Search results for: compensation of variation parameters

Authors: Ravi Shah, V. L. Manekar, R. A. Christian, N. J. Mistry

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There are two types of drought as conceptual drought and operational drought. The three parameters as the beginning, the end and the degree of severity of the drought can be identifying in operational drought by average precipitation in the whole region. One of the methods classified to measure drought is Reconnaissance Drought Index (RDI). Evapotranspiration is calculated using Penman-Monteith method by analyzing thirty nine years prolong climatic data. The evapotranspiration is then utilized in RDI to classify normalized and standardized RDI. These RDI classifications led to what kind of drought faced in Bhavnagar region on 12 month time scale basis. The comparison between actual drought conditions and RDI method used to find out drought are also illustrated. It can be concluded that the index results of drought in a particular year are same in both methods but having different index values where as severity remain same.

Keywords: Drought, Drought index, Reconnaissance Drought Index (RDI), Precipitation.

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Authors: Neetu Rani, Hema Setia, Marut Dutt. R.K. Wanchoo

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An empirical correlation for predicting the heat transfer coefficient for a cylinder under free convection, inclined at any arbitrary angle with the horizontal has been developed in terms of Nusselt number, Prandtl number and Grashof number. Available experimental data was used to determine the parameters for the proposed correlation. The proposed correlation predicts the available data well within ±10%, for Prandtl number in the range 0.68-0.72 and Grashof number in the range 1.4×10⁴–1.2×10¹⁰.

Keywords: Heat transfer, inclined cylinders, natural convection, Nusselt number, Prandtl number, Grashof number.

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Authors: M. Rehor, V. Ondracek

Abstract:

Restoration research has become important on principle recently in Czech Republic. The reason is simple. More than 70 % of mined brown coal comes from the North Bohemian Basin these days. Open cast brown coal mining has lead to large damage on the landscape. Reclamation of phytotoxic areas is one of the serious problems in the North Bohemian Basin. It mainly concerns the areas with the occurrence of overburden rocks from the coal bