Search results for: Numerical simulation.

Authors: Mohd Tarmizi Ali, Mohd Khairul Mohd Salleh, Md. Mahfudz Md. Zan

Abstract:

Dielectric sheet perturbation to the dominant TE111 mode resonant frequency of a circular cavity is studied and presented in this paper. The dielectric sheet, placed at the middle of the airfilled cavity, introduces discontinuities and disturbs the configuration of electromagnetic fields in the cavity. For fixed dimensions of cavity and fixed thickness of the loading dielectric, the dominant resonant frequency varies quite linearly with the permittivity of the dielectric. This quasi-linear relationship is plotted using Maple software and verified using 3D electromagnetic simulations. Two probes are used in the simulation for wave excitation into and from the cavity. The best length of probe is found to be 3 mm, giving the closest resonant frequency to the one calculated using Maple. A total of fourteen different dielectrics of permittivity ranging from 1 to 12.9 are tested one by one in the simulation. The works show very close agreement between the results from Maple and the simulation. A constant difference of 0.04 GHz is found between the resonant frequencies collected during simulation and the ones from Maple. The success of this project may lead to the possibility of using the middle loaded cavity at TE111 mode as a microwave non-destructive testing of solid materials.

Keywords: Middle-loaded cavity, dielectric sheet perturbation.

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Authors: Mojahid F. Saeed Osman

Abstract:

Repairable items inventory system is a management tool used to incorporate all information concerning inventory levels and movements for repaired and new items. This paper presents development of an effective simulation model for managing the inventory of repairable items for a production system where production lines send their faulty items to a repair shop considering the stochastic failure behavior and repair times. The developed model imitates the process of handling the on-hand inventory of repaired items and the replenishment of the inventory of new items using Economic Order Quantity and Reorder Point ordering policy in a flexible and risk-free environment. We demonstrate the appropriateness and effectiveness of the proposed simulation model using an illustrative case problem. The developed simulation model can be used as a reliable tool for estimating a healthy on-hand inventory of new and repaired items, backordered items, and downtime due to unavailability of repaired items, and validating and examining Economic Order Quantity and Reorder Point ordering policy, which would further be compared with other ordering strategies as future work.

Keywords: Inventory system, repairable items, simulation, maintenance, economic order quantity, reorder point.

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Authors: Wei-Hwa Chiang, Hao-Hsiang Hsu, Jian-Sheng Huang

Abstract:

Appropriate ventilation in a classroom is helpful for enhancing air exchange rate and student concentration. This study focuses on the effects of fenestration in a four-story school building by performing numerical simulation of a building when considering indoor and outdoor environments simultaneously. The wind profile function embedded in PHOENICS code was set as the inlet boundary condition in a suburban environment. Sixteen fenestration combinations were compared in a classroom containing thirty seats. This study evaluates mean age of air (AGE) and airflow pattern of a classroom on different floors. Considering both wind profile and fenestration effects, the airflow on higher floors is channeled toward the area near ceiling in a room and causes older mean age of air in the breathing zone. The results in this study serve as a useful guide for enhancing natural ventilation in a typical school building.

Keywords: Cross ventilation, Fenestration effect, Wind profile, Mean age of air, CFD

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Authors: Tayeb Lardjane, Rabah Messaci

Abstract:

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

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Authors: Abhay Bodake, Ping Sui, Hafeez Syed, Ratish Kadam

Abstract:

Real-time measurement of applied forces, like tension, compression, torsion, and bending moment, identifies the transferred energies being applied to the bottomhole assembly (BHA). These forces are highly detrimental to measurement/logging-while-drilling tools and downhole equipment. Real-time measurement of the dynamic downhole behavior, including weight, torque, bending on bit, and vibration, establishes a real-time feedback loop between the downhole drilling system and drilling team at the surface. This paper describes the numerical analysis of the strain data acquired by the measurement tool at different locations on the strain pockets. The strain values obtained by FEA for various loading conditions (tension, compression, torque, and bending moment) are compared against experimental results obtained from an identical experimental setup. Numerical analyses results agree with experimental data within 8% and, therefore, substantiate and validate the FEA model. This FEA model can be used to analyze the combined loading conditions that reflect the actual drilling environment.

Keywords: FEA, M/LWD, Oil & Gas, Strain Measurement.

