Search results for: surgical simulation.

Authors: Mingren Shi, Michael Renton

Abstract:

There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

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Authors: Cuiran Li, Jianli Xie, Chengshu Li

Abstract:

In the paper, the performance of quasi-synchronous CDMA (QS-CDMA) system, which can allow an increased timing error in synchronized access, is discussed. Average BER performance of the system is analyzed in the condition of different access timing error and different asynchronous users by simulation in AWGN channel. The results show that QS-CDMA system is shown to have great performance gain over the asynchronous system when access timing error is within a few chips and asynchronous users is tolerable. However, with access timing error increasing and asynchronous users increasing, the performance of QS-CDMA will degrade. Also, we can determine the number of tolerable asynchronous users for different access timing error by simulation figures.

Keywords: Code-division multiple access, Quasi-SynchronousCDMA, Access timing error

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Authors: Zarita Zainuddin, Kumatha Thinakaran, Mohammed Shuaib

Abstract:

In today-s modern world, the number of vehicles is increasing on the road. This causes more people to choose walking instead of traveling using vehicles. Thus, proper planning of pedestrians- paths is important to ensure the safety of pedestrians in a walking area. Crowd dynamics study the pedestrians- behavior and modeling pedestrians- movement to ensure safety in their walking paths. To date, many models have been designed to ease pedestrians- movement. The Social Force Model is widely used among researchers as it is simpler and provides better simulation results. We will discuss the problem regarding the ritual of circumambulating the Ka-aba (Tawaf) where the entrances to this area are usually congested which worsens during the Hajj season. We will use the computer simulation model SimWalk which is based on the Social Force Model to simulate the movement of pilgrims in the Tawaf area. We will first discuss the effect of uni and bi-directional flows at the gates. We will then restrict certain gates to the area as the entrances only and others as exits only. From the simulations, we will study the effect of the distance of other entrances from the beginning line and their effects on the duration of pilgrims circumambulate Ka-aba. We will distribute the pilgrims at the different entrances evenly so that the congestion at the entrances can be reduced. We would also discuss the various locations and designs of barriers at the exits and its effect on the time taken for the pilgrims to exit the Tawaf area.

Keywords: circumambulation, Ka'aba, pedestrian flow, SFM, Tawaf , entrance, exit

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Authors: M. Raciti Castelli, P. Cioppa, E. Benini

Abstract:

The flow field around a flat plate of infinite span has been investigated for several values of the angle of attack. Numerical predictions have been compared to experimental measurements, in order to examine the effect of turbulence model and grid resolution on the resultant aerodynamic forces acting on the plate. Also the influence of the free-stream turbulence intensity, at the entrance of the computational domain, has been investigated. A full campaign of simulations has been conducted for three inclination angles (9°, 15° and 30°), in order to obtain some practical guidelines to be used for the simulation of the flow field around inclined plates and discs.

Keywords: CFD, lift, drag, flat plate

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

Abstract:

In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

Abstract:

Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers’ equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile.

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Authors: Yiping Wang, Zhengqi Gu, Weiping Li, Xiaohui Lin

Abstract:

The aerodynamic noise radiation from a side view mirror (SVM) in the high-speed airflow is calculated by the combination of unsteady incompressible fluid flow analysis and acoustic analysis. The transient flow past the generic SVM is simulated with variable turbulence model, namely DES Detached Eddy Simulation and LES (Large Eddy Simulation). Detailed velocity vectors and contour plots of the time-varying velocity and pressure fields are presented along cut planes in the flow-field. Mean and transient pressure are also monitored at several points in the flow field and compared to corresponding experimentally data published in literature. The acoustic predictions made using the Ffowcs-Williams-Hawkins acoustic analogy (FW-H) and the boundary element (BEM).

Keywords: Aerodynamic noise, BEM, DES, FW-H acousticanalogy, LES

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Authors: João Vilas-Boas, Abdul Suleman, Luis Moreira

Abstract:

This research tested the performance of alternative warehouse designs concerning the picking process. The chosen performance measures were Travel Distance and Total Fulfilment Time. An explanatory case study was built up around a model implemented with SIMUL8. Hypotheses were set by selecting outcomes from the literature survey matching popular empirical findings. 17.4% reductions were found for Total Fulfilment Time and Resource Utilisation. The latter was then used as a proxy for operational efficiency. Literal replication of theoretical data-patterns was considered as an internal validity sign. Assessing the estimated changes benefits ahead of implementation was found to be a contribution to practice.

