Search results for: elastoplastic spring model

Authors: Kazeem K. Adewole, Julia M. Race, Steve J. Bull

Abstract:

The fracture performance of steel wires for civil engineering applications remains a major concern in civil engineering construction and maintenance of wire reinforced structures. The need to employ approaches that simulate micromechanical material processes which characterizes fracture in civil structures has been emphasized recently in the literature. However, choosing from the numerous micromechanics-based fracture models, and identifying their applicability and reliability remains an issue that still needs to be addressed in a greater depth. Laboratory tensile testing and finite element tensile testing simulations with the shear, ductile and Gurson-Tvergaard-Needleman’s micromechanics-based models conducted in this work reveal that the shear fracture model is an appropriate fracture model to predict the fracture performance of steel wires used for civil engineering applications. The need to consider the capability of the micromechanics-based fracture model to predict the “cup and cone” fracture exhibited by the wire in choosing the appropriate fracture model is demonstrated.

Keywords: Fracture performance, FE simulation, Shear fracture model, Ductile fracture model, Gurson-Tvergaard-Needleman fracture model, Wires.

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Authors: Attila Vámosi, Tamás Mankovits, Dávid Huri, Imre Kocsis, Tamás Szabó

Abstract:

Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. For example rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. The shape optimization problem of rubber parts led to the study of FEM based calculation processes. This type of problems was posed and investigated by several authors. In this paper the time demand of certain calculation methods are studied and the possibilities of time reduction is presented.

Keywords: Rubber bumper, data acquisition, finite element analysis, support vector regression.

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Authors: Karina Natali, Wei-Hwa Chiang

Abstract:

This study examines the stack ventilation performance of an office building located in Taipei, Taiwan. Atriums in this building act as stacks that facilitate buoyancy-driven ventilation. Computational Fluid Dynamic (CFD) simulations are used to identify interior airflow patterns, and then used these patterns to assess the building’s heat expulsion efficiency. Ambient temperatures of 20°C were adopted as the typical seasonal spring temperature range in Taipei. Further, “zero-wind” conditions are established to ensure simulation results reflected only the buoyancy effect. After checking results against neutral pressure level (NPL) level, airflow, air velocity, and indoor temperature stratification, the lower stack is modified to reduce the NPL in order to remove heat accumulated on the top floor.

Keywords: Natural ventilation, side outlet, stack effect, thermal comfort.

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Authors: Costas S. Iliopoulos, Spiros Michalakopoulos

Abstract:

A new, combinatorial model for analyzing and inter- preting an electrocardiogram (ECG) is presented. An application of the model is QRS peak detection. This is demonstrated with an online algorithm, which is shown to be space as well as time efficient. Experimental results on the MIT-BIH Arrhythmia database show that this novel approach is promising. Further uses for this approach are discussed, such as taking advantage of its small memory requirements and interpreting large amounts of pre-recorded ECG data.

Keywords: Combinatorics, ECG analysis, MIT-BIH Arrhythmia Database, QRS Detection, String Algorithms

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Authors: M.Sujaritha, S. Annadurai

Abstract:

An adaptive spatial Gaussian mixture model is proposed for clustering based color image segmentation. A new clustering objective function which incorporates the spatial information is introduced in the Bayesian framework. The weighting parameter for controlling the importance of spatial information is made adaptive to the image content to augment the smoothness towards piecewisehomogeneous region and diminish the edge-blurring effect and hence the name adaptive spatial finite mixture model. The proposed approach is compared with the spatially variant finite mixture model for pixel labeling. The experimental results with synthetic and Berkeley dataset demonstrate that the proposed method is effective in improving the segmentation and it can be employed in different practical image content understanding applications.

Keywords: Adaptive; Spatial, Mixture model, Segmentation, Color.

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Authors: Jiashang Jiang

Abstract:

Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

Keywords: Model updating, iterative algorithm, damped structural system, optimal approximation.

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Authors: Li Yu, Chenlu Jiao, Hongrun Xin, Yan Wang, Kaiyang Wang

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In order to study the impact of various factors on the housing price, we propose to build different prediction models based on deep learning to determine the existing data of the real estate in order to more accurately predict the housing price or its changing trend in the future. Considering that the factors which affect the housing price vary widely, the proposed prediction models include two categories. The first one is based on multiple characteristic factors of the real estate. We built Convolution Neural Network (CNN) prediction model and Long Short-Term Memory (LSTM) neural network prediction model based on deep learning, and logical regression model was implemented to make a comparison between these three models. Another prediction model is time series model. Based on deep learning, we proposed an LSTM-1 model purely regard to time series, then implementing and comparing the LSTM model and the Auto-Regressive and Moving Average (ARMA) model. In this paper, comprehensive study of the second-hand housing price in Beijing has been conducted from three aspects: crawling and analyzing, housing price predicting, and the result comparing. Ultimately the best model program was produced, which is of great significance to evaluation and prediction of the housing price in the real estate industry.

Keywords: Deep learning, convolutional neural network, LSTM, housing prediction.

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Authors: S. F. Wong, S. S. Dol

Abstract:

Automotive designers have been trying to use dimples to reduce drag in vehicles. In this work, a car model has been applied with dimple surface with a parameter called dimple ratio DR, the ratio between the depths of the half dimple over the print diameter of the dimple, has been introduced and numerically simulated via k-ε turbulence model to study the aerodynamics performance with the increasing depth of the dimples The Ahmed body car model with 25 degree slant angle is simulated with the DR of 0.05, 0.2, 0.3 0.4 and 0.5 at Reynolds number of 176387 based on the frontal area of the car model. The geometry of dimple changes the kinematics and dynamics of flow. Complex interaction between the turbulent fluctuating flow and the mean flow escalates the turbulence quantities. The maximum level of turbulent kinetic energy occurs at DR = 0.4. It can be concluded that the dimples have generated extra turbulence energy at the surface and as a result, the application of dimples manages to reduce the drag coefficient of the car model compared to the model with smooth surface.

Keywords: Aerodynamics, Boundary Layer, Dimple, Drag, Kinetic Energy, Turbulence.

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Authors: László Lengyel, Tihamér Levendovszky, Gergely Mezei, Hassan Charaf

Abstract:

Graph rewriting-based visual model processing is a widely used technique for model transformation. Visual model transformations often need to follow an algorithm that requires a strict control over the execution sequence of the transformation steps. Therefore, in Visual Model Processors (VMPs) the execution order of the transformation steps is crucial. This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This paper introduces VCFL, discusses its termination properties and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual ModelTransformation, OCL, Termination Properties, UML.

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Authors: Ahmed Amin Mousa, M. Abd El Salam

Abstract:

The current study presents a proposed program for acquisition the skills and techniques needed to produce concept cartoon. The proposed program has been prepared for non-specialist students who have never used neither graphics nor animating software. It was presented to postgraduates in Faculty of Education for Early Childhood, Cairo University, during the spring term of the 2014-2015 academic year. The program works in three different aspects: Drawing and images editing, sound manipulation, and creating animation. In addition, the researchers have prepared a questionnaire for measuring the quality of the concept cartoons produced by the students. The questionnaire was used as a pre-test and post-test, and at the end of the study, a significant difference was determined in favour of post-test results.

Keywords: Cartoon, concept cartoon, kindergarten, animation.

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Authors: V. Weinzettl, M. Imrisek, J. Havlicek, J. Mlynar, D. Naydenkova, P. Hacek, M. Hron, F. Janky, D. Sarychev, M. Berta, A. Bencze, T. Szabolics

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Semiconductor detector arrays are widely used in high-temperature plasma diagnostics. They have a fast response, which allows observation of many processes and instabilities in tokamaks. In this paper, there are reviewed several diagnostics based on semiconductor arrays as cameras, AXUV photodiodes (referred often as fast “bolometers") and detectors of both soft X-rays and visible light installed on the COMPASS tokamak recently. Fresh results from both spring and summer campaigns in 2012 are introduced. Examples of the utilization of the detectors are shown on the plasma shape determination, fast calculation of the radiation center, two-dimensional plasma radiation tomography in different spectral ranges, observation of impurity inflow, and also on investigation of MHD activity in the COMPASS tokamak discharges.

Keywords: Bolometry, plasma diagnostics, soft X-rays, tokamak.

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Authors: Guilherme B. B. Vieira, Rafael M. da Silva, Eliana T. P. Senna, Luiz A. S. Senna, Francisco J. Kliemann Neto

Abstract:

Due to the importance of ports to trade and economic development of the regions in which they are inserted, in recent decades the number of studies devoted to this subject has increased. Part of these studies considers the ports as business agglomerations and focuses on port governance. This is an important approach since the port performance is the result of activities performed by actors belonging to the port-logistics chain, which need to be properly coordinated. This coordination takes place through a port governance model. Given this context, this study aims to analyze the governance model of the port of Santos from the perspective of port customers. To do this, a closed-ended questionnaire based on a conceptual model that considers the key dimensions associated with port governance was applied to the international freight forwarders that operate in the port. The results show the applicability of the considered model and highlight improvement opportunities to be implemented at the port of Santos.

Keywords: Port Governance, Model, Port of Santos, Customers’ Perception.

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Authors: Abderrahmane Diaf, Kamel Benabdellaziz

Abstract:

Remote arid areas of the vast expanses of the African deserts hold huge subterranean reserves of brackish water resources waiting for economic development. This work presents design guidelines as well as initial performance data of new autonomous solar desalination equipment which could help local communities produce their own fresh water using solar energy only and, why not, contribute to transforming desert lands into lush gardens. The output of solar distillation equipments are typically low and in the range of 3 l/m2/day on the average. This new design with an integrated, water based, environmentally-friendly solar heat storage system produced 5 l/m2/day in early spring weather. Equipment output during summer exceeded 9 liters per m2 per day.

Keywords: Multiple trough distillation, solar desalination, solar distillation with heat storage, water based heat storage system.

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Authors: Parvinder S. Sandhu, Manisha Prashar, Pourush Bassi, Atul Bisht

Abstract:

Software effort estimation is the process of predicting the most realistic use of effort required to develop or maintain software based on incomplete, uncertain and/or noisy input. Effort estimates may be used as input to project plans, iteration plans, budgets. There are various models like Halstead, Walston-Felix, Bailey-Basili, Doty and GA Based models which have already used to estimate the software effort for projects. In this study Statistical Models, Fuzzy-GA and Neuro-Fuzzy (NF) Inference Systems are experimented to estimate the software effort for projects. The performances of the developed models were tested on NASA software project datasets and results are compared with the Halstead, Walston-Felix, Bailey-Basili, Doty and Genetic Algorithm Based models mentioned in the literature. The result shows that the NF Model has the lowest MMRE and RMSE values. The NF Model shows the best results as compared with the Fuzzy-GA based hybrid Inference System and other existing Models that are being used for the Effort Prediction with lowest MMRE and RMSE values.

Keywords: Neuro-Fuzzy Model, Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model, GA Based Model, Genetic Algorithm.

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Authors: Yasmeen A. S. Essawy, Khaled Nassar

Abstract:

With the rapid increase of complexity in the building industry, professionals in the A/E/C industry were forced to adopt Building Information Modeling (BIM) in order to enhance the communication between the different project stakeholders throughout the project life cycle and create a semantic object-oriented building model that can support geometric-topological analysis of building elements during design and construction. This paper presents a model that extracts topological relationships and geometrical properties of building elements from an existing fully designed BIM, and maps this information into a directed acyclic Elemental Graph Data Model (EGDM). The model incorporates BIM-based search algorithms for automatic deduction of geometrical data and topological relationships for each building element type. Using graph search algorithms, such as Depth First Search (DFS) and topological sortings, all possible construction sequences can be generated and compared against production and construction rules to generate an optimized construction sequence and its associated schedule. The model is implemented in a C# platform.

Keywords: Building information modeling, elemental graph data model, geometric and topological data models, and graph theory.

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Authors: Antonio Di Leva, Roberto Berchi, Gianpiero Pescarmona, Michele Sonnessa

Abstract:

The aim of a biological model is to understand the integrated structure and behavior of complex biological systems as a function of the underlying molecular networks to achieve simulation and forecast of their operation. Although several approaches have been introduced to take into account structural and environment related features, relatively little attention has been given to represent the behavior of biological systems. The Abstract Biological Process (ABP) model illustrated in this paper is an object-oriented model based on UML (the standard object-oriented language). Its main objective is to bring into focus the functional aspects of the biological system under analysis.

Keywords: Biological processes, system dynamics, systemmodeling, UML.

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Authors: A. Jrade, N. Markiz, N. Albelwi

Abstract:

Optimizing equipment selection in heavy earthwork operations is a critical key in the success of any construction project. The objective of this research incentive was geared towards developing a computer model to assist contractors and construction managers in estimating the cost of heavy earthwork operations. Economical operation analysis was conducted for an equipment fleet taking into consideration the owning and operating costs involved in earthwork operations. The model is being developed in a Microsoft environment and is capable of being integrated with other estimating and optimization models. In this study, Caterpillar® Performance Handbook [5] was the main resource used to obtain specifications of selected equipment. The implementation of the model shall give optimum selection of equipment fleet not only based on cost effectiveness but also in terms of versatility. To validate the model, a case study of an actual dam construction project was selected to quantify its degree of accuracy.

Keywords: Operation analysis, optimization model, equipment economics, equipment selection.

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Authors: Khawla Ben Abderrahim

Abstract:

In order to define a new model of Tunisian foot sizes and for building the most comfortable shoes, Tunisian industrialists must be able to offer for their customers products able to put on and adjust the majority of the target population concerned. Moreover, the use of models of shoes, mainly from others country, causes a mismatch between the foot and comfort of the Tunisian shoes. But every foot is unique; these models become uncomfortable for the Tunisian foot. We have a set of measures produced from a 3D scan of the feet of a diverse population (women, men ...) and we try to analyze this data to define a model of foot specific to the Tunisian footwear design. In this paper we propose tow new approaches to modeling a new foot sizes model. We used, indeed, the neural networks, and specially the Kohonen network. Next, we combine neural networks with the concept of half-foot size to improve the models already found. Finally, it was necessary to compare the results obtained by applying each approach and we decide what-s the best approach that give us the most model of foot improving more comfortable shoes.

Keywords: Morphology of the foot, foot size, half foot size, neural network, Kohonen network, model of foot size.

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Authors: R.M.V. Silva, D.N. Souza

Abstract:

This paper presents a model for the characterization and selection of beeswaxes for use as base substitute tissue for the manufacture of objects suitable for external radiotherapy using megavoltage photon beams. The model of characterization was divided into three distinct stages: 1) verification of aspects related to the origin of the beeswax, the bee species, the flora in the vicinity of the beehives and procedures to detect adulterations; 2) evaluation of physical and chemical properties; and 3) evaluation of beam attenuation capacity. The chemical composition of the beeswax evaluated in this study was similar to other simulators commonly used in radiotherapy. The behavior of the mass attenuation coefficient in the radiotherapy energy range was comparable to other simulators. The proposed model is efficient and enables convenient assessment of the use of any particular beeswax as a base substitute tissue for radiotherapy.