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Authors: I. Ioannou, I. M. Gitman

Abstract:

This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Effective properties, representative volume element, short fiber reinforced composites.

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Authors: P. Lauk, K. E. Seegel, T. Tähemaa

Abstract:

The fuel consumption of modern, high wing loading, commercial aircraft in the first stage of flight is high because the usable flight level is lower and the weather conditions (jet stream) have great impact on aircraft performance. To reduce the fuel consumption, it is necessary to raise during first stage of flight the L/D ratio value within Cl 0.55-0.65. Different variable geometrical wing trailing edge modifications of SC(2)-410 airfoil were compared at M 0.78 using the CFD software STAR-CCM+ simulation based Reynolds-averaged Navier-Stokes (RANS) equations. The numerical results obtained show that by increasing the width of the airfoil by 4% and by modifying the trailing edge airfoil, it is possible to decrease airfoil drag at Cl 0.70 for up to 26.6% and at the same time to increase commercial aircraft L/D ratio for up to 5.0%. Fuel consumption can be reduced in proportion to the increase in L/D ratio.

Keywords: L/D ratio, miniflaps, mini-TED, supercritical airfoil.

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Authors: Shield B. Lin, Ziraguen O. Williams

Abstract:

In a task to assist NASA in analyzing the dynamic forces caused by operational countermeasures of an astronaut’s exercise platform impacting the spacecraft, an active proportional-integral-derivative controller commanding a linear actuator is proposed in a vibration isolation system to regulate the movement of the exercise platform. Computer simulation shows promising results that most exciter forces can be reduced or even eliminated. This paper emphasizes on parameter uncertainties, variations and exciter force variations. Drift and variations of system parameters in the vibration isolation system for astronaut’s exercise platform are analyzed. An active controlled scheme is applied with the goals to reduce the platform displacement and to minimize the force being transmitted to the spacecraft structure. The controller must be robust enough to accommodate the wide variations of system parameters and exciter forces. Computer simulation for the vibration isolation system was performed via MATLAB/Simulink and Trick. The simulation results demonstrate the achievement of force reduction with small platform displacement under wide ranges of variations in system parameters. 

Keywords: control, counterweight, isolation, vibration

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Authors: Berardina De Carolis, Giovanni Cozzolongo

Abstract:

In this paper, we present C@sa, a multiagent system aiming at modeling, controlling and simulating the behavior of an intelligent house. The developed system aims at providing to architects, designers and psychologists a simulation and control tool for understanding which is the impact of embedded and pervasive technology on people daily life. In this vision, the house is seen as an environment made up of independent and distributed devices, controlled by agents, interacting to support user's goals and tasks.

Keywords: Ambient intelligence, agent-based systems, influence diagrams.

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Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

Abstract:

Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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Authors: Xin H. Zou, Qiang Wang

Abstract:

The comparisons of two typical fluidic thrust vectoring exhaust nozzles including two-dimensional(2-D) nozzle and axisymmetric nozzle on aerodynamic characteristics was presented by numerical simulation. The results show: the thrust vector angles increased with the increasing secondary flow but decreased with the nozzle pressure ratio (NPR) increasing. With the same secondary flow and NPR, the thrust vector angles of 2-D nozzle were higher than the axisymmetric nozzle-s. So with the lower NPR and more secondary weight flow, the much higher thrust vector angle was caused by 2-D fluidic nozzle. And with the higher NPR and less secondary weight flow, there was not much difference in angular dimension between two nozzles.

Keywords: Aerodynamic characteristics, fluidic nozzle, vector angle, thrust coefficient comparison.

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Authors: Wang Jing, Liu Shouwen, Pei Yifei

Abstract:

A satellite is being integrated and tested by BISEE (Beijing Institute of Spacecraft Environment Engineering). This paper describes the infrared lamp array simulation technology used for satellite thermal balance and thermal vacuum test. These tests were performed in KM6 space environmental simulator in Beijing, China. New software and hardware developed by BISEE, along with enhanced heat flux uniformity, provided for well accomplished thermal balance and thermal vacuum tests. The flux uniformity of lamp array was satisfied with test requirement. Monitored background radiometer offered reliable heat flux measurements with remarkable repeatability. Simulation software supplied accurate thermal flux distribution predictions.