Keywords: Warehouse discrete-event simulation, Storage policy selection and assessment, Performance evaluation of order picking.

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Authors: Rakesh Kumar, Piush Verma, Yaduvir Singh

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A mobile ad hoc network (MANET) is a self configuring network, without any centralized control. The topology of this network is not always defined. The main objective of this paper is to introduce the fundamental concepts of MANETs to the researchers and practitioners, who are involved in the work in the area of modeling and simulation of MANETs. This paper begins with an overview of mobile ad hoc networks. Then it proceeds with the overview of routing protocols used in the MANETS, their properties and simulation methods. A brief tabular comparison between the routing protocols is also given in this paper considering different routing protocol parameters. This paper introduces a new routing scheme developed by the use of evolutionary algorithms (EA) and analytical hierarchy process (AHP) which will be used for getting the optimized output of MANET. In this paper cryptographic technique, ceaser cipher is also employed for making the optimized route secure.

Keywords: AHP, AODV, Cryptography, EA, MANET, Optimized output.

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Authors: L. Novakova-Marcincinova, J. Novak-Marcincin, M. Janak

Abstract:

The computer aided for design, analysis, control, visualization and simulation of robotized workcells is very interesting in this time. Computer Aided Robot Control (CARC) is a subsystem of the system CIM including the computer aided systems of all activities connected with visualization and working of robotized workcells. There are three basic ideas: current CAD/CAM/CAE systems for design and 3D visualization, special PC based control and simulation systems and Augmented Reality Aided Manufacturing (ARAM) systems. This paper describes example of Open Source software application that can to be utilized at planning of the robotized workcells, visualization and off-line programming the automated processes realized by authors.

Keywords: Intelligent control, augmented reality, robot.

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Authors: Xu Du, Aparna S. Varde

Abstract:

In this research, we propose to conduct diagnostic and predictive analysis about the key factors and consequences of urban population relocation. To achieve this goal, urban simulation models extract the urban development trends as land use change patterns from a variety of data sources. The results are treated as part of urban big data with other information such as population change and economic conditions. Multiple data mining methods are deployed on this data to analyze nonlinear relationships between parameters. The result determines the driving force of population relocation with respect to urban sprawl and urban sustainability and their related parameters. This work sets the stage for developing a comprehensive urban simulation model for catering to specific questions by targeted users. It contributes towards achieving sustainability as a whole.

Keywords: Data Mining, Environmental Modeling, Sustainability, Urban Planning.

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Authors: Salem Belhaj, Moncef Tagina

Abstract:

This paper is aimed at describing a delay-based endto- end (e2e) congestion control algorithm, called Very FAST TCP (VFAST), which is an enhanced version of FAST TCP. The main idea behind this enhancement is to smoothly estimate the Round-Trip Time (RTT) based on a nonlinear filter, which eliminates throughput and queue oscillation when RTT fluctuates. In this context, an evaluation of the suggested scheme through simulation is introduced, by comparing our VFAST prototype with FAST in terms of throughput, queue behavior, fairness, stability, RTT and adaptivity to changes in network. The achieved simulation results indicate that the suggested protocol offer better performance than FAST TCP in terms of RTT estimation and throughput.

Keywords: Fast tcp, RTT, delay estimation, delay-based congestion control, high speed TCP, large bandwidth delay product.

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Authors: Karel Frydrýšek, Pavel Koštial, Karla Barabaszová, Jana Kukutschová

Abstract:

This paper deals with a new way for designing external fixators applied in traumatology and orthopaedics. These fixators can be applied in the treatment of open and unstable fractures or for lengthening human or animal bones etc. The new design is based on the development of Ilizarov and other techniques (i.e. shape and weight optimalization based on composite materials, application of smart materials, nanotechnology, low x-ray absorption, antibacterial protection, patient's comfort, reduction in the duration of the surgical treatment, and cost).

