Search results for: Free convection; Non-isothermal; Thermodynamic second law; Entropy

Authors: A. Zerkane, K. El Bikri, R. Benamar

Abstract:

The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

Keywords: Nonlinear vibrations, functionally graded materials, homogenization procedure.

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Authors: Ahmed A. Hussain, Abbas A. Mohammed, Heba. H. Ibrahim, Amir H. Abbas

Abstract:

In this study the extracts of the Iraqi herb Tribulus terrestris (Al-Hassage or Al-Kutub) was done by using of polar and non polar solvents, then the biological activity of these extractants was studied in three fields, First, the antibacterial activity (in vitro) on gram positive bacteria (Staphylococcus aureus), and gram negative bacteria (E. coli, Proteus vulgaris, Pseudomonas aerugiuosa, and Klebsiella), all extracts showed considerable activity against all bacteria. Second, the effect of extracts on free serum testosterone level in male mice (in vivo), the alcoholic, and acetonitrilic extracts showed significant (P < 0.05) increase in free serum testosterone level, and we found that the extracts contained compounds with less genotoxic effects in mice germ cells. 3rd, was to study the effect of methanolic extract of T. terrestris in diabetes management.

Keywords: Genotoxic, germ cells, tribulus terrestris, testosterone.

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Authors: Zundong Zhang, Limin Jia, Xiaoliang Sun

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The Beijing road traffic system, as a typical huge urban traffic system, provides a platform for analyzing the complex characteristics and the evolving mechanisms of urban traffic systems. Based on dynamic network theory, we construct the dynamic model of the Beijing road traffic system in which the dynamical properties are described completely. Furthermore, we come into the conclusion that urban traffic systems can be viewed as static networks, stochastic networks and complex networks at different system phases by analyzing the structural randomness. As well as, we demonstrate the evolving process of the Beijing road traffic network based on real traffic data, validate the stochastic characteristics and the scale-free property of the network at different phases

Keywords: Dynamic Network Models, Structural Randomness, Scale-free Property, Multi-mode character

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Authors: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

Abstract:

Aeolian vibrations are the major cause for the failure of conductor cables. Using a Stockbridge damper reduces these vibrations and increases the life span of the conductor cable. Designing an efficient Stockbridge damper that suits the conductor cable requires a robust mathematical model with minimum assumptions. However it is not easy to analytically model the complex geometry of the messenger. Therefore an equivalent stiffness must be determined so that it can be used in the analytical model. This paper examines the bending stiffness of the cable and discusses the effect of this stiffness on the natural frequencies. The obtained equivalent stiffness compensates for the assumption of modeling the messenger as a rod. The results from the free vibration analysis of the analytical model with the equivalent stiffness is validated using the full scale finite element model of the Stockbridge damper.

Keywords: Equivalent stiffness, finite element model, free vibration response, Stockbridge damper.

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Authors: Kyaw Myo Lin

Abstract:

This paper presents small signal stability study carried over the 140-Bus, 31-Machine, 5-Area MEPE system and validated on free and open source software: PSAT. Well-established linearalgebra analysis, eigenvalue analysis, is employed to determine the small signal dynamic behavior of test system. The aspects of local and interarea oscillations which may affect the operation and behavior of power system are analyzed. Eigenvalue analysis is carried out to investigate the small signal behavior of test system and the participation factors have been determined to identify the participation of the states in the variation of different mode shapes. Also, the variations in oscillatory modes are presented to observe the damping performance of the test system.

Keywords: Eigenvalue analysis, Mode shapes, MEPE test system, Participation factors, Power System oscillations.

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Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

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Authors: Makan Cheraghpour, Seyed Ahmad Hosseini, Damoon Ashtary-Larky, Saeed Shirali, Matin Ghanavati, Meysam Alipour

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Background: In addition to reducing body weight, the low-calorie diets can reduce the lean body mass. It is hypothesized that in addition to reducing the body weight, the low-calorie diets can maintain the lean body mass. So, the current study aimed at evaluating the effects of high-protein diet with calorie restriction on body composition in overweight and obese individuals. Methods: 36 obese and overweight subjects were divided randomly into two groups. The first group received a normal-protein, low-energy diet (RDA), and the second group received a high-protein, low-energy diet (2×RDA). The anthropometric indices including height, weight, body mass index, body fat mass, fat free mass, and body fat percentage were evaluated before and after the study. Results: A significant reduction was observed in anthropometric indices in both groups (high-protein, low-energy diets and normal-protein, low-energy diets). In addition, more reduction in fat free mass was observed in the normal-protein, low-energy diet group compared to the high -protein, low-energy diet group. In other the anthropometric indices, significant differences were not observed between the two groups. Conclusion: Independently of the type of diet, low-calorie diet can improve the anthropometric indices, but during a weight loss, high-protein diet can help the fat free mass to be maintained.

Keywords: Diet, high-protein, body mass index, body fat percentage.

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Authors: Aleksandra Yu. Sazonova, Valentina M. Raeva

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The aim of this work was to apply extractive distillation for acetonitrile removal from water solutions, to validate thermodynamic criterion based on excess Gibbs energy to entrainer selection process for acetonitrile – water mixture separation and show its potential efficiency at isothermal conditions as well as at isobaric (conditions of real distillation process), to simulate and analyze an extractive distillation process with chosen entrainers: optimize amount of trays and feeds, entrainer/original mixture and reflux ratios. Equimolar composition of the feed stream was chosen for the process, comparison of the energy consumptions was carried out. Glycerol was suggested as the most energetically and ecologically suitable entrainer.

Keywords: Acetonitrile, entrainer, extractive distillation, water.

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Authors: Achouri Ryma, Hatem Dhaouadi, Hatem Mhiri, and Philippe Bournot

Abstract:

For many chemical and biological processes, the understanding of the mixing phenomenon and flow behavior in a stirred tank is of major importance. A three-dimensional numerical study was performed using the software Fluent, to study the flow field in a stirred tank with a Rushton turbine. In this work, we first studied the flow generated in the tank with a Rushton turbine. Then, we studied the effect of the variation of turbine’s submergence on the thermodynamic quantities defining the flow field. For that, four submergences were considered, while maintaining the same rotational speed (N =250rpm). This work intends to optimize the aeration performances of a Rushton turbine in a stirred tank.

Keywords: Aeration, CFD, Rushton turbine, mixing, submergence

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Authors: Jung Hyun Kim, Gyo Woo Lee

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In this study, the enhancement of the heat release performance of an extruded-type heat sink to prepare the large-capacity solar inverter thru the flow holes in the base plate near the heat sources was investigated. Optimal location and number of the holes in the baseplate were determined by using a commercial computation program. The heat release performance of the shape-modified heat sink was measured experimentally and compared with that of the simulation. The heat sink with 12 flow holes in the 18-mm-thick base plate has a 8.1% wider heat transfer area, a 2.5% more mass flow of air, and a 2.7% higher heat release rate than those of the original heat sink. Also, the surface temperature of the base plate was lowered 1.5^oC by the holes.

Keywords: Heat Sink, Forced Convection, Heat Transfer, Performance Evaluation, Flow Holes.

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Authors: H. El Fadili, K. Zenkouar, H. Qjidaa

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This paper proposes a neural network weights and topology optimization using genetic evolution and the backpropagation training algorithm. The proposed crossover and mutation operators aims to adapt the networks architectures and weights during the evolution process. Through a specific inheritance procedure, the weights are transmitted from the parents to their offsprings, which allows re-exploitation of the already trained networks and hence the acceleration of the global convergence of the algorithm. In the preprocessing phase, a new feature extraction method is proposed based on Legendre moments with the Maximum entropy principle MEP as a selection criterion. This allows a global search space reduction in the design of the networks. The proposed method has been applied and tested on the well known MNIST database of handwritten digits.

Keywords: Genetic algorithm, Legendre Moments, MEP, Neural Network.

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Authors: D. Zabala, N. Sánchez, J. Pinto

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A transient heat transfer mathematical model for the prediction of temperature distribution in the car body during primer baking has been developed by considering the thermal radiation and convection in the furnace chamber and transient heat conduction governing equations in the car framework. The car cockpit is considered like a structure with six flat plates, four vertical plates representing the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transient heat conduction in each flat plate is modeled by the lumped capacitance method. Comparison with the experimental data shows that the heat transfer model works well for the prediction of thermal behavior of the car body in the curing furnace, with deviations below 5%.

Keywords: Transient heat transfer, car body, lumpedcapacitance, primer baking.

