Search results for: Negative hypergeometric distribution

Authors: Dehghan Manshadi M., Mirzaei M., Soltani M. R., Ghorbanian K.

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Subsonic wind tunnel experiments were conducted to study the effect of tripped boundary layer on the pressure distribution in the contraction region of the tunnel. Measurements were performed by installing trip strip at two different positions in the concave portion of the contraction. The results show that installation of the trip strips, have significant effects on both turbulence and pressure distribution. The reduction in the free stream turbulence and reduction of the wall static pressure distribution deferred signified with the location of the trip strip.

Keywords: Contraction, pressure distribution, trip strip, turbulence intensity.

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Authors: Ahmed Mateen, Zhu Qingsheng, Ahmad Bilal

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In the current age of technology, information is the most precious asset of a company. Today, companies have a large amount of data. As the data become larger, access to data for some particular information is becoming slower day by day. Faster data processing to shape it in the form of information is the biggest issue. The major problems in distributed databases are the efficiency of data distribution and response time of data distribution. The security of data distribution is also a big issue. For these problems, we proposed a strategy that can maximize the efficiency of data distribution and also increase its response time. This technique gives better results for secure data distribution from multiple heterogeneous sources. The newly proposed technique facilitates the companies for secure data sharing efficiently and quickly.

Keywords: ER-schema, electronic record, P2P framework, API, query formulation.

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Authors: Mohammad Shoyaib, M. Abdullah-Al-Wadud, Oksam Chae

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Proteomics is one of the largest areas of research for bioinformatics and medical science. An ambitious goal of proteomics is to elucidate the structure, interactions and functions of all proteins within cells and organisms. Predicting Protein-Protein Interaction (PPI) is one of the crucial and decisive problems in current research. Genomic data offer a great opportunity and at the same time a lot of challenges for the identification of these interactions. Many methods have already been proposed in this regard. In case of in-silico identification, most of the methods require both positive and negative examples of protein interaction and the perfection of these examples are very much crucial for the final prediction accuracy. Positive examples are relatively easy to obtain from well known databases. But the generation of negative examples is not a trivial task. Current PPI identification methods generate negative examples based on some assumptions, which are likely to affect their prediction accuracy. Hence, if more reliable negative examples are used, the PPI prediction methods may achieve even more accuracy. Focusing on this issue, a graph based negative example generation method is proposed, which is simple and more accurate than the existing approaches. An interaction graph of the protein sequences is created. The basic assumption is that the longer the shortest path between two protein-sequences in the interaction graph, the less is the possibility of their interaction. A well established PPI detection algorithm is employed with our negative examples and in most cases it increases the accuracy more than 10% in comparison with the negative pair selection method in that paper.

Keywords: Interaction graph, Negative training data, Protein-Protein interaction, Support vector machine.

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Authors: Abdullah M. Alodhaiani, Yasir A. Alturki, Mohamed A. Elkady

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Complex power flow distribution factors, which relate line complex power flows to the bus injected complex powers, have been widely used in various power system planning and analysis studies. In particular, AC distribution factors have been used extensively in the recent power and energy pricing studies in free electricity market field. As was demonstrated in the existing literature, many of the electricity market related costing studies rely on the use of the distribution factors. These known distribution factors, whether the injection shift factors (ISF’s) or power transfer distribution factors (PTDF’s), are linear approximations of the first order sensitivities of the active power flows with respect to various variables. This paper presents a novel model for evaluating the universal distribution factors (UDF’s), which are appropriate for an extensive range of power systems analysis and free electricity market studies. These distribution factors are used for the calculations of lines complex power flows and its independent of bus power injections, they are compact matrix-form expressions with total flexibility in determining the position on the line at which line flows are measured. The proposed approach was tested on IEEE 9-Bus system. Numerical results demonstrate that the proposed approach is very accurate compared with exact method.

Keywords: Distribution Factors, Power System, Sensitivity Factors, Electricity Market.

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Authors: M. A. Hasan, M. R. Islam, R. A. Tarefder

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This study investigates how the site specific traffic data differs from the Mechanistic Empirical Pavement Design Software default values. Two Weigh-in-Motion (WIM) stations were installed in Interstate-40 (I-40) and Interstate-25 (I-25) to developed site specific data. A computer program named WIM Data Analysis Software (WIMDAS) was developed using Microsoft C-Sharp (.Net) for quality checking and processing of raw WIM data. A complete year data from November 2013 to October 2014 was analyzed using the developed WIM Data Analysis Program. After that, the vehicle class distribution, directional distribution, lane distribution, monthly adjustment factor, hourly distribution, axle load spectra, average number of axle per vehicle, axle spacing, lateral wander distribution, and wheelbase distribution were calculated. Then a comparative study was done between measured data and AASHTOWare default values. It was found that the measured general traffic inputs for I-40 and I-25 significantly differ from the default values.