Keywords: Satellite, Thermal test, Infrared lamp array, Heatflux

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Authors: Mohammad Najafi, Hossein Roghani-Mamaqani, Mehdi Salami-Kalajahi, Vahid Haddadi-Asl

Abstract:

A high-performance Monte Carlo simulation, which simultaneously takes diffusion-controlled and chain-length-dependent bimolecular termination reactions into account, is developed to simulate atom transfer radical copolymerization of styrene and nbutyl acrylate. As expected, increasing initial feed fraction of styrene raises the fraction of styrene-styrene dyads (fAA) and reduces that of n-butyl acrylate dyads (fBB). The trend of variation in randomness parameter (fAB) during the copolymerization also varies significantly. Also, there is a drift in copolymer heterogeneity and the highest drift occurs in the initial feeds containing lower percentages of styrene, i.e. 20% and 5%.

Keywords: Atom Transfer Radical Copolymerization, MonteCarlo Simulation, Copolymer Heterogeneity, Styrene n-ButylAcrylate

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Authors: U. Narumitbowonkul, P. Keangin, P. Rattanadecho

Abstract:

The characteristics of temperature distribution and electric field in a natural rubber glove (NRG) using microwave energy during microwave heating process are investigated numerically and experimentally. A three-dimensional model of NRG and microwave oven are considered in this work. The influences of position, heating time and rotation angle of NRG on temperature distribution and electric field are presented in details. The coupled equations of electromagnetic wave propagation and heat transfer are solved using the finite element method (FEM). The numerical model is validated with an experimental study at a frequency of 2.45 GHz. The results show that the numerical results closely match the experimental results. Furthermore, it is found that the temperature distribution and electric field increases with increasing heating time. The hot spot zone appears in NRG at the tip of middle finger while the maximum temperature occurs in case of rotation angle of NRG = 60 degree. This investigation provides the essential aspects for a fundamental understanding of heat transport of NRG using microwave energy in industry.

Keywords: Electric field, Finite element method, Microwave energy, Natural rubber glove.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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Authors: Mohamed. A. Shrud, Ahmad H. Kharaz, Ahmed. S. Ashur, Ahmed Faris, Mustafa Benamar

Abstract:

This paper will focus on modeling, analysis and simulation of a 42V/14V dc/dc converter based architecture. This architecture is considered to be technically a viable solution for automotive dual-voltage power system for passenger car in the near further. An interleaved dc/dc converter system is chosen for the automotive converter topology due to its advantages regarding filter reduction, dynamic response, and power management. Presented herein, is a model based on one kilowatt interleaved six-phase buck converter designed to operate in a Discontinuous Conduction Mode (DCM). The control strategy of the converter is based on a voltagemode- controlled Pulse Width Modulation (PWM) with a Proportional-Integral-Derivative (PID). The effectiveness of the interleaved step-down converter is verified through simulation results using control-oriented simulator, MatLab/Simulink.

Keywords: Automotive, dc-to-dc power modules, design, interleaved, Matlab\Simulink and PID control.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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Authors: M.V. Shyla, K.B. Naidu

Abstract:

The objective of this paper is to develop a computational model of human nasal cavity from computed tomography (CT) scans using MIMICS software. Computational fluid dynamic techniques were employed to understand nasal airflow. Gambit and Fluent software was used to perform CFD simulation. Velocity profiles, iteration plots, pressure distribution, streamline and pathline patterns for steady, laminar airflow inside the human nasal cavity of healthy and also infected persons are presented in detail. The implications for olfaction are visualized. Results are validated with the available numerical and experimental data. The graphs reveal that airflow varies with different anatomical nasal structures and only fraction of the inspired air reaches the olfactory region. The Deviations in the results suggest that the treatment of infected volunteers will improve the olfactory function.

Keywords: CFD techniques, Finite Volume Method, Fluid dynamic sniffing, Human nasal cavity.

