Search results for: implicit fracture model

Authors: Mehrdad Shahrbanozadeh, Gholam Abbas Barani, Saeed Shojaee

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In this study, a finite element (Seep3D model) and an artificial neural network (ANN) model were developed to simulate flow through dam foundation. Seep3D model is capable of simulating three-dimensional flow through a heterogeneous and anisotropic, saturated and unsaturated porous media. Flow through the Shahid Abbaspour dam foundation has been used as a case study. The FEM with 24960 triangular elements and 28707 nodes applied to model flow through foundation of this dam. The FEM being made denser in the neighborhood of the curtain screen. The ANN model developed for Shahid Abbaspour dam is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning. The water level elevations of the upstream and downstream of the dam have been used as input variables and the piezometric heads as the target outputs in the ANN model. The two models are calibrated and verified using the Shahid Abbaspour’s dam piezometric data. Results of the models were compared with those measured by the piezometers which are in good agreement. The model results also revealed that the ANN model performed as good as and in some cases better than the FEM.

Keywords: seepage, dam foundation, finite element method, neural network, seep 3D model

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Authors: Luis Marquez, Ge Zhu, Vikas Srivastava

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High-density polyethylene (HDPE) is one of the most commonly used thermoplastic polymer materials for water and gas pipelines. Slow crack growth failure is a well-known phenomenon in high-density polyethylene material and causes brittle failure well below the yield point with no obvious sign. The failure of transportation pipelines can cause catastrophic environmental and economic consequences. Using the non-destructive testing method to predict slow crack growth failure behavior is the primary preventative measurement employed by the pipeline industry but is often costly and time-consuming. Phenomenological slow crack growth models are useful to predict the slow crack growth behavior in the polymer material due to their ability to evaluate slow crack growth under different temperature and loading conditions. We developed a quantitative method to assess the slow crack growth behavior in the high-density polyethylene pipeline material under different thermal conditions based on existing physics-based phenomenological models. We are also working on developing an experimental protocol and quantitative model that can address slow crack growth behavior under different chemical exposure conditions to improve the safety, reliability, and resilience of HDPE-based pipeline infrastructure.

Keywords: mechanics of materials, physics-based modeling, civil engineering, fracture mechanics

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Authors: Mohsen Ziaee

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In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: scheduling, flexible job shop, makespan, mixed integer linear programming

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Authors: D. Mohammadzadeh S., J. Bolouri Bazaz

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This paper presents a new prediction model for compression index of fine-grained soils using multi-gene genetic programming (MGGP) technique. The proposed model relates the soil compression index to its liquid limit, plastic limit and void ratio. Several laboratory test results for fine-grained were used to develop the models. Various criteria were considered to check the validity of the model. The parametric and sensitivity analyses were performed and discussed. The MGGP method was found to be very effective for predicting the soil compression index. A comparative study was further performed to prove the superiority of the MGGP model to the existing soft computing and traditional empirical equations.

Keywords: new prediction model, compression index soil, multi-gene genetic programming, MGGP

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Authors: Gang Liu, Can Wang, Runnan Zhang, Quan Wang, Huimin Song, Shaomin Ji

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Biba model can protect information integrity but might deny various non-malicious access requests of the subjects, thereby decreasing the availability in the system. Therefore, a mechanism that allows exceptional access control is needed. Break the Glass (BTG) strategies refer an efficient means for extending the access rights of users in exceptional cases. These strategies help to prevent a system from stagnation. An approach is presented in this work for integrating Break the Glass strategies into the Biba model. This research proposes a model, BTG-Biba, which provides both an original Biba model used in normal situations and a mechanism used in emergency situations. The proposed model is context aware, can implement a fine-grained type of access control and primarily solves cross-domain access problems. Finally, the flexibility and availability improvement with the use of the proposed model is illustrated.

Keywords: Biba model, break the glass, context, cross-domain, fine-grained

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Authors: Ferhat Demir

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Even if strategic management is highly critical for all types of organizations, only a few maturity models have been proposed in business literature for the area of strategic management activities. This paper updates previous studies and presents a new conceptual model for assessing the maturity of strategic management in any organization. Strategic management maturity model (S-3M) is basically composed of 6 maturity levels with 7 dimensions. The biggest contribution of S-3M is to put innovation into agenda of strategic management. The main objective of this study is to propose a model to align innovation with business strategies. This paper suggests that innovation (breakthrough new products/services and business models) is the only way of creating sustainable growth and strategy studies cannot ignore this aspect. Maturity models should embrace innovation to respond dynamic business environment and rapidly changing customer behaviours.

Keywords: strategic management, innovation, business model, maturity model

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Authors: Muhammad Tariq, Hammad Tahir, Fawwad Mahmood Butt

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Purpose: This study attempts to examine the best forecasting methodologies in the time series. The time series forecasting models such as VAR, ARCH and the ARMA are considered for the analysis. Methodology: The Bench Marks or the parameters such as Adjusted R square, F-stats, Durban Watson, and Direction of the roots have been critically and empirically analyzed. The empirical analysis consists of time series data of Consumer Price Index and Closing Stock Price. Findings: The results show that the VAR model performed better in comparison to other models. Both the reliability and significance of VAR model is highly appreciable. In contrary to it, the ARCH model showed very poor results for forecasting. However, the results of ARMA model appeared double standards i.e. the AR roots showed that model is stationary and that of MA roots showed that the model is invertible. Therefore, the forecasting would remain doubtful if it made on the bases of ARMA model. It has been concluded that VAR model provides best forecasting results. Practical Implications: This paper provides empirical evidences for the application of time series forecasting model. This paper therefore provides the base for the application of best time series forecasting model.

Keywords: forecasting, time series, auto regression, ARCH, ARMA

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Authors: Athmane Bakhta, Sebastien Leclaire, David Vidal, Francois Bertrand, Mohamed Cheriet

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This work presents a new three-dimensional variational model proposed for the simulation of ink seepage into paper sheets at the fiber level. The model, inspired by the Hising model, takes into account a finite volume of ink and describes the system state through gravity, cohesion, and adhesion force interactions. At the mesoscopic scale, the paper substrate is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Besides, a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters, and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.

Keywords: fibrous media, lattice Boltzmann, modelling and simulation, Monte Carlo, variational model

Procedia PDF Downloads 134

Authors: Suparman

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Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: piecewise regression, bayesian, reversible jump MCMC, segmentation

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Authors: Batuhan Kocaoglu

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Although using powerful systems like ERP (Enterprise Resource Planning), companies still cannot benchmark their processes and measure their process performance easily based on predefined SCOR (Supply Chain Operation References) terms. The purpose of this research is to identify common and corresponding processes to present a conceptual model to model and measure the purchasing process of an organization. The main steps for the research study are: Literature review related to 'procure to pay' process in ERP system; Literature review related to 'sourcing' process in SCOR model; To develop a conceptual model integrating 'sourcing' of SCOR model and 'procure to pay' of ERP model. In this study, we examined the similarities and differences between these two models. The proposed framework is based on the assumptions that are drawn from (1) the body of literature, (2) the authors’ experience by working in the field of enterprise and logistics information systems. The modeling framework provides a structured and systematic way to model and decompose necessary information from conceptual representation to process element specification. This conceptual model will help the organizations to make quality purchasing system measurement instruments and tools. And offered adaptation issues for ERP systems and SCOR model will provide a more benchmarkable and worldwide standard business process.

Keywords: SCOR, ERP, procure to pay, sourcing, reference model

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Authors: M. Kumpugdee-Vollrath, T. G. D. Phu, M. Helmis

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A suitable model membrane to study the pharmacological effect of pharmaceutical products is human stratum corneum because this layer of human skin is the outermost layer and it is an important barrier to be passed through. Other model membranes which were also used are for example skins from pig, mouse, reptile or fish. We are interested in fish skins in this project. The advantages of the fish skins are, that they can be obtained from the supermarket or fish shop. However, the fish skins should be freshly prepared and used directly without storage. In order to understand the effect of different model drugs e.g. lidocaine HCl, resveratrol, paracetamol, ibuprofen, acetyl salicylic acid on the properties of the model membrane from various types of fishes e.g. trout, salmon, cod, plaice permeation tests were performed and differential scanning calorimetry was applied.

Keywords: fish skin, model membrane, permeation, DSC, lidocaine HCl, resveratrol, paracetamol, ibuprofen, acetyl salicylic acid

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Authors: Rahele Mosleh

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This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.

Keywords: global stability, invariant solutions, Lyapunov function, stationary points

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Authors: Sina Saadati, Mohammadreza Razzazi

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Since Java is an object-oriented language, It can be used to solve a wide range of problems. One of the considerable usages of this language can be found in Agent-based modeling and simulation. Despite the significant power of Java, There is not an easy method to render a 3-dimensional human model. In this article, we are about to develop a library which helps modelers present a 3D human model and control it with Java. The library runs two server programs. The first one is a web page server that can connect to any browser and present an HTML code. The second server connects to the browser and controls the movement of the model. So, the modeler will be able to develop a simulation and display a good-looking human model without any knowledge of any graphical tools.

Keywords: agent-based modeling and simulation, human model, graphics, Java, distributed systems

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Authors: Jeffrey Tzu-Hao Tsai, Yi-Shan Wong

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This article proposes a cohort-age-period (CAP) model to characterize multi-population mortality processes using cohort, age, and period variables. Distinct from the factor-based Lee-Carter-type decomposition mortality model, this approach is empirically based and includes the age, period, and cohort variables into the equation system. The model not only provides a fruitful intuition for explaining multivariate mortality change rates but also has a better performance in forecasting future patterns. Using the US and the UK mortality data and performing ten-year out-of-sample tests, our approach shows smaller mean square errors in both countries compared to the models in the literature.

Keywords: longevity risk, stochastic mortality model, multivariate mortality rate, risk management

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Authors: Hadi Farhadian, Homayoon Katibeh

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Groundwater inflow to the tunnels is one of the most important problems in tunneling operation. The objective of this study is the investigation of model dimension effects on tunnel inflow assessment in discontinuous rock masses using numerical modeling. In the numerical simulation, the model dimension has an important role in prediction of water inflow rate. When the model dimension is very small, due to low distance to the tunnel border, the model boundary conditions affect the estimated amount of groundwater flow into the tunnel and results show a very high inflow to tunnel. Hence, in this study, the two-dimensional universal distinct element code (UDEC) used and the impact of different model parameters, such as tunnel radius, joint spacing, horizontal and vertical model domain extent has been evaluated. Results show that the model domain extent is a function of the most significant parameters, which are tunnel radius and joint spacing.

Keywords: water inflow, tunnel, discontinues rock, numerical simulation

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Authors: D. A. Carnegie

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Whilst there is a movement towards increased digital augmentation in order to facilitate effective tertiary learning, this must come with an awareness of the limitations of such an approach. Learning is best achieved in an environment that includes their learning peers where difficulties can be shared and learning enabled. Policy that advocates for digital technology in place of a physical classroom is dangerous and is often driven by financial concerns rather than pedagogical ones. In this paper, a mostly digital-less form of teaching is presented – one that has proven to be extremely effective. Implicit is anecdotal evidence that student prefer the old overhead transparencies to PowerPoint presentations. Varying and reinforcing assessment, facilitation of effective note-taking, and just actively engaging with students is at the core of a good tertiary education experience. Digital techniques can augment and complement, but not replace these core personal teaching requirements.

Keywords: engineering education, active classroom engagement, effective note taking, reinforcing assessment

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Authors: Othman Y. Alothman

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The study aims to investigate the effects of blend ratio, VA content and temperature on the rheological properties of PPEVA blends. The results show that all pure polymers and their blends show typical shear thinning behaviour. All neat polymers exhibit power-low type flow behaviour, with the viscosity order as EVA328 > EVA206 > PP in almost all frequency ranges. As temperature increases, the viscosity of all polymers decreases as expected, and the viscosity becomes more sensitive to the addition of EVA. Two different regions can be observed on the flow curve of some of the polymers and their blends, which is thought to be due to slip-stick transition or melt fracture.

Keywords: polypropylene, ethylene vinyl acetate, blends, rheological properties

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Authors: Thien X. Dinh, Peter Witt

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A one-dimensional model for the simulation of condensation and solidification of a metallurgical vapor in the mixture of gas during supersonic expansion is presented. In the model, condensation is based on critical nucleation and drop-growth theory. When the temperature falls below the supercooling point, all the formed liquid droplets in the condensation phase are assumed to solidify at an infinite rate. The model was verified with a Computational Fluid Dynamics simulation of magnesium vapor condensation and solidification. The obtained results are in reasonable agreement with CFD data. Therefore, the model is a promising, efficient tool for use in the design process for supersonic nozzles applied in mineral processes since it is faster than the CFD counterpart by an order of magnitude.

Keywords: condensation, metallurgical flow, solidification, supersonic expansion

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Authors: Meriem Mossaddek, El Mehdi Laadissi, El Mehdi Loualid, Chouaib Ennawaoui, Sohaib Bouzaid, Abdelowahed Hajjaji

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An electrochemical system is a subset of mechatronic systems that includes a wide variety of batteries and nickel-cadmium, lead-acid batteries, and lithium-ion. Those structures have several non-linear behaviors and uncertainties in their running range. This paper studies an effective technique for modeling Lithium-Ion (Li-Ion) batteries using a Nonlinear Auto-Regressive model with exogenous input (NARX). The Artificial Neural Network (ANN) is trained to employ the data collected from the battery testing process. The proposed model is implemented on a Li-Ion battery cell. Simulation of this model in MATLAB shows good accuracy of the proposed model.

Keywords: lithium-ion battery, neural network, energy storage, battery model, nonlinear models

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Authors: Rose J. Thazhathukunnel, A. G. Smitha

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In the wake of social development, humans overlook the ideal physical appearance, and there is an increasing trend of criticising other’s bodies or offering tips to hide imperfections. Social appearance anxiety demonstrates the association with body dissatisfaction and disordered eating behavior. In this study, we examined the hypothesis that social appearance anxiety, body dissatisfaction, and disordered eating behavior would predict the relation between each among cancer survivors. It was observed that implicit belief to be thin was more pronounced in people with low body dissatisfaction than those with high body dissatisfaction. Results of the study indicated that overall body dissatisfaction and social appearance anxiety were correlated with disordered eating behavior for both men and women cancer survivors of all ages.

Keywords: social appearance anxiety, body dissatisfaction, disordered eating behavior, cancer survivors

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Authors: Chayaporn Kaensar

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Recently, Job Recommender Systems have gained much attention in industries since they solve the problem of information overload on the recruiting website. Therefore, we proposed Extended Personalized Job System that has the capability of providing the appropriate jobs for job seeker and recommending some suitable information for them using Data Mining Techniques and Dynamic User Profile. On the other hands, company can also interact to the system for publishing and updating job information. This system have emerged and supported various platforms such as web application and android mobile application. In this paper, User profiles, Implicit User Action, User Feedback, and Clustering Techniques in WEKA libraries have gained attention and implemented for this application. In additions, open source tools like Yii Web Application Framework, Bootstrap Front End Framework and Android Mobile Technology were also applied.

Keywords: recommendation, user profile, data mining, web and mobile technology

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Authors: Bijit Kalita, K. V. N. Surendra

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The pulley works under both compressive loading due to contacting belt in tension and central torque due to cause rotation. In a power transmission system, the belt pulley assemblies offer a contact problem in the form of two mating cylindrical parts. In this work, we modeled a pulley as a heavy two-dimensional circular disk. Stress analysis due to contact loading in the pulley mechanism is performed. Finite element analysis (FEA) is conducted for a pulley to investigate the stresses experienced on its inner and outer periphery. In most of the heavy-duty applications, most frequently used mechanisms to transmit power in applications such as automotive engines, industrial machines, etc. is Belt Drive. Usually, very heavy circular disks are used as pulleys. A pulley could be entitled as a drum and may have a groove between two flanges around the circumference. A rope, belt, cable or chain can be the driving element of a pulley system that runs over the pulley inside the groove. A pulley is experienced by normal and shear tractions on its contact region in the process of motion transmission. The region may be belt-pulley contact surface or pulley-shaft contact surface. In 1895, Hertz solved the elastic contact problem for point contact and line contact of an ideal smooth object. Afterward, this hypothesis is generally utilized for computing the actual contact zone. Detailed stress analysis in such contact region of such pulleys is quite necessary to prevent early failure. In this paper, the results of the finite element analyses carried out on the compressed disk of a belt pulley arrangement using fracture mechanics concepts are shown. Based on the literature on contact stress problem induced in the wide field of applications, generated stress distribution on the shaft-pulley and belt-pulley interfaces due to the application of high-tension and torque was evaluated in this study using FEA concepts. Finally, the results obtained from ANSYS (APDL) were compared with the Hertzian contact theory. The study is mainly focused on the fatigue life estimation of a rotating part as a component of an engine assembly using the most famous Paris equation. Digital Image Correlation (DIC) analyses have been performed using the open-source software. From the displacement computed using the images acquired at a minimum and maximum force, displacement field amplitude is computed. From these fields, the crack path is defined and stress intensity factors and crack tip position are extracted. A non-linear least-squares projection is used for the purpose of the estimation of fatigue crack growth. Further study will be extended for the various application of rotating machinery such as rotating flywheel disk, jet engine, compressor disk, roller disk cutter etc., where Stress Intensity Factor (SIF) calculation plays a significant role on the accuracy and reliability of a safe design. Additionally, this study will be progressed to predict crack propagation in the pulley using maximum tangential stress (MTS) criteria for mixed mode fracture.

Keywords: crack-tip deformations, contact stress, stress concentration, stress intensity factor

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Authors: Asaiel Alohaly

Abstract:

A theoretical framework for corporate governance is needed to bridge the gap between the corporate governance of private companies and State-owned Enterprises (SOEs). The two dominant models, being shareholder and stakeholder, do not always address the specific requirements and challenges posed by ‘hybrid’ companies; namely, previously national bodies that have been privatised bffu t where the government retains significant control or holds a majority of shareholders. Thus, an exploratory theoretical study is needed to identify how ‘hybrid’ companies should be defined and why the state model should be acknowledged since it is the less conspicuous model in comparison with the shareholder and stakeholder models. This research focuses on ‘the state model of corporate governance to understand the complex ownership, control pattern, goals, and corporate governance of these hybrid companies. The significance of this research lies in the fact that there is a limited available publication on the state model. The outcomes of this research are as follows. It became evident that the state model exists in the ecosystem. However, corporate governance theories have not extensively covered this model. Though, there is a lot being said about it by OECD and the World Bank. In response to this gap between theories and industry practice, this research argues for the state model, which proceeds from an understanding of the institutionally embedded character of hybrid companies where the government is either a majority of the total shares or a controlling shareholder.

Keywords: corporate governance, control, shareholders, state model

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Authors: Bin Wang, Hengyu Ji, Zhifeng Ye

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Fuel Metering Unit (FMU) in fuel system of an aeroengine sometimes has direct influence on the engine performance, which is neglected for the sake of easy access to mathematical model of the engine in most cases. In order to verify the influence of FMU on an engine model, this paper presents a co-simulation of a stepping motor driven FMU (digital FMU) in a turboshaft aeroengine, using AMESim and MATLAB to obtain the steady and dynamic characteristics of the FMU. For this method, mechanical and hydraulic section of the unit is modeled through AMESim, while the stepping motor is mathematically modeled through MATLAB/Simulink. Combining these two sub-models yields an AMESim/MATLAB co-model of the FMU. A simplified component level model for the turboshaft engine is established and connected with the FMU model. Simulation results on the full model show that the engine model considering FMU characteristics describes the engine more precisely especially in its transition state. An FMU dynamics will cut down the rotation speed of the high pressure shaft and the inlet pressure of the combustor during the step response. The work in this paper reveals the impact of FMU on engine operation characteristics and provides a reference to an engine model for ground tests.

Keywords: fuel metering unit, stepping motor, AMESim/Matlab, full digital simulation

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Authors: Abdelraheem M. Aly, Minh Tuan Nguyen, Sang-Wook Lee

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The incompressible smoothed particle hydrodynamics (ISPH) is used to simulate impact free surface flows. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. The current ISPH method is applied to simulate dam break flow over an inclined plane with different inclination angles. The effects of inclination angle in the velocity of wave front and pressure distribution is discussed. The impact of circular cylinder over water in tank has also been simulated using ISPH method. The computed pressures on the solid boundaries is studied and compared with the experimental results.

Keywords: incompressible smoothed particle hydrodynamics, free surface flow, inclined plane, water entry impact

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Authors: A. L. Qureshi, A. A. Mahessar, A. Baloch

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Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. However, it is difficult to find analytical solution of these complex non-linear equations. Hence, verification of the numerical model should be carried out against field data and numerical predictions. This paper presents the verification of developed finite element model applying for unsteady flow in the open channels. The results of a proposed model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29 km at both sites (15 km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400 km downstream from Sukkur barrage, which demonstrates accurate model predictions with observed daily discharges. Hence, this model may be utilized for predicting and issuing flood warnings about flood hazardous in advance.

Keywords: finite element method, Preissmann scheme, HEC-RAS, flood forecasting, Indus river

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Authors: Zongjie Wang, Zhizhong Guo

Abstract:

While the regular optimal power flow model focuses on a single time scan, the optimization of power systems is typically intended for a time duration with respect to a desired objective function. In this paper, a temporal optimal power flow model for a time period is proposed. To reduce the computation burden needed for calculating temporal optimal power flow, a characteristic optimal power flow model is proposed, which employs different characteristic load patterns to represent the objective function and security constraints. A numerical method based on the interior point method is also proposed for solving the characteristic optimal power flow model. Both the temporal optimal power flow model and characteristic optimal power flow model can improve the systems’ desired objective function for the entire time period. Numerical studies are conducted on the IEEE 14 and 118-bus test systems to demonstrate the effectiveness of the proposed characteristic optimal power flow model.

Keywords: optimal power flow, time period, security, economy

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Authors: Li Donghong, Peng Fuyang, Yang Guanghua, Su Xiaoyan

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Using open source code is a popular method of software development. How to evaluate the quality of software becomes more important. This paper introduces an evaluation model. The model evaluates the quality from four dimensions: technology, production, management, and development. Each dimension includes many indicators. The weight of indicator can be modified according to the purpose of evaluation. The paper also introduces a method of using the model. The evaluating result can provide good advice for evaluating or purchasing the software.

Keywords: evaluation model, software quality, open source code, evaluation indicator

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Authors: A. Amar

Abstract:

The angular distributions of the nuclear systems under consideration have been analyzed in the framework of the optical model (OM), where the real part was taken in the crystal model form. A crystal model (CM) has been applied to deuteron elastically scattered by ⁶,⁷Li and ⁹Be. A crystal model (CM) + distorted-wave Born approximation (DWBA) + dynamic polarization potential (DPP) potential has been applied to deuteron elastically scattered by ⁶,⁷Li and 9Be. Also, a crystal model has been applied to ⁶Li elastically scattered by ¹⁶O and ²⁸Sn in addition to the ⁷Li+⁷Li system and the ¹²C(alpha,⁸Be) ⁸Be reaction. The continuum-discretized coupled-channels (CDCC) method has been applied to the ⁷Li+⁷Li system and agreement between the crystal model and the continuum-discretized coupled-channels (CDCC) method has been observed. In general, the models succeeded in reproducing the differential cross sections at the full angular range and for all the energies under consideration.

Keywords: optical model (OM), crystal model (CM), distorted-wave born approximation (DWBA), dynamic polarization potential (DPP), the continuum-discretized coupled-channels (CDCC) method, and deuteron elastically scattered by ⁶, ⁷Li and ⁹Be

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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