Keywords: Beeswaxes, characterization, model, radiotherapy

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Authors: M. Ndaw, G. Mendy, S. Ouya

Abstract:

Risk management in banking sector is a key issue linked to financial system stability and its importance has been elevated by technological developments and emergence of new financial instruments. In this paper, we improve the model previously defined for quantifying internal control impact on banking risks by automatizing the residual criticality estimation step of FMECA. For this, we defined three equations and a maturity coefficient to obtain a mathematical model which is tested on all banking processes and type of risks. The new model allows an optimal assessment of residual criticality and improves the correlation rate that has become 98%.

Keywords: Risk, Control, Banking, FMECA.

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Authors: S. Swain, P. S. Khuntia

Abstract:

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

Keywords: Convex Optimization, Kharitonov Stability Criterion, Model Reduction, Robust Stability.

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Authors: Ardeshir Karami Mohammadi, Mohammadreza Saee

Abstract:

A variable structure model reference adaptive control (VS-MRAC) strategy for active steering assistance of a two wheel steering car is proposed. An ideal steering system with fixed properties and moving on an ideal road is used as the reference model, and the active steering assistance system is forced to attain the same behavior as the reference model. The proposed system can treat the nonlinear relationships between the side slip angles and lateral forces on tire, and the uncertainties on friction of the road surface, whose compensation are very important under critical situations. Simulation results show improvements on yaw rate and side slip.

Keywords: Variable Structure, Adaptive Control, Model reference, Active steering assistance.

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Authors: RajPal Garg, Kapil Sharma, Rajive Kumar, R. K. Garg

Abstract:

This paper presents a computational methodology based on matrix operations for a computer based solution to the problem of performance analysis of software reliability models (SRMs). A set of seven comparison criteria have been formulated to rank various non-homogenous Poisson process software reliability models proposed during the past 30 years to estimate software reliability measures such as the number of remaining faults, software failure rate, and software reliability. Selection of optimal SRM for use in a particular case has been an area of interest for researchers in the field of software reliability. Tools and techniques for software reliability model selection found in the literature cannot be used with high level of confidence as they use a limited number of model selection criteria. A real data set of middle size software project from published papers has been used for demonstration of matrix method. The result of this study will be a ranking of SRMs based on the Permanent value of the criteria matrix formed for each model based on the comparison criteria. The software reliability model with highest value of the Permanent is ranked at number – 1 and so on.

Keywords: Matrix method, Model ranking, Model selection, Model selection criteria, Software reliability models.

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Authors: David W.S. Tai, Ren-Cheng Zhang, Sheng-Hung Chang, Chin-Pin Chen, Jia-Ling Chen

Abstract:

This study reports results of a meta-analytic path analysis e-learning Acceptance Model with k = 27 studies, Databases searched included Information Sciences Institute (ISI) website. Variables recorded included perceived usefulness, perceived ease of use, attitude toward behavior, and behavioral intention to use e-learning. A correlation matrix of these variables was derived from meta-analytic data and then analyzed by using structural path analysis to test the fitness of the e-learning acceptance model to the observed aggregated data. Results showed the revised hypothesized model to be a reasonable, good fit to aggregated data. Furthermore, discussions and implications are given in this article.

Keywords: E-learning, Meta Analytic Path Analysis, Technology Acceptance Model

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Authors: Devdutt

Abstract:

In this paper, passenger seat vibration control of an active quarter car model under random road excitations is considered. The designed ANFIS and Summing ANFIS PID controllers are assembled in primary suspension system of quarter car model. Simulation work is performed in time and frequency domain to obtain passenger seat acceleration and displacement responses. Simulation results show that Summing ANFIS PID based controller is highly suitable to suppress the road induced vibrations in quarter car model to achieve desired passenger ride comfort and safety compared to ANFIS and passive system.

Keywords: Quarter car model, Active suspension system, Summing ANFIS PID controller, Passenger ride comfort.

