Search results for: two phase flows

Authors: Stéphanie Pellerin, Bérengére Podvin, Luc Pastur

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In aerovehicles context, the flow around an Ahmed body profile is simulated using the velocity-vorticity formulation of the Navier-Stokes equations, associated to a penalization method for solids and Large Eddy Simulation for turbulence. The study focuses both on the ground influence on the flow and on the dissymetry of the wake, observed for a ground clearance greater than 10% of the body height H. Unsteady and mean flows are presented and analyzed. POD study completes the analysis and gives information on the most energetic structures of the flow.

Keywords: Ahmed body, bi-stability, LES, near wake.

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Authors: Y. L. Yung, Kong Mun Lo

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In this study, solid phase micro-extraction (SPME) was optimized to improve the sensitivity and accuracy in formaldehyde determination for plywood panels. Further work has been carried out to compare the newly developed technique with existing method which reacts formaldehyde collected in desiccators with acetyl acetone reagent (DC-AA). In SPME, formaldehyde was first derivatized with O-(2,3,4,5,6 pentafluorobenzyl)-hydroxylamine hydrochloride (PFBHA) and analysis was then performed by gas chromatography in combination with mass spectrometry (GC-MS). SPME data subjected to various wood species gave satisfactory results, with relative standard deviations (RSDs) obtained in the range of 3.1-10.3%. It was also well correlated with DC values, giving a correlation coefficient, RSQ, of 0.959. The quantitative analysis of formaldehyde by SPME was an alternative in wood industry with great potential

Keywords: Formaldehyde, GCMS, Plywood and SPME

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Authors: I. Grigoraviciute-Puroniene, K. Tsuru, E. Garskaite, Z. Stankeviciute, A. Beganskiene, K. Ishikawa, A. Kareiva

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Tricalcium phosphate (β-Ca₃(PO₄)₂, β-TCP) powders were synthesized using wet polymeric precipitation method for the first time to our best knowledge. The results of X-ray diffraction analysis showed the formation of almost single a Ca-deficient hydroxyapatite (CDHA) phase of a poor crystallinity already at room temperature. With continuously increasing the calcination temperature up to 800 °C, the crystalline β-TCP was obtained as the main phase. It was demonstrated that infrared spectroscopy is very effective method to characterize the formation of β-TCP. The SEM results showed that β-TCP solids were homogeneous having a small particle size distribution. The β-TCP powders consisted of spherical particles varying in size from 100 to 300 nm. Fabricated β-TCP specimens were placed to the bones of the rats and maintained for 1-2 months.

Keywords: β-TCP, bone regeneration, wet chemical processing, polymeric precipitation.

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Authors: Z. Ž. Lazarević, D. L. Sekulić, V. N. Ivanovski, N. Ž. Romčević

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NiFe2O4 (nickel ferrite), ZnFe2O4 (zinc ferrite) and Ni0.5Zn0.5Fe2O4 (nickel-zinc ferrite) were prepared by mechanochemical route in a planetary ball mill starting from mixture of the appropriate quantities of the Ni(OH)2/Fe(OH)3, Zn(OH)2/Fe(OH)3 and Ni(OH)2/Zn(OH)2/Fe(OH)3 hydroxide powders. In order to monitor the progress of chemical reaction and confirm phase formation, powder samples obtained after 25 h, 18 h and 10 h of milling were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), IR, Raman and Mössbauer spectroscopy. It is shown that the soft mechanochemical method, i.e. mechanochemical activation of hydroxides, produces high quality single phase ferrite samples in much more efficient way. From the IR spectroscopy of single phase samples it is obvious that energy of modes depends on the ratio of cations. It is obvious that all samples have more than 5 Raman active modes predicted by group theory in the normal spinel structure. Deconvolution of measured spectra allows one to conclude that all complex bands in the spectra are made of individual peaks with the intensities that vary from spectrum to spectrum. The deconvolution of Raman spectra allows to separate contributions of different cations to a particular type of vibration and to estimate the degree of inversion.