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Authors: Michael Tupý, Dagmar Měřínská, Alice Tesaříková-Svobodová, Christian Carrot, Caroline Pillon, Vít Petránek

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The mechanical properties of blends consisting of plasticized poly(vinyl butyral) (PVB) and plasticized poly(vinyl chloride) (PVC) are studied, in order to evaluate the possibility of using recycled PVB waste derived from windshields. PVC was plasticized with 38% of diisononyl phthalate (DINP), while PVB was plasticized with 28% of triethylene glycol, bis(2-ethylhexanoate) (3GO). The optimal process conditions for the PVB/PVC blend in 1:1 ratio were determined. Entropy was used in order to theoretically predict the blends miscibility. The PVB content of each blend composition used was ranging from zero to 100%. Tensile strength and strain were tested. In addition, a comparison between recycled and original PVB, used as constituents of the blend, was performed.

Keywords: Poly(vinyl butyral), poly(vinyl chloride), windshield, polymer waste, mechanical properties.

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Authors: Gulshan Sachdeva, Vaibhav Jain

Abstract:

In present paper, the performance of various alternative refrigerants is compared to find the substitute of R22, the widely used hydrochlorofluorocarbon refrigerant in developing countries. These include the environmentally friendly hydrofluorocarbon (HFC) refrigerants such as R134A, R410A, R407C and M20. In the present study, a steady state thermodynamic model (includes both first and second law analysis) which simulates the working of an actual vapor-compression system is developed. The model predicts the performance of system with alternative refrigerants. Considering the recent trends of replacement of ozone depleting refrigerants and improvement in system efficiency, R407C is found to be potential candidate to replace R22 refrigerant in the present study.

Keywords: Refrigeration, compression system, performance study, modeling, R407C.

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Authors: Basma M. Mohammad El-Basioni, Sherine M. Abd El-kader, Hussein S. Eissa

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This paper proposes an implementation for the directed diffusion paradigm aids in studying this paradigm-s operations and evaluates its behavior according to this implementation. The directed diffusion is evaluated with respect to the loss percentage, lifetime, end-to-end delay, and throughput. From these evaluations some suggestions and modifications are proposed to improve the directed diffusion behavior according to this implementation with respect to these metrics. The proposed modifications reflect the effect of local path repair by introducing a technique called Loop-free Local Path Repair (LLPR) which improves the directed diffusion behavior especially with respect to packet loss percentage by about 92.69%. Also LLPR improves the throughput and end-to-end delay by about 55.31% and 14.06% respectively, while the lifetime decreases by about 29.79%.

Keywords: Attribute-value based naming scheme, data gathering, data-centric routing, energy-efficiency, locality, wireless sensor network.

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Authors: B. Chetti, W. A. Crosby

Abstract:

The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: Two-lobe bearing, thermal effect, static and dynamic characteristics.

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Authors: Joseph Ignagni, Rebecca E. Deen

Abstract:

There are many views on how human decision makers behave. In this work, the Justices of the United States Supreme Court will be viewed in terms of constrained maximization and cognitivecybernetic theory. This paper will integrate research in such fields as law, political science, psychology, economics and decision making theory. It will be argued that due to its heavy workload, the Supreme Court is forced to make decisions in a boundedly rational manner. The ideas and theory put forward here will be tested in the area of the Court’s decisions involving religion. Therefore, the cases involving the U.S. Constitution’s Free Exercise Clause and Establishment Clause will be analyzed. Also, variables such as the U.S. government’s involvement in these cases will be considered. The years to be studied will be 1987-2011.

Keywords: Establishment Clause, Free Exercise Clause, U.S. Constitution, U.S. Supreme Court.

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Authors: Khin Thida Latt, Mineo Kaneko, Yoichi Shinoda

Abstract:

In Partitioned Optical Passive Stars POPS network,nodes and couplers become free after slot to slot in some computation.It is necessary to efficiently utilize free couplers and nodes to be cost effective. Improving parallelism, we present the fast data summation algorithm for multiple problem spaces on P OP S(g, g) with smaller number of nodes for the case of d =n = g. For the case of d >n > g, we simulate the calculation of large number of data items dedicated to larger system with many nodes on smaller system with smaller number of nodes. The algorithm is faster than the best know algorithm and using smaller number of nodes and groups make the system low cost and practical.

Keywords: Partitioned optical passive stars network, parallelcomputing, optical computing, data sum

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Authors: Alessandro Bevilacqua, Alessandro Gherardi, Ludovico Carozza, Filippo Piccinini

Abstract:

The last years have seen an increasing use of image analysis techniques in the field of biomedical imaging, in particular in microscopic imaging. The basic step for most of the image analysis techniques relies on a background image free of objects of interest, whether they are cells or histological samples, to perform further analysis, such as segmentation or mosaicing. Commonly, this image consists of an empty field acquired in advance. However, many times achieving an empty field could not be feasible. Or else, this could be different from the background region of the sample really being studied, because of the interaction with the organic matter. At last, it could be expensive, for instance in case of live cell analyses. We propose a non parametric and general purpose approach where the background is built automatically stemming from a sequence of images containing even objects of interest. The amount of area, in each image, free of objects just affects the overall speed to obtain the background. Experiments with different kinds of microscopic images prove the effectiveness of our approach.

Keywords: Microscopy, flat field correction, background estimation, image segmentation.

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Authors: S. Parida, S. C. Mohanty

Abstract:

The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C⁰ finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.

Keywords: FGM, pretwisted plate, thermal environment, HOST, simple power law.

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Authors: Jutta Hämmerle-Uhl, Georg Penn, Gerhard Pötzelsberger, Andreas Uhl

Abstract:

Iris codes contain bits with different entropy. This work investigates different strategies to reduce the size of iris code templates with the aim of reducing storage requirements and computational demand in the matching process. Besides simple subsampling schemes, also a binary multi-resolution representation as used in the JBIG hierarchical coding mode is assessed. We find that iris code template size can be reduced significantly while maintaining recognition accuracy. Besides, we propose a two-stage identification approach, using small-sized iris code templates in a pre-selection stage, and full resolution templates for final identification, which shows promising recognition behaviour.

Keywords: Iris recognition, compact iris code, fast matching, best bits, pre-selection identification, two-stage identification.

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Authors: V. E. Messerle, O. A. Lavrichshev, A. B. Ustimenko

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The article presents a plasma chemical technology for processing solid fuels, using examples of bituminous and brown coals. Thermodynamic and experimental investigation of the technology was made. The technology allows producing synthesis gas from the coal organic mass and valuable components (technical silicon, ferrosilicon, aluminum, and carbon silicon, as well as microelements of rare metals, such as uranium, molybdenum, vanadium, etc.) from the mineral mass. The thusly produced highcalorific synthesis gas can be used for synthesis of methanol, as a high-calorific reducing gas instead of blast-furnace coke as well as power gas for thermal power plants.

Keywords: Gasification, mineral mass, organic mass, plasma, processing, solid fuel, synthesis gas, valuable components.

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Authors: Kai-Lin Hsu, Jie-Chung Lou, Jia-Yun Han

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In recent years, the underground water sources in southern Taiwan have become salinized because of saltwater intrusions. This study explores the adsorption characteristics of activated carbon on salinizing inorganic salts using isothermal adsorption experiments and provides a model analysis. The temperature range for the isothermal adsorption experiments ranged between 5 to 45 ℃, and the amount adsorbed varied between 28.21 to 33.87 mg/g. All experimental data of adsorption can be fitted to both the Langmuir and the Freundlich models. The thermodynamic parameters for per chlorate onto granular activated carbon were calculated as -0.99 to -1.11 kcal/mol for DG°, -0.6 kcal/mol for DH°, and 1.21 to 1.84 kcal/mol for DS°. This shows that the adsorption process of granular activated carbon is spontaneously exothermic. The observation of adsorption behaviors under low ionic strength, low pH values, and low temperatures is beneficial to the adsorption removal of perchlorate with granular activated carbon.

Keywords: Water Treatment, Per Chlorate, Adsorption, Granular Activated Carbon

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Authors: Hamioud Saida, Khalfallah Salah

Abstract:

In this study, a spectral element method (SEM) is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: Elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation.

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Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: M. Margoudi, Z. Smyrnaiou

Abstract:

The current paper presents the results of a conducted case study. During the past few years the number of children diagnosed with Learning Difficulties has drastically augmented and especially the cases of ADHD (Attention Deficit Hyperactivity Disorder). One of the core characteristics of ADHD is a deficit in working memory functions. The review of the literature indicates a plethora of educational software that aim at training and enhancing the working memory. Nevertheless, in the current paper, the possibility of using for the same purpose free, online games will be explored. Another issue of interest is the potential effect of the working memory training to the core symptoms of ADHD. In order to explore the abovementioned research questions, three digital tests are employed, all of which are developed on the E-slate platform by the author, in order to check the levels of ADHD’s symptoms and to be used as diagnostic tools, both in the beginning and in the end of the case study. The tools used during the main intervention of the research are free online games for the training of working memory. The research and the data analysis focus on the following axes: a) the presence and the possible change in two of the core symptoms of ADHD, attention and impulsivity and b) a possible change in the general cognitive abilities of the individual. The case study was conducted with the participation of a thirteen year-old, female student, diagnosed with ADHD, during after-school hours. The results of the study indicate positive changes both in the levels of attention and impulsivity. Therefore, we conclude that the training of working memory through the use of free, online games has a positive impact on the characteristics of ADHD. Finally, concerning the second research question, the change in general cognitive abilities, no significant changes were noted.

Keywords: ADHD, attention, impulsivity, online games.

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Authors: G. Kehl, P. Wagner

Abstract:

A novel simulation method to determine the displacements of machine tools due to thermal factors is presented. The specific characteristic of this method is the employment of original CAD data from the design process chain, which is interpreted by an algorithm in terms of geometry-based allocation of convection and radiation parameters. Furthermore analogous models relating to the thermal behaviour of machine elements are automatically implemented, which were gained by extensive experimental testing with thermography imaging. With this a transient simulation of the thermal field and in series of the displacement of the machine tool is possible simultaneously during the design phase. This method was implemented and is already used industrially in the design of machining centres in order to improve the quality of herewith manufactured workpieces.

Keywords: Accuracy, design process, finite element analysis, machine tools, thermal simulation.

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Authors: G. de la Rosa, H. E. Reynel-Avila, A. Bonilla-Petriciolet, I. Cano-Rodríguez, C. Velasco-Santos, and A. L. Martínez-Hernández

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Chicken feathers were used as biosorbent for Pb removal from aqueous solution. In this paper, the kinetics and equilibrium studies at several pH, temperature, and metal concentration values are reported. For tested conditions, the Pb sorption capacity of this poultry waste ranged from 0.8 to 8.3 mg/g. Optimal conditions for Pb removal by chicken feathers have been identified. Pseudo-first order and pseudo-second order equations were used to analyze the experimental data. In addition, the sorption isotherms were fitted to classical Langmuir and Freundlich models. Finally, thermodynamic parameters for the sorption process have been determined. In summary, the results showed that chicken feathers are an alternative and promising sorbent for the treatment of effluents polluted by Pb ions.

Keywords: Sorption, chicken feathers, Pb, water treatment.

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Authors: T. Zitoun, M. Bouhadef

Abstract:

When a partially or completely immersed solid moves in a liquid such as water, it undergoes a force called hydrodynamic drag. Reducing this force has always been the objective of hydrodynamic engineers to make water slide better on submerged bodies. This paper deals with the examination of the different terms composing the analytical solution of the flow over an obstacle embedded at the bottom of a hydraulic channel. We have chosen to use a linear method to study a two-dimensional flow over an obstacle, in order to understand the evolution of the drag. We set the following assumptions: incompressible inviscid fluid, irrotational flow, low obstacle height compared to the water height. Those assumptions allow overcoming the difficulties associated with modelling these waves. We will mathematically formulate the equations that allow the determination of the stream function, and then the free surface equation. A similar method is used to determine the exact analytical solution for an obstacle in the shape of a sinusoidal arch.

Keywords: Free-surface wave, inviscid fluid, analytical solution, hydraulic channel.

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Authors: A. Shooshtari, A. R. Masoodi, S. Heyrani Moghaddam

Abstract:

Free vibration analysis of a gabled frame with elastic support and semi-rigid connections is performed by using a program in OpenSees software. Natural frequencies and mode shape details of frame are obtained for two states, which are semi-rigid connections and elastic supports, separately. The members of this structure are analyzed as a prismatic nonlinear beam-column element in software. The mass of structure is considered as two equal lumped masses at the head of two columns in horizontal and vertical directions. Note that the degree of freedom, allocated to all nodes, is equal to three. Furthermore, the mode shapes of frame are achieved. Conclusively, the effects of connections and supports flexibility on the natural frequencies and mode shapes of structure are investigated.  

Keywords: Natural frequency, mode shape, gabled frame, semi-rigid connection, elastic support, OpenSees software.

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