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Authors: Y. Li, Q. S. Zhang, H. Z. Huang, B. Y. Wu

Abstract:

The mechanism behind the electromigration and thermomigration failure in flip-chip solder joints with Cu-pillar bumps was investigated in this paper through using finite element method. Hot spot and the current crowding occurrs in the upper corner of copper column instead of solders of the common solder ball. The simulation results show that the change in thermal gradient is noticeable, which might greatly affect the reliability of solder joints with Cu-pillar bumps under current stressing. When the average applied current density is increased from 1×104 A/cm2 to 3×104 A/cm2 in solders, the thermal gradient would increase from 74 K/cm to 901 K/cm at an ambient temperature of 25°C. The force from thermal gradient of 901 K/cm can nearly induce thermomigration by itself. With the increase in applied current, the thermal gradient is growing. It is proposed that thermomigration likely causes a serious reliability issue for Cu column based interconnects.

Keywords: Simulation, Cu-pillar bumps, Electromigration, Thermomigration.

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Authors: Muhammad Marsudi, Hani Shafeek

Abstract:

The purpose of this paper is to simulate the production process of a metal stamping industry and to evaluate the utilization of the production line by using ARENA simulation software. The process time and the standard time for each process of the production line is obtained from data given by the company management. Other data are collected through direct observation of the line. There are three work stations performing ten different types of processes in order to produce a single product type. Arena simulation model is then developed based on the collected data. Verification and validation are done to the Arena model, and finally the result of Arena simulation can be analyzed. It is found that utilization at each workstation will increase if batch size is increased although throughput rate remains/is kept constant. This study is very useful for the company because the company needs to improve the efficiency and utilization of its production lines.

Keywords: Arena software, case study, production line, utilization.

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Authors: P. Bárta

Abstract:

Increasing demand on the performance of Subsea Production Systems (SPS) suggests a need for more detailed investigation of fluid behavior taking place in subsea equipment. Complete CFD cool down analyses of subsea equipment are very time demanding. The objective of this paper is to investigate a Locked CFD approach, which enables significant reduction of the computational time and at the same time maintains sufficient accuracy during thermal cool down simulations. The result comparison of a dead leg simulation using the Full CFD and the three LCFD-methods confirms the validity of the locked flow field assumption for the selected case. For the tested case the LCFD simulation speed up by factor of 200 results in the absolute thermal error of 0.5 °C (3% relative error), speed up by factor of 10 keeps the LCFD results within 0.1 °C (0.5 % relative error) comparing to the Full CFD.

Keywords: CFD, Locked Flow Field, Speed up of CFD simulation time, Subsea

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Authors: Ming-Hui Lee, Iau-Teh Wang

Abstract:

The innovative fuzzy estimator is used to estimate the ground motion acceleration of the retaining structure in this study. The Kalman filter without the input term and the fuzzy weighting recursive least square estimator are two main portions of this method. The innovation vector can be produced by the Kalman filter, and be applied to the fuzzy weighting recursive least square estimator to estimate the acceleration input over time. The excellent performance of this estimator is demonstrated by comparing it with the use of difference weighting function, the distinct levels of the measurement noise covariance and the initial process noise covariance. The availability and the precision of the proposed method proposed in this study can be verified by comparing the actual value and the one obtained by numerical simulation.

Keywords: Earthquake, Fuzzy Estimator, Kalman Filter, Recursive Least Square Estimator.

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: Image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation scheme, finite differences.

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Authors: R. Rezaeipour

Abstract:

One of the key aspects of power quality improvement in power system is the mitigation of voltage sags/swells and flicker. Custom power devices have been known as the best tools for voltage disturbances mitigation as well as reactive power compensation. Dynamic Voltage Restorer (DVR) which is the most efficient and effective modern custom power device can provide the most commercial solution to solve several problems of power quality in distribution networks. This paper deals with analysis and simulation technique of DVR based on instantaneous power theory which is a quick control to detect signals. The main purpose of this work is to remove three important disturbances including voltage sags/swells and flicker. Simulation of the proposed method was carried out on two sample systems by using Matlab software environment and the results of simulation show that the proposed method is able to provide desirable power quality in the presence of wide range of disturbances.

Keywords: DVR, Power quality, Voltage sags, Voltage swells, Flicker.

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Authors: P. Mohajeri Khameneh, I. Mirzaie, N. Pourmahmoud, M. Rahimi, S. Majidyfar

Abstract:

Three dimensional simulations in tube in tube heat exchangers are investigated numerically in this study. In these simulations forced convective heat transfer and laminar flow of single-phase water are considered. In order to measure heat transfer parameters in these heat exchangers, FLUENT CFD Solver is used in this numerical method. For the purpose of creating geometry and exert boundary and initial conditions in the present model, finite volume method in Computational Fluid Dynamics is used in this study. In the present study, at each Z-location, variation of local temperatures, heat flux and Nusselt number at the whole tube is investigated in detail. Thereafter, averaged computational Nusselt number in this model is calculated. In addition, conceivable pressure drops have been obtained at each Z-location in this model. Then, pressure drop values in the present model are explored. Finally, all the numerical results for this kind of heat exchanger will be discussed precisely.

Keywords: Heat exchanger, Laminar flow, CFD, Nusseltnumber, Tube in tube, pressure drop.

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Authors: Mark Watson, J.-F. Bousquet, Adam Forget

Abstract:

A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell’s equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coils may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.

Keywords: Magnetic Induction, FDTD, Underwater Communication, Sommerfeld.

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Authors: M. Sadeghi, A.H. Jafari, S.M.P. Firoozabadi

Abstract:

Deep Brain Stimulation or DBS is the second solution for Parkinson's Disease. Its three parameters are: frequency, pulse width and voltage. They must be optimized to achieve successful treatment. Nowadays it is done clinically by neurologists and there is not certain numerical method to detect them. The aim of this research is to introduce simulation and modeling of Parkinson's Disease treatment as a computational procedure to select optimum voltage. We recorded finger tremor signals of some Parkinsonian patients under DBS treatment at constant frequency and pulse width but variable voltages; then, we adapted a new model to fit these data. The optimum voltages obtained by data fitting results were the same as neurologists- commented voltages, which means modeling can be used as an engineering method to select optimum stimulation voltages.

Keywords: modeling, Deep Brain Stimulation, Parkinson'sdisease, tremor.

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Authors: Aliakbar Golshani, Armin Ramezanzad

Abstract:

Tensile strength which is an important parameter of the rock for engineering applications is difficult to measure directly through physical experiment (i.e. uniaxial tensile test). Therefore, indirect experimental methods such as Brazilian test have been taken into consideration and some relations have been proposed in order to obtain the tensile strength for rocks indirectly. In this research, to calculate numerically the tensile strength for granitic rocks, Particle Flow Code in three-dimension (PFC3D) software were used. First, uniaxial compression tests were simulated and the tensile strength was determined for Inada granite (from a quarry in Kasama, Ibaraki, Japan). Then, by simulating Brazilian test condition for Inada granite, the tensile strength was indirectly calculated again. Results show that the tensile strength calculated numerically agrees well with the experimental results obtained from uniaxial tensile tests on Inada granite samples.

Keywords: Numerical Simulation, PFC, Tensile Strength, Brazilian Test.

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Authors: Rooholah Hasanizadeh, Saadan Zokaei

Abstract:

In the context of sensor networks, where every few dB saving counts, the novel node cooperation schemes are reviewed where MIMO techniques play a leading role. These methods could be treated as joint approach for designing physical layer of their communication scenarios. Then we analyzed the BER performance of transmission diversity schemes under a general fading channel model and proposed a power allocation strategy to the transmitting sensor nodes. This approach is then compared to an equal-power assignment method and its performance enhancement is verified by the simulation. Another key point of the contribution lies in the combination of optimal power allocation and sensor nodes- cooperation in a transmission diversity regime (MISO). Numerical results are given through figures to demonstrate the optimality and efficiency of proposed combined approach.

Keywords: Optimal power allocation, cooperative MISO scheme, sensor networks, diversity branch.

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Authors: Boubekeur Dokkar, Nasreddine Chennouf, Noureddine Settou, Belkhir Negrou, Abdesslam Benmhidi

Abstract:

The optimal operation of proton exchange membrane fuel cell (PEMFC) requires good water management which is presented under two forms vapor and liquid. Moreover, fuel cells have to reach higher output require integration of some accessories which need electrical power. In order to analyze fuel cells operation and different species transport phenomena a biphasic mathematical model is presented by governing equations set. The numerical solution of these conservation equations is calculated by Matlab program. A multi-criteria optimization with weighting between two opposite objectives is used to determine the compromise solutions between maximum output and minimal stack size. The obtained results are in good agreement with available literature data.

Keywords: Biphasic model, PEM fuel cell, optimization, simulation, specie transport.

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