Keywords: Ferrites, Raman spectroscopy, IR spectroscopy, Mössbauer measurements.

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Authors: Takaaki Ishibashi

Abstract:

Frequency domain independent component analysis has a scaling indeterminacy and a permutation problem. The scaling indeterminacy can be solved by use of a decomposed spectrum. For the permutation problem, we have proposed the rules in terms of gain ratio and phase difference derived from the decomposed spectra and the source-s coarse directions. The present paper experimentally clarifies that the gain ratio and the phase difference work effectively in a real environment but their performance depends on frequency bands, a microphone-space and a source-microphone distance. From these facts it is seen that it is difficult to attain a perfect solution for the permutation problem in a real environment only by either the gain ratio or the phase difference. For the perfect solution, this paper gives a solution to the problems in a real environment. The proposed method is simple, the amount of calculation is small. And the method has high correction performance without depending on the frequency bands and distances from source signals to microphones. Furthermore, it can be applied under the real environment. From several experiments in a real room, it clarifies that the proposed method has been verified.

Keywords: blind source separation, frequency domain independent component analysys, permutation correction, scale adjustment, target extraction.

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Authors: Tadashi Watanabe, Jinya Katsuyama, Akihiro Mano

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The estimation of leak flow rates through narrow cracks in structures is of importance for nuclear reactor safety, since the leak flow could be detected before occurrence of loss-of-coolant accidents. The two-phase critical leak flow rates are calculated using the system analysis code, and two representative non-homogeneous critical flow models, Henry-Fauske model and Ransom-Trapp model, are compared. The pressure decrease and vapor generation in the crack, and the leak flow rates are found to be larger for the Henry-Fauske model. It is shown that the leak flow rates are not affected by the structural temperature, but affected largely by the roughness of crack surface.

Keywords: Crack, critical flow, leak, roughness.

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Authors: Waseem Khan

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In this paper a technique for increasing the convergence rate of fractionally spaced channel equalizer is proposed. Instead of symbol-spaced updating of the equalizer filter, a mechanism has been devised to update the filter at a higher rate. This ensures convergence of the equalizer filter at a higher rate and therefore less time-consuming. The proposed technique has been simulated and tested for two-ray modeled channels with various delay spreads. These channels include minimum-phase and nonminimum- phase channels. Simulation results suggest that that proposed technique outperforms the conventional technique of symbol-spaced updating of equalizer filter.

Keywords: Channel equalization, Fractionally-spaced equalizer

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Authors: A. M. Tahsini

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Solid fuel transient burning behavior under oxidizer gas flow is numerically investigated. It is done using analysis of the regression rate responses to the imposed sudden and oscillatory variation at inflow properties. The conjugate problem is considered by simultaneous solution of flow and solid phase governing equations to compute the fuel regression rate. The advection upstream splitting method is used as flow computational scheme in finite volume method. The ignition phase is completely simulated to obtain the exact initial condition for response analysis. The results show that the transient burning effects which lead to the combustion instabilities and intermittent extinctions could be observed in solid fuels as the solid propellants.

Keywords: Extinction, Oscillation, Regression rate, Response, Transient burning.

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Authors: Nabil A. Ahmed

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This paper presents a novel three-phase utility frequency to high frequency soft switching power conversion circuit with dual mode pulse width modulation and pulse density modulation for high power induction heating applications as melting of steel and non ferrous metals, annealing of metals, surface hardening of steel and cast iron work pieces and hot water producers, steamers and super heated steamers. This high frequency power conversion circuit can operate from three-phase systems to produce high current for high power induction heating applications under the principles of ZVS and it can regulate its ac output power from the rated value to a low power level. A dual mode modulation control scheme based on high frequency PWM in synchronization with the utility frequency positive and negative half cycles for the proposed high frequency conversion circuit and utility frequency pulse density modulation is produced to extend its soft switching operating range for wide ac output power regulation. A dual packs heat exchanger assembly is designed to be used in consumer and industrial fluid pipeline systems and it is proved to be suitable for the hot water, steam and super heated steam producers. Experiment and simulation results are given in this paper to verify the operation principles of the proposed ac conversion circuit and to evaluate its power regulation and conversion efficiency. Also, the paper presents a mutual coupling model of the induction heating load instead of equivalent transformer circuit model.

Keywords: Induction heating, three-phase, conversion circuit, pulse width modulation, pulse density modulation, high frequency, soft switching.

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Authors: H. Ait Abderrahmane, M. Fayed, H. D. Ng, G. H. Vatistas

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The present paper expands details and confirms the transition mechanism between two subsequent polygonal patterns of the hollow-core vortex. Using power spectral analysis, we confirm in this work that the transition from any N-gon to (N+1)-gon pattern observed within a hollow-core vortex of shallow rotating flows occurs in two steps. The regime was quasi-periodic before the frequencies lock (synchronization). The ratios of locking frequencies were found to be equal to (N-1)/N.

Keywords: Patterns, quasi-periodic, swirling, synchronization, transition.

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Authors: Cherif Haddad, Faouzi Ben Charrada

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On a such wide-area environment as a Grid, data placement is an important aspect of distributed database systems. In this paper, we address the problem of initial placement of database no-replicated fragments in Grid architecture. We propose a graph based approach that considers resource restrictions. The goal is to optimize the use of computing, storage and communication resources. The proposed approach is developed in two phases: in the first phase, we perform fragment grouping using knowledge about fragments dependency and, in the second phase, we determine an efficient placement of the fragment groups on the Grid. We also show, via experimental analysis that our approach gives solutions that are close to being optimal for different databases and Grid configurations.

Keywords: Grid computing, Distributed systems, Data resourcesmanagement, Database systems, Database placement.

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Authors: Jamal Moshtagh, Hassan Pourvali Souraki

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In North America, Most power distribution systems employ a four-wire multi-grounded neutral (MGN) design. This paper has explained the inherent characteristics of multi-grounded three-phase four-wire distribution systems under unbalanced situations. As a result, the mechanism of voltage swell and voltage sag in MGN feeders becomes difficult to understand. The simulation tool that has been used in this paper is MATLAB under Windows software. In this paper the equivalent model of a full-scale multigrounded distribution system implemented by MATLAB is introduced. The results are expected to help utility engineers to understand the impact of MGN on distribution system operations.

Keywords: Distribution systems, multi- grounded, neutral, three-phase four-wire, ground.

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

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

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

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Authors: Majed Omar Al-Dwairi

Abstract:

This paper evaluate the multilevel modulation for different techniques such as amplitude shift keying (M-ASK), MASK, differential phase shift keying (M-ASK-Bipolar), Quaternary Amplitude Shift Keying (QASK) and Quaternary Polarization-ASK (QPol-ASK) at a total bit rate of 107 Gbps. The aim is to find a costeffective very high speed transport solution. Numerical investigation was performed using Monte Carlo simulations. The obtained results indicate that some modulation formats can be operated at 100Gbps in optical communication systems with low implementation effort and high spectral efficiency.

Keywords: Optical communication, multilevel amplitude shift keying (M-ASK), Differential phase shift keying (DPSK), Quaternary Amplitude Shift Keying (QASK), Quaternary Polarization-ASK (QPol-ASK).

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Authors: Mounira Taileb, Sid Lamrous, Sami Touati

Abstract:

In order to accelerate the similarity search in highdimensional database, we propose a new hierarchical indexing method. It is composed of offline and online phases. Our contribution concerns both phases. In the offline phase, after gathering the whole of the data in clusters and constructing a hierarchical index, the main originality of our contribution consists to develop a method to construct bounding forms of clusters to avoid overlapping. For the online phase, our idea improves considerably performances of similarity search. However, for this second phase, we have also developed an adapted search algorithm. Our method baptized NOHIS (Non-Overlapping Hierarchical Index Structure) use the Principal Direction Divisive Partitioning (PDDP) as algorithm of clustering. The principle of the PDDP is to divide data recursively into two sub-clusters; division is done by using the hyper-plane orthogonal to the principal direction derived from the covariance matrix and passing through the centroid of the cluster to divide. Data of each two sub-clusters obtained are including by a minimum bounding rectangle (MBR). The two MBRs are directed according to the principal direction. Consequently, the nonoverlapping between the two forms is assured. Experiments use databases containing image descriptors. Results show that the proposed method outperforms sequential scan and SRtree in processing k-nearest neighbors.

Keywords: K-nearest neighbour search, multi-dimensional indexing, multimedia databases, similarity search.

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Authors: Sezen Yildirim, Tahir Çetin Akinci, Serhat Seker, Nazmi Ekren

Abstract:

Ferroresonance is an electrical phenomenon in nonlinear character, which frequently occurs in power system due to transmission line faults and single or more-phase switching on the lines as well as usage of the saturable transformers. In this study, the ferroresonance phenomena are investigated under the modeling of the West Anatolian Electric Power Network of 380 kV in Turkey. The ferroresonance event is observed as a result of removing the loads at the end of the lines. In this sense, two different cases are considered. At first, the switching is applied at 2nd second and the ferroresonance affects are observed between 2nd and 4th seconds in the voltage variations of the phase-R. Hence the ferroresonance and nonferroresonance parts of the overall data are compared with each others using the Fourier transform techniques to show the ferroresonance affects.

Keywords: Ferroresonance, West Anatolian Electric Power System, Power System Modeling, Switching, Spectral Analysis.

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Authors: P. Varalaxmi, A. Kirubakaran

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This paper presents a thirteen-level asymmetrical cascaded H-bridge single phase inverter. In this configuration, the desired output voltage level is achieved by connecting the DC sources in different combinations by triggering the switches. The modes of operation are explained well for positive level generations. Moreover, a comparison is made with conventional topologies of diode clamped, flying capacitors and cascaded-H-bridge and some recently proposed topologies to show the significance of the proposed topology in terms of reduced part counts. The simulation work has been carried out in MATLAB/Simulink environment. The experimental work is also carried out for lower rating to verify the performance and feasibility of the proposed topology. Further the results are presented for different loading conditions.

Keywords: Multilevel inverter, pulse width modulation, total harmonic distortion, THD.

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Authors: Khaled A. Madi

Abstract:

Induction motors are being used in greater numbers throughout a wide variety of industrial and commercial applications because it provides many benefits and reliable device to convert the electrical energy into mechanical motion. In some application it-s desired to control the speed of the induction motor. Because of the physics of the induction motor the preferred method of controlling its speed is to vary the frequency of the AC voltage driving the motor. In recent years, with the microcontroller incorporated into an appliance it becomes possible to use it to generate the variable frequency AC voltage to control the speed of the induction motor. This study investigates the microcontroller based variable frequency power inverter. the microcontroller is provide the variable frequency pulse width modulation (PWM) signal that control the applied voltage on the gate drive, which is provides the required PWM frequency with less harmonics at the output of the power inverter. The fully controlled bridge voltage source inverter has been implemented with semiconductors power devices isolated gate bipolar transistor (IGBT), and the PWM technique has been employed in this inverter to supply the motor with AC voltage. The proposed drive system for three & single phase power inverter is simulated using Matlab/Simulink. The Matlab Simulation Results for the proposed system were achieved with different SPWM. From the result a stable variable frequency inverter over wide range has been obtained and a good agreement has been found between the simulation and hardware of a microcontroller based single phase inverter.

Keywords: Power, inverter, PWM, microcontroller.

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Authors: Michael P. Herring, Lavrent Khachatryan, Barry Dellinger

Abstract:

Low Temperature Matrix Isolation - Electron Paramagnetic Resonance (LTMI-EPR) Spectroscopy was utilized to identify the species of iron oxide nanoparticles generated during the oxidative pyrolysis of 1-methylnaphthalene (1-MN). The otherwise gas-phase reactions of 1--MN were impacted by a polypropylenimine tetra-hexacontaamine dendrimer complexed with iron (III) nitrate nonahydrate diluted in air under atmospheric conditions. The EPR fine structure of Fe (III)2O3 nanoparticles clusters, characterized by gfactors of 2.00, 2.28, 3.76 and 4.37 were detected on a cold finger maintained at 77 K after accumulation over a multitude of experiments. Additionally, a high valence Fe (IV) paramagnetic intermediate and superoxide anion-radicals, O2•- adsorbed on nanoparticle surfaces in the form of Fe (IV) --- O2•- were detected from the quenching area of Zone 1 in the gas-phase.

Keywords: Cryogenic trapping, EPFRs, dendrimer, Fe2O3 doped silica, soot.

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Authors: E. H. N. Gashti, J. Razzaghi, K. Kujala

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In general, codes and regulations consider seismic loads only for completed structures of the bridges while, evaluation of incomplete structure of bridges, especially those constructed by free cantilever method, under these loads is also of great importance. Hence, this research tried to study the behavior of incomplete structure of common bridge type (box girder bridge), in construction phase under vertical seismic loads. Subsequently, the paper provided suitable guidelines and solutions to resist this destructive phenomenon. Research results proved that use of preventive methods can significantly reduce the stresses resulted from vertical seismic loads in box cross sections to an acceptable range recommended by design codes.

Keywords: Box girder bridges, Prestress loads, Free cantilever method, Seismic loads, Construction phase.

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Authors: K. Derradji Belloum, A. Moussi

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Most high-performance ac drives utilize a current controller. The controller switches a voltage source inverter (VSI) such that the motor current follows a set of reference current waveforms. Fixed-band hysteresis (FBH) current control has been widely used for the PWM inverter. We want to apply the same controller for the PWM AC chopper. The aims of the controller is to optimize the harmonic content at both input and output sides, while maintaining acceptable losses in the ac chopper and to control in wide range the fundamental output voltage. Fixed band controller has been simulated and analyzed for a single-phase AC chopper and are easily extended to three-phase systems. Simulation confirmed the advantages and the excellent performance of the modulation method applied for the AC chopper.

Keywords: AC chopper, Current controller, Distortion factor, Hysteresis, Input Power Factor, PWM.

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Authors: Sikder Mohammad Faruk, Mir Mofajjal Hossain, Muhibul Haque Bhuyan

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In this investigative research paper, we have presented the simulation results of a three-phase rectifier circuit to improve the input side current using the passive filters, such as capacitors and inductors at the output and input terminals of the rectifier circuit respectively. All simulation works were performed in a personal computer using the PSPICE simulator software, which is a virtual circuit design and simulation software package. The output voltages and currents were measured across a resistive load of 1 k. We observed that the output voltage levels, input current wave shapes, harmonic contents through the harmonic spectrum, and total harmonic distortion improved due to the use of such filters.

Keywords: input current wave, three-phase rectifier, passive filter, PSPICE Simulation

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Authors: Nasrul Amri Mohd Amin, Martin Belusko, Frank Bruno

Abstract:

PCMs have always been viewed as a suitable candidate for off peak thermal storage, particularly for refrigeration systems, due to the high latent energy densities of these materials. However, due to the need to have them encapsulated within a container this density is reduced. Furthermore, PCMs have a low thermal conductivity which reduces the useful amount of energy which can be stored. To consider these factors, the true energy storage density of a PCM system was proposed and optimised for PCMs encapsulated in slabs. Using a validated numerical model of the system, a parametric study was undertaken to investigate the impact of the slab thickness, gap between slabs and the mass flow rate. The study showed that, when optimised, a PCM system can deliver a true energy storage density between 53% and 83% of the latent energy density of the PCM.

Keywords: Phase change material, refrigeration, sustainability, thermal energy storage.

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Authors: Pei-Syuan Ruan, Ya-Chi Yu, Shao-Wen Chen, Jin-Der Lee, Jong-Rong Wang, Chunkuan Shih

Abstract:

This study investigated the void fraction characteristics under low superficial gas velocity (J_g) and low superficial fluid velocity (J_f) conditions in a 3x3 rod bundle geometry. Three arrangements of conductivity probes were set to measure the void fraction at various cross-sectional regions, including rod-gap, sub-channel and rod-wall regions. The experimental tests were performed under the flow conditions of J_g = 0-0.236 m/s and J_f = 0-0.142 m/s, and the time-averaged void fractions were recorded at each flow condition. It was observed that while the superficial gas velocity increases, the small bubbles started to cluster together and become big bubbles. As the superficial fluid velocity increases, the local void fractions of the three test regions will get closer and the bubble distribution will be more uniform across the cross section.

Keywords: Conductivity probes, rod bundles, two-phase flow, void fraction.

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Authors: Hany Mahgoub, Dietmar Rösner, Nabil Ismail, Fawzy Torkey

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This paper describes text mining technique for automatically extracting association rules from collections of textual documents. The technique called, Extracting Association Rules from Text (EART). It depends on keyword features for discover association rules amongst keywords labeling the documents. In this work, the EART system ignores the order in which the words occur, but instead focusing on the words and their statistical distributions in documents. The main contributions of the technique are that it integrates XML technology with Information Retrieval scheme (TFIDF) (for keyword/feature selection that automatically selects the most discriminative keywords for use in association rules generation) and use Data Mining technique for association rules discovery. It consists of three phases: Text Preprocessing phase (transformation, filtration, stemming and indexing of the documents), Association Rule Mining (ARM) phase (applying our designed algorithm for Generating Association Rules based on Weighting scheme GARW) and Visualization phase (visualization of results). Experiments applied on WebPages news documents related to the outbreak of the bird flu disease. The extracted association rules contain important features and describe the informative news included in the documents collection. The performance of the EART system compared with another system that uses the Apriori algorithm throughout the execution time and evaluating extracted association rules.

Keywords: Text mining, data mining, association rule mining

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Authors: A. Ourici

Abstract:

Rapid progress in process automation and tightening quality standards result in a growing demand being placed on fault detection and diagnostics methods to provide both speed and reliability of motor quality testing. Doubly fed induction generators are used mainly for wind energy conversion in MW power plants. This paper presents a detection of an inter turn stator and an open phase faults, in a doubly fed induction machine whose stator and rotor are supplied by two pulse width modulation (PWM) inverters. The method used in this article to detect these faults, is based on Park-s Vector Approach, using a neural network.

Keywords: Doubly fed induction machine, inter turn stator fault, neural network, open phase fault, Park's vector approach, PWMinverter.

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Authors: Alibek Issakhov

Abstract:

In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics.

Keywords: MPI, OpenMP, three dimensional Poisson equation

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Authors: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Mhand Hifi, Hedi Mhalla

Abstract:

In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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Authors: Domingo López-Rodríguez, Enrique Mérida-Casermeiro, Juan M. Ortiz-de-Lazcano-Lobato

Abstract:

Hopfield model of associative memory is studied in this work. In particular, two main problems that it possesses: the apparition of spurious patterns in the learning phase, implying the well-known effect of storing the opposite pattern, and the problem of its reduced capacity, meaning that it is not possible to store a great amount of patterns without increasing the error probability in the retrieving phase. In this paper, a method to avoid spurious patterns is presented and studied, and an explanation of the previously mentioned effect is given. Another technique to increase the capacity of a network is proposed here, based on the idea of using several reference points when storing patterns. It is studied in depth, and an explicit formula for the capacity of the network with this technique is provided.

Keywords: Associative memory, Hopfield network, network capacity, spurious patterns.

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