Keywords: AASHTOWare, Traffic, Weigh-in-Motion, Axle load Distribution.

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Authors: Kasthurirangan Gopalakrishnan, Naga Shashidhar

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The mechanical properties of granular solids are dependent on the flow of stresses from one particle to another through inter-particle contact. Although some experimental methods have been used to study the inter-particle contacts in the past, preliminary work with these techniques indicated that they do not have the necessary resolution to distinguish between those contacts that transmit the load and those that do not, especially for systems with a wide distribution of particle sizes. In this research, computer simulations are used to study the nature and distribution of contacts in a compact with wide particle size distribution, representative of aggregate size distribution used in asphalt pavement construction. The packing fraction, the mean number of contacts and the distribution of contacts were studied for different scenarios. A methodology to distinguish and compute the fraction of load-bearing particles and the fraction of space-filling particles (particles that do not transmit any force) is needed for further investigation.

Keywords: Computer simulation, three-dimensional particlepacking, coordination number, asphalt concrete, aggregates.

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Authors: Mehdi Seifbarghy, Sajjad Jalali, Seyed Habib A. Rahmati

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Recently studies in area of supply chain network (SCN) have focused on the disruption issues in distribution systems. Also this paper extends the previous literature by providing a new biobjective model for cost minimization of designing a three echelon SCN across normal and failure scenarios with considering multi capacity option for manufacturers and distribution centers. Moreover, in order to solve the problem by means of LINGO software, novel model will be reformulated through a branch of LP-Metric method called Min-Max approach.

Keywords: Scenario programming, Distribution, Multi-echelon supply chain design, Reliable facility

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, Nonlinearity distribution, Particle filter.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

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This paper presents a simple three phase power flow method for solution of three-phase unbalanced radial distribution system (RDN) with voltage dependent loads. It solves a simple algebraic recursive expression of voltage magnitude, and all the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily understood. Mutual coupling between the phases has been included in the mathematical model. The proposed algorithm has been tested with several unbalanced radial distribution networks and the results are presented in the article. 8- bus and IEEE 13 bus unbalanced radial distribution system results are in agreements with the literature and show that the proposed model is valid and reliable.

Keywords: radial distribution networks, load flow, circuitmodel, three-phase four-wire, unbalance.

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Authors: Zakir Husain, Neem Sagar, Neeraj Gupta

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Due to the increased penetration of renewable energy resources in the distribution system, the system is no longer passive in nature. In this paper, a steady state analysis of the distribution system has been done with the inclusion of wind generation. The modeling of wind turbine generator system and wind generator has been made to obtain the average active and the reactive power injection into the system. The study has been conducted on a IEEE-33 bus system with two wind generators. The present research work is useful not only to utilities but also to customers.

Keywords: Distributed generation, distribution network, radial network, wind turbine generating system.

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Authors: Chang-il Kang, Yoon-Hong Park, Tae-Hyun Kim, Yu Wann

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In this paper, we analyzed the pattern of urban spatial structure of Siheung City that had been divided into two parts and presented alternative plans in order to get rid of these phenomena. Concerning patterns of urban spatial structure, we examined it through means of analyzing status of land use, population density and distribution of residence, status of distribution of main facilities, medical facilities, status of distribution of cultural facilities, distribution of land prices and traffic volume trends. The results of study revealed that status of facilities distribution and distribution of land prices, etc. were bisected by the surrounding area of former municipal office and the district of Sihwa, which were both regarded as one apex of the city divide, forming a duo-centric city. In order to get rid of this problem concerned with urban spatial structure that has been bisected, it is required that measures in order to expand facilities in Siheung City should be taken.

Keywords: Urban Spatial Structure, Duo-centric City, Siheung City.

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Authors: Sheng-Shu Cheng, Fong-Jung Yu

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C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.

Keywords: Nonconformities, Compound Poisson distribution, CUSUM control chart.

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Authors: Chengming Li, Yong Yin, Peipei Guo, Xiaoli Liu

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Without taking account of the attribute richness of POI (point of interest) data and spatial distribution limited by roads, a POI generalization method considering both attribute information and spatial distribution has been proposed against the existing point generalization algorithm merely focusing on overall information of point groups. Hierarchical characteristic of urban POI information expression has been firstly analyzed to point out the measurement feature of the corresponding hierarchy. On this basis, an urban POI generalizing strategy has been put forward: POIs urban road network have been divided into three distribution pattern; corresponding generalization methods have been proposed according to the characteristic of POI data in different distribution patterns. Experimental results showed that the method taking into account both attribute information and spatial distribution characteristics of POI can better implement urban POI generalization in the mapping presentation.

Keywords: POI, Road network, spatial information expression, selection method, distribution pattern.