Keywords: biomechanics, design, external fixators, newmaterials, traumatology

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Authors: Abdelghafour Galadi

Abstract:

In this paper, accurate power MOSFET models including quasi-saturation effect are presented. These models have no internal node voltages determined by the circuit simulator and use one JFET or one depletion mode MOSFET transistors controlled by an “effective” gate voltage taking into account the quasi-saturation effect. The proposed models achieve accurate simulation results with an average error percentage less than 9%, which is an improvement of 21 percentage points compared to the commonly used standard power MOSFET model. In addition, the models can be integrated in any available commercial circuit simulators by using their analytical equations. A description of the models will be provided along with the parameter extraction procedure.

Keywords: Power MOSFET, drift layer, quasi-saturation effect, SPICE model, circuit simulation.

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Authors: Srikanta Bose, Sudip K. Mazumder

Abstract:

We report here, the results of molecular dynamics simulation of p-doped (Ga-face)GaN over n-doped (Siface)( 0001)4H-SiC hetero-epitaxial material system with one-layer each of Ga-flux and (Al-face)AlN, as the interface materials, in the form of, the total Density of States (DOS). It is found that the total DOS at the Fermi-level for the heavily p-doped (Ga-face)GaN and ndoped (Si-face)4H-SiC hetero-epitaxial system, with one layer of (Al-face)AlN as the interface material, is comparatively higher than that of the various cases studied, indicating that there could be good vertical conduction across the (Ga-face)GaN over (Si-face)(0001)4HSiC hetero-epitaxial material system.

Keywords: Molecular dynamics, GaN, 4H-SiC, hetero-epitaxy.

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Authors: Tae Kyung Kim, Hee Suk Seo

Abstract:

Sensor networks are often deployed in unattended environments, thus leaving these networks vulnerable to false data injection attacks in which an adversary injects forged reports into the network through compromised nodes, with the goal of deceiving the base station or depleting the resources of forwarding nodes. Several research solutions have been recently proposed to detect and drop such forged reports during the forwarding process. Each design can provide the equivalent resilience in terms of node compromising. However, their energy consumption characteristics differ from each other. Thus, employing only a single filtering scheme for a network is not a recommendable strategy in terms of energy saving. It's very important the threshold determination for message authentication to identify. We propose the recursive contract net protocols which less energy level of terminal node in wireless sensor network.

Keywords: Data filtering, recursive CNP, simulation.

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Authors: H.-H. Doh, J.-M. Yu, Y.-J. Kwon, J.-H. Shin, H.-W. Kim, S.-H. Nam, D.-H. Lee

Abstract:

This paper suggests a decision tree based approach for flexible job shop scheduling with multiple process plans, i.e. each job can be processed through alternative operations, each of which can be processed on alternative machines. The main decision variables are: (a) selecting operation/machine pair; and (b) sequencing the jobs assigned to each machine. As an extension of the priority scheduling approach that selects the best priority rule combination after many simulation runs, this study suggests a decision tree based approach in which a decision tree is used to select a priority rule combination adequate for a specific system state and hence the burdens required for developing simulation models and carrying out simulation runs can be eliminated. The decision tree based scheduling approach consists of construction and scheduling modules. In the construction module, a decision tree is constructed using a four-stage algorithm, and in the scheduling module, a priority rule combination is selected using the decision tree. To show the performance of the decision tree based approach suggested in this study, a case study was done on a flexible job shop with reconfigurable manufacturing cells and a conventional job shop, and the results are reported by comparing it with individual priority rule combinations for the objectives of minimizing total flow time and total tardiness.

Keywords: Flexible job shop scheduling, Decision tree, Priority rules, Case study.

