. Egidio Raimundo, L. Alexandre Baratella, C. H. João Paulo
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This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.
Keywords: Controllers, drones, quadcopter, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10651966 Numerical Simulation of the Flow Field around a 30° Inclined Flat Plate
Authors: M. Raciti Castelli, P. Cioppa, E. Benini
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This paper presents a CFD analysis of the flow around a 30° inclined flat plate of infinite span. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a flat plate invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested and flow field characteristics in the neighborhood of the flat plate have been numerically investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a twodimensional inclined plate.Keywords: CFD, lift, drag, flat plate
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33091965 Modeling UWSN Simulators – A Taxonomy
Authors: Christhu Raj, Rajeev Sukumaran
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In this research article of modeling Underwater Wireless Sensor Network Simulators, we provide a comprehensive overview of the various currently available simulators used in UWSN modeling. In this work, we compare their working environment, software platform, simulation language, key features, limitations and corresponding applications. Based on extensive experimentation and performance analysis, we provide their efficiency for specific applications. We have also provided guidelines for developing protocols in different layers of the protocol stack, and finally these parameters are also compared and tabulated. This analysis is significant for researchers and designers to find the right simulator for their research activities.Keywords: Underwater Wireless Sensor networks (UWSN), SUNSET, NS2, OPNET, WOSS, DESERT, RECORDS, Aqua- Sim, Aqua- Net Mate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31111964 PSS and SVC Controller Design by Chaos and PSO Algorithms to Enhancing the Power System Stability
Authors: Saeed jalilzadeh, Mohammad Reza Safari Tirtashi, Mohsen Sadeghi
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this paper focuses on designing of PSS and SVC controller based on chaos and PSO algorithms to improve the stability of power system. Single machine infinite bus (SMIB) system with SVC located at the terminal of generator has been considered to evaluate the proposed controllers where both SVC and PSS have the same controller. The coefficients of PSS and SVC controller have been optimized by chaos and PSO algorithms. Finally the system with proposed controllers has been simulated for the special disturbance in input power of generator, and then the dynamic responses of generator have been presented. The simulation results showed that the system composed with recommended controller has outstanding operation in fast damping of oscillations of power system.Keywords: PSS, CHAOS, PSO, Stability
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16551963 Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation
Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong
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In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.
Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25841962 Real-Time Digital Oscilloscope Implementation in 90nm CMOS Technology FPGA
Authors: Nasir Mehmood, Jens Ogniewski, Vinodh Ravinath
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This paper describes the design of a real-time audiorange digital oscilloscope and its implementation in 90nm CMOS FPGA platform. The design consists of sample and hold circuits, A/D conversion, audio and video processing, on-chip RAM, clock generation and control logic. The design of internal blocks and modules in 90nm devices in an FPGA is elaborated. Also the key features and their implementation algorithms are presented. Finally, the timing waveforms and simulation results are put forward.Keywords: CMOS, VLSI, Oscilloscope, Field Programmable Gate Array (FPGA), VHDL, Video Graphics Array (VGA)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30831961 GA based Optimal Sizing and Placement of Distributed Generation for Loss Minimization
Authors: Deependra Singh, Devender Singh, K. S. Verma
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This paper addresses a novel technique for placement of distributed generation (DG) in electric power systems. A GA based approach for sizing and placement of DG keeping in view of system power loss minimization in different loading conditions is explained. Minimal system power loss is obtained under voltage and line loading constraints. Proposed strategy is applied to power distribution systems and its effectiveness is verified through simulation results on 16, 37-bus and 75-bus test systems.