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Authors: Worachat Wannawong, Usa W. Humphries, Prungchan Wongwises, Suphat Vongvisessomjai

Abstract:

The three steps of the standard one-way nested grid for a regional scale of the third generation WAve Model Cycle 4 (WAMC4) is scrutinized. The model application is enabled to solve the energy balance equation on a coarse resolution grid in order to produce boundary conditions for a smaller area by the nested grid technique. In the present study, the model takes a full advantage of the fine resolution of wind fields in space and time produced by the available U.S. Navy Global Atmospheric Prediction System (NOGAPS) model with 1 degree resolution. The nested grid application of the model is developed in order to gradually increase the resolution from the open ocean towards the South China Sea (SCS) and the Gulf of Thailand (GoT) respectively. The model results were compared with buoy observations at Ko Chang, Rayong and Huahin locations which were obtained from the Seawatch project. In addition, the results were also compared with Satun based weather station which was provided from Department of Meteorology, Thailand. The data collected from this station presented the significant wave height (Hs) reached 12.85 m. The results indicated that the tendency of the Hs from the model in the spherical coordinate propagation with deep water condition in the fine grid domain agreed well with the Hs from the observations.

Keywords: energy balance equation, Gulf of Thailand, nested gridapplication, South China Sea, wave model.

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Authors: A. Majid Bahari, Kourosh Hejazi

Abstract:

Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds- Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model.

Keywords: Buoyant flows, Buoyant k-ε turbulence model, saline gravity current.

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Authors: David Lávicka

Abstract:

This paper looks into detailed investigation of thermal-hydraulic characteristics of the flow field in a fuel rod model, especially near the spacer. The area investigate represents a source of information on the velocity flow field, vortex, and on the amount of heat transfer into the coolant all of which are critical for the design and improvement of the fuel rod in nuclear power plants. The flow field investigation uses three-dimensional Computational Fluid Dynamics (CFD) with the Reynolds stresses turbulence model (RSM). The fuel rod model incorporates a vertical annular channel where three different shapes of spacers are used; each spacer shape is addressed individually. These spacers are mutually compared in consideration of heat transfer capabilities between the coolant and the fuel rod model. The results are complemented with the calculated heat transfer coefficient in the location of the spacer and along the stainless-steel pipe.

Keywords: CFD, fuel rod model, heat transfer, spacer

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Authors: J. Fernandez, N. Aguilar, R. Fernandez de Canete, J. C. Ramos-Diaz

Abstract:

In this paper, a simulation model of the glucose-insulin system for a patient undergoing diabetes Type 1 is developed by using a causal modeling approach under system dynamics. The OpenModelica simulation environment has been employed to build the so called causal model, while the glucose-insulin model parameters were adjusted to fit recorded mean data of a diabetic patient database. Model results under different conditions of a three-meal glucose and exogenous insulin ingestion patterns have been obtained. This simulation model can be useful to evaluate glucose-insulin performance in several circumstances, including insulin infusion algorithms in open-loop and decision support systems in closed-loop.

Keywords: Causal modeling, diabetes, glucose-insulin system, diabetes, causal modeling, OpenModelica software.

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Authors: B. Vahdani, R. Tavakkoli-Moghaddam, A. Baboli, S. M. Mousavi

Abstract:

Focusing on the environmental issues, including the reduction of scrap and consumer residuals, along with the benefiting from the economic value during the life cycle of goods/products leads the companies to have an important competitive approach. The aim of this paper is to present a new mixed nonlinear facility locationallocation model in recycling collection networks by considering multi-echelon, multi-suppliers, multi-collection centers and multifacilities in the recycling network. To make an appropriate decision in reality, demands, returns, capacities, costs and distances, are regarded uncertain in our model. For this purpose, a fuzzy mathematical programming-based possibilistic approach is introduced as a solution methodology from the recent literature to solve the proposed mixed-nonlinear programming model (MNLP). The computational experiments are provided to illustrate the applicability of the designed model in a supply chain environment and to help the decision makers to facilitate their analysis.

Keywords: Location-allocation model, recycling collection networks, fuzzy mathematical programming.

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