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Authors: Carmen Maria Moraru, Iuliana Stefan, Ovidiu Balteanu, Ciprian Bucur, Liviu Stefan, Anisia Bornea, Ioan Stefanescu

Abstract:

The implementation of the new software and hardware-s technologies for tritium processing nuclear plants, and especially those with an experimental character or of new technology developments shows a coefficient of complexity due to issues raised by the implementation of the performing instrumentation and equipment into a unitary monitoring system of the nuclear technological process of tritium removal. Keeping the system-s flexibility is a demand of the nuclear experimental plants for which the change of configuration, process and parameters is something usual. The big amount of data that needs to be processed stored and accessed for real time simulation and optimization demands the achievement of the virtual technologic platform where the data acquiring, control and analysis systems of the technological process can be integrated with a developed technological monitoring system. Thus, integrated computing and monitoring systems needed for the supervising of the technological process will be executed, to be continued with the execution of optimization system, by choosing new and performed methods corresponding to the technological processes within the tritium removal processing nuclear plants. The developing software applications is executed with the support of the program packages dedicated to industrial processes and they will include acquisition and monitoring sub-modules, named “virtually" as well as the storage sub-module of the process data later required for the software of optimization and simulation of the technological process for tritium removal. The system plays and important role in the environment protection and durable development through new technologies, that is – the reduction of and fight against industrial accidents in the case of tritium processing nuclear plants. Research for monitoring optimisation of nuclear processes is also a major driving force for economic and social development.

Keywords: Monitoring system, process simulation.

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Authors: Jairo Aparecido Martins, Estaner Claro Romão

Abstract:

This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: Aluminum, industrial clutch, static and dynamic loading, numerical simulation.

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Authors: S. Parasuraman

Abstract:

In this work, a new approach is proposed to control the manipulators for Humanoid robot. The kinematics of the manipulators in terms of joint positions, velocity, acceleration and torque of each joint is computed using the Denavit Hardenberg (D-H) notations. These variables are used to design the manipulator control system, which has been proposed in this work. In view of supporting the development of a controller, a simulation of the manipulator is designed for Humanoid robot. This simulation is developed through the use of the Virtual Reality Toolbox and Simulink in Matlab. The Virtual Reality Toolbox in Matlab provides the interfacing and controls to an environment which is developed based on the Virtual Reality Modeling Language (VRML). Chains of bones were used to represent the robot.

Keywords: Mobile robot, Robot Kinematics, Robot Navigation, MATLAB.

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Authors: Dongwon Lee, Eon Kyeong Joo

Abstract:

In this paper, the performance of three types of serial concatenated convolutional codes (SCCC) is compared and analyzed in additive white Gaussian noise (AWGN) channel. In Type I, only the parity bits of outer encoder are passed to inner encoder. In Type II and Type III, both the information bits and the parity bits of outer encoder are transferred to inner encoder. As results of simulation, Type I shows the best bit error rate (BER) performance at low signal-to-noise ratio (SNR). On the other hand, Type III shows the best BER performance at high SNR in AWGN channel. The simulation results are analyzed using the distance spectrum.

Keywords: Distance spectrum, MAP algorithm, SCCC.

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Authors: Nitish Sharma, G. G. Karady

Abstract:

This paper presents a scheme for the protection of loop system from all type of faults using the direction of fault current. The presence of distributed generation in today’s system increases the complexity of fault detection as the power flow is bidirectional. Hence, protection scheme specific to this purpose needs to be developed. This paper shows a fast protection scheme using communication which can be fiber optic or wireless. In this paper, the possibility of wireless communication for protection is studied to exchange the information between the relays. The negative sequence and positive sequence directional elements are used to determine the direction of fault current. A PSCAD simulation is presented and validated using commercial SEL relays.

Keywords: Smart grid protection, pilot protection, power system simulation, wireless communication.

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Authors: Sérgio S. de Jesus, Edgar Leonardo Martínez, Aulus R.R. Binelli, Aline Santana, Rubens Maciel Filho

Abstract:

The speed profiles, gas holdup (e_G) and global oxygen transfer coefficient (k_La) from a stirred airlift bioreactor using water as the fluid model, was investigated by computational fluid dynamics modeling. The parameters predicted by the computer model were validated with the experimental dates. The CFD results were very close to those obtained experimentally. During the simulation it was verified a prevalent impeller effect at low speeds, propelling a large volume of fluid against the walls of the vessel, which without recirculation, results in low values of e_G and k_La; however, by increasing air velocity, the impeller effect is smaller with the air flow being greater, in the region of the riser, causing fluid recirculation, which explains the increase in e_G and k_La.