Keywords: Distributed generation (DG), Genetic algorithms (GA), optimal sizing and placement, Power loss.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34681960 A Digitally Programmable Voltage-mode Multifunction Biquad Filter with Single-Output
Authors: C. Ketviriyakit, W. Kongnun, C. Chanapromma, P. Silapan
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This article proposes a voltage-mode multifunction filter using differential voltage current controllable current conveyor transconductance amplifier (DV-CCCCTA). The features of the circuit are that: the quality factor and pole frequency can be tuned independently via the values of capacitors: the circuit description is very simple, consisting of merely 1 DV-CCCCTA, and 2 capacitors. Without any component matching conditions, the proposed circuit is very appropriate to further develop into an integrated circuit. Additionally, each function response can be selected by suitably selecting input signals with digital method. The PSpice simulation results are depicted. The given results agree well with the theoretical anticipation.Keywords: DV-CCCCTA, Voltage-mode, Multifunction filter
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13571959 Tabu Search Approach to Solve Routing Issues in Communication Networks
Authors: Anant Oonsivilai, Wichai Srisuruk, Boonruang Marungsri, Thanatchai Kulworawanichpong
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Optimal routing in communication networks is a major issue to be solved. In this paper, the application of Tabu Search (TS) in the optimum routing problem where the aim is to minimize the computational time and improvement of quality of the solution in the communication have been addressed. The goal is to minimize the average delays in the communication. The effectiveness of Tabu Search method is shown by the results of simulation to solve the shortest path problem. Through this approach computational cost can be reduced.Keywords: Communication networks, optimum routing network, tabu search algorithm, shortest path.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20961958 Numerical Simulation of Interfacial Flow with Volume-Of-Fluid Method
Authors: Afshin Ahmadi Nadooshan
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In this article, various models of surface tension force (CSF, CSS and PCIL) for interfacial flows have been applied to dynamic case and the results were compared. We studied the Kelvin- Helmholtz instabilities, which are produced by shear at the interface between two fluids with different physical properties. The velocity inlet is defined as a sinusoidal perturbation. When gravity and surface tension are taking into account, we observe the development of the Instability for a critic value of the difference of velocity of the both fluids. The VOF Model enables to simulate Kelvin-Helmholtz Instability as dynamic case.
Keywords: Interfacial flow, Incompressible flow, surface tension, Volume-Of-Fluid, Kelvin-Helmholtz.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25611957 Detection of Black Holes in MANET Using Collaborative Watchdog with Fuzzy Logic
Authors: Y. Harold Robinson, M. Rajaram, E. Golden Julie, S. Balaji
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Mobile ad hoc network (MANET) is a self-configuring network of mobile node connected without wires. A Fuzzy Logic Based Collaborative watchdog approach is used to reduce the detection time of misbehaved nodes and increase the overall truthfulness. This methodology will increase the secure efficient routing by detecting the Black Holes attacks. The simulation results proved that this method improved the energy, reduced the delay and also improved the overall performance of the detecting black hole attacks in MANET.
Keywords: MANET, collaborative watchdog, fuzzy logic, AODV.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13511956 Evaluation of the Elastic Mechanical Properties of a Hybrid Adhesive Material
Authors: Moudar H. A. Zgoul, Amin Al Zamer
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Adhesive materials and adhesion have been the focal point of multiple research works related to numerous applications, particularly, aerospace, and aviation industries. To enhance the properties of conventional adhesive materials, additives have been introduced to the mix in order to enhance their mechanical and physical properties by creating a hybrid adhesive material. The evaluation of the mechanical properties of such hybrid adhesive materials is thus of an essential requirement for the purpose of properly modeling their behavior accurately. This paper presents an approach/tool to simulate the behavior such hybrid adhesives in a way that will allow researchers to better understand their behavior while in service.
Keywords: Adhesive materials, analysis, hybrid adhesives, mechanical properties, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11141955 Numerical Study on the Hazards of Gravitational Forces on Cerebral Aneurysms
Authors: Hashem M. Alargha, Mohammad O. Hamdan, Waseem H. Aziz
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Aerobatic and military pilots are subjected to high gravitational forces that could cause blackout, physical injuries or death. A CFD simulation using fluid-solid interactions scheme has been conducted to investigate the gravitational effects and hazards inside cerebral aneurysms. Medical data have been used to derive the size and geometry of a simple aneurysm on a T-shaped bifurcation. The results show that gravitational force has no effect on maximum Wall Shear Stress (WSS); hence, it will not cause aneurysm initiation/formation. However, gravitational force cause causes hypertension which could contribute to aneurysm rupture.
Keywords: Aneurysm, CFD, wall shear stress, gravity, fluid dynamics, bifurcation artery.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14071954 Fuzzy Boundary Layer Solution to Nonlinear Hydraulic Position Control Problem
Authors: Mustafa Resa Becan
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Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.
Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.
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