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Authors: H. Kazemi Karegar, S. Jalilzadeh, V. Nabaei, A. Shabani

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In this paper, the problem of finding the optimal topological configuration of a deregulated distribution network is considered. The new features of this paper are proposing a multiobjective function and its application on deregulated distribution networks for finding the optimal configuration. The multi-objective function will be defined for minimizing total Energy Supply Costs (ESC) and energy losses subject to load flow constraints. The optimal configuration will be obtained by using Binary Genetic Algorithm (BGA).The proposed method has been tested to analyze a sample and a practical distribution networks.

Keywords: Binary Genetic Algorithm, Deregulated Distribution Network, Minimizing Cost, Reconfiguration.

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

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Numerical study is performed to investigate the temperature distribution in an annular diffuser fitted with helical tape hub. Different pitches (Y = 20 mm, and Y = 30 mm) for the helical tape are studied with different heights (H = 20 mm, 22 mm, and 24 mm) to be compared. The geometry of the annular diffuser and the inlet condition for both hub arrangements are kept constant. The result obtains that using helical tape insert with different pitches and different heights will force the temperature to distribute in a helical direction; however the use of helical tape hub with height (H = 22 mm) for both pitches enhance the temperature distribution in a good manner.

Keywords: Helical tape, divergent fluid flow, temperature distribution, swirl flow, CFD.

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Authors: R. K. Saxena, Ravi Saxena

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In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Keke Gao, Tao Lin, Yonghui Xie, Di Zhang

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Complicated unsteady flow in axial turbines produces high-frequency unsteady aerodynamic exciting force, which threatens the safe operation of turbines. This paper illustrates how negative-bowed stator reduces the rotor unsteady aerodynamic exciting force by unsteady flow field. With the support of three-dimensional viscous compressible Navier-Stokes equation, the single axial turbines with 0, -10 and -20 degree bowed stator are comparably investigated, aiming to identify the flow field structure difference caused by various negative-bowed degrees. The results show that negative-bowed stator strengthens the turbulence kinetic energy, which is further strengthened with the increase of negative-bowed degree. Meanwhile, the flow phenomenon including stator wakes and passage vortex is shown. In addition, the interaction of upstream negative-bowed wakes contributes to the reduction of unsteady blade load fluctuation. Furthermore, the aerodynamic exciting force decreases with the increasing negative bowed degree, while the efficiency is correspondingly reduced. This paper provides the reference for the alleviation of the harmful impact caused by unsteady interaction with the method of wake control.

Keywords: Unsteady flow, axial turbine, wake, aerodynamic force, loss.

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Authors: Yueying Wu, Fengzhu Lv, Yihe Zhang, Zixian Xu

Abstract:

Antimosy-doped tin oxide (ATO) particles were prepared via chemical coprecipitation and reverse emulsion. The size and size distribution of ATO particles were obviously decreased via reverse microemulsion method. At the relatively high yield the ATO particles were nearly spherical in shape, meanwhile the crystalline structure and excellent conductivity were reserved, which could satisfy the requirement as composite fillers, such as dielectric filler of polyimide film.

Keywords: ATO particle, Conductivity, Distribution, Reverse emulsion

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Authors: A. R. Malekpour, A.R. Seifi

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This paper discusses a genetic algorithm (GA) based optimal load shedding that can apply for electrical distribution networks with and without dispersed generators (DG). Also, the proposed method has the ability for considering constant and variable capacity deficiency caused by unscheduled outages in the bulked generation and transmission system of bulked power supply. The genetic algorithm (GA) is employed to search for the optimal load shedding strategy in distribution networks considering DGs in two cases of constant and variable modelling of bulked power supply of distribution networks. Electrical power distribution systems have a radial network and unidirectional power flows. With the advent of dispersed generations, the electrical distribution system has a locally looped network and bidirectional power flows. Therefore, installed DG in the electrical distribution systems can cause operational problems and impact on existing operational schemes. Introduction of DGs in electrical distribution systems has introduced many new issues in operational and planning level. Load shedding as one of operational issue has no exempt. The objective is to minimize the sum of curtailed load and also system losses within the frame-work of system operational and security constraints. The proposed method is tested on a radial distribution system with 33 load points for more practical applications.

Keywords: DG, Load shedding, Optimization, Capacity Deficiency Modelling.

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Authors: Volker Lange, Stephanie Moede, Christiane Auffermann

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From an economic standpoint the current and future road traffic situation in urban areas is a cost factor. Traffic jams and congestion prolong journey times and tie up resources in trucks and personnel. Many discussions about imposing charges or tolls for cities in Europe in order to reduce traffic congestion are currently in progress. Both of these effects lead – directly or indirectly - to additional costs for the urban distribution systems in retail companies. One approach towards improving the efficiency of retail distribution systems, and thus towards avoiding negative environmental factors in urban areas, is horizontal collaboration for deliveries to retail outlets – Urban Retail Logistics. This paper presents a classification system to help reveal where cooperation between retail companies is possible and makes sense for deliveries to retail outlets in urban areas.