Keywords: CFD, Hydrodynamics, Mass transfer, Stirred airlift bioreactor.

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Authors: Li Zhu, Binghua Wang, Yong Sun

Abstract:

China is experiencing the rural development process, with the agritourism complex becoming one of the significant modes. Therefore, it is imperative to understand the energy performance of agritourism complex. This study focuses on a typical case of the agritourism complex and simulates the energy consumption performance on condition of the regular energy system. It was found that HVAC took 90% of the whole energy demand range. In order to optimize the energy supply structure, the hierarchical analysis was carried out on the level of architecture with three main factors such as construction situation, building types and energy demand types. Finally, the energy planning suggestion of the agritourism complex was put forward and the relevant results were obtained.

Keywords: Agritourism complex, energy planning, energy demand simulation, hierarchical structure model.

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Authors: Akram Golestani, Mohammad Kazemeini, Farhad Khorasheh, Moslem Fattahi

Abstract:

Modeling and simulation of fixed bed three-phase catalytic reactors are considered for wet air catalytic oxidation of phenol to perform a comparative numerical analysis between tricklebed and packed-bubble column reactors. The modeling involves material balances both for the catalyst particle as well as for different fluid phases. Catalyst deactivation is also considered in a transient reactor model to investigate the effects of various parameters including reactor temperature on catalyst deactivation. The simulation results indicated that packed-bubble columns were slightly superior in performance than trickle beds. It was also found that reaction temperature was the most effective parameter in catalyst deactivation.

Keywords: Catalyst deactivation, Catalytic wet air oxidation, Trickle-bed, Wastewater.

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Authors: Liu-Chao Qiu

Abstract:

The damage caused by surge waves generated in water bodies by flow-like landslides can be very high in terms of human lives and economic losses. The complicated phenomena occurred in this highly unsteady process are difficult to model because three interacting phases: air, water and sediment are involved. The problem therefore is challenging since the effects of non-Newtonian fluid describing the rheology of the flow-like landslides, multi-phase flow and free surface have to be included in the simulation. In this work, the commercial computational fluid dynamics (CFD) package FLUENT is used to model the surge waves due to flow-like landslides. The comparison between the numerical results and experimental data reported in the literature confirms the accuracy of the method.

Keywords: Flow-like landslide, surge wave, VOF, non-Newtonian fluids, multi-phase flows, free surface flow.

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Authors: Hou Youfu, Wang Daoming, Meng Qingrui

Abstract:

To reveal the temperature field distribution of disc brake in downward belt conveyor, mathematical models of heat transfer for disc brake were established combined with heat transfer theory. Then, the simulation process was stated in detail and the temperature field of disc brake under conditions of dynamic speed and dynamic braking torque was numerically simulated by using ANSYS software. Finally the distribution and variation laws of temperature field in the braking process were analyzed. Results indicate that the maximum surface temperature occurs at a time before the brake end and there exist large temperature gradients in both radial and axial directions, while it is relatively small in the circumferential direction.

Keywords: Downward belt conveyor, Disc brake, Temperature field, Numerical simulation.

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Authors: Masataka Ohta

Abstract:

The Internet telephony employs a new type of Internet communication on which a mutual communication is realized by establishing sessions. Session Initiation Protocol (SIP) is used to establish sessions between end-users. For unreliable transmission (UDP), SIP message should be retransmitted when it is lost. The retransmissions increase a load of the SIP signaling network, and sometimes lead to performance degradation when a network is overloaded. The paper proposes an overload control for a SIP signaling network to protect from a performance degradation. Introducing two thresholds in a queue of a SIP proxy server, the SIP proxy server detects a congestion. Once congestion is detected, a SIP signaling network restricts to make new calls. The proposed overload control is evaluated using the network simulator (ns-2). With simulation results, the paper shows the proposed overload control works well.

Keywords: SIP signalling congestion overload control retransmission throughput simulation.

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Authors: F. Z. Doğru, O. Arslan

Abstract:

In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. The simulation results show that the proposed robust estimators generally outperform the classical estimators in terms of bias and root mean square errors when there are outliers in data.

Keywords: Burr XII distribution, robust estimator, M-estimator, maximum likelihood, least squares.

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