Keywords: City Logistics, Horizontal Collaboration, Urban Freight Transport, Urban Retail Logistics.

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Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.

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Authors: Ei Ei Phyu, Kyaw Myo Lin, Thin Thin Moe

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The paper presents an approach to improve the reliability and reduce line losses of practical distribution system applying network reconfiguration. The change of the topology redirects the power flow within the distribution network to obtain better performance of the system. Practical distribution network (Pyigyitagon Industrial Zone (I)) is used as the case study network. The detailed calculations of the reliability indices are done by using analytical method and power flow calculation is performed by Newton-Rephason solver. The comparison of various network reconfiguration techniques are described with respect to power loss and reliability index levels. Finally, the optimal reconfigured network is selected among difference cases based on the two factors: the most reliable network and the least loss minimization.

Keywords: Distribution system reliability, loss reduction, network reconfiguration, reliability enhancement, reliability indices.

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

Abstract:

The influence of twist arrangement on the temperature distribution in an annular diffuser fitted with twisted rectangular hub is investigated. Different pitches (Y = 120 mm, 100 mm, 80 mm, and 60 mm) for the twist arrangements are simulated to be compared. The geometry of the annular diffuser and the inlet condition for the hub arrangements are kept constant. The result reveals that using twisted rectangular hub insert with different pitches will force the temperature to distribute in a circular direction. However, temperature distribution will be enhanced with the length pitch increases.

Keywords: Numerical simulation, twist arrangement, annular diffuser, temperature distribution, swirl flow, pitches.

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Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

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This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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Authors: N. Ruangkajonmathee, R. Thiamsri, B. Marungsri

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This paper presents the experimental results on space charge distribution in cross-linked polyethylene (XLPE) insulating material for 22 kV power distribution system cable by using pulse electroacoustic measurement technique (PEA). Numbers of XLPE insulating material ribbon having thickness 60 μm taken from unused 22 kV high voltage cable were used as specimen in this study. DC electric field stress was applied to test specimen at room temperature (25°C). Four levels of electric field stress, 25 kV/mm, 50 kV/mm, 75 kV/mm and 100 kV/mm, were used. In order to investigate space charge distribution characteristic, space charge distribution characteristics were measured after applying electric field stress 15 min, 30 min and 60 min, respectively. The results show that applied time and magnitude of dc electric field stress play an important role to the formation of space charge.

Keywords: Space charge distribution, pulsed electroacoustic(PEA) technique, cross-linked polyethylene (XLPE), DC electrical fields stress.

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Authors: Siti Aisyah Zakaria, Nor Azrita Mohd Amin, Noor Fadhilah Ahmad Radi, Nasrul Hamidin

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Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.

Keywords: Extreme value theory, generalized extreme value distribution, ground-level ozone, return level.

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Authors: Snehasis Kundu, Koeli Ghoshal

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In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

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Authors: S. Chebbi, A. Meddeb

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The distribution networks are often exposed to harmful incidents which can halt the electricity supply of the customer. In this context, we studied a real case of a critical zone of the Tunisian network which is currently characterized by the dysfunction of its plan of protection. In this paper, we were interested in the harmonization of the protection plan settings in order to ensure a perfect selectivity and a better continuity of service on the whole of the network.

Keywords: Distribution network Gabes-Tunisia, NEPLAN©DACH, protection plan settings, selectivity.

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Authors: Kun Lei, Hongfang Ma, Haitao Zhang, Weiyong Ying, Dingye Fang

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This paper reported an experimental research of steady-state heat transfer behaviour of a gas flowing through a fixed bed under the different operating conditions. Studies had been carried out in a fixed-bed packed methanol synthesis catalyst percolated by air at appropriate flow rate. Both radial and axial direction temperature distribution had been investigated under the different operating conditions. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on temperature distribution was investigated and the experimental results showed that a higher inlet air temperature was conducive to uniform temperature distribution in the fixed bed. A large temperature drop existed at the radial direction, and the temperature drop increased with the heating pipe temperature increasing under the experimental conditions; the temperature profile of the vicinity of the heating pipe was strongly affected by the heating pipe temperature. A higher air flow rate can improve the heat transfer in the fixed bed. Based on the thermal distribution, heat transfer models of the fixed bed could be established, and the characteristics of the temperature distribution in the fixed bed could be finely described, that had an important practical significance.

Keywords: Thermal distribution, heat transfer, axial-flow, fixed bed.

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Authors: Lloyd G. Allred

Abstract:

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: Cosmology, EMP, Euclidean, plasma physics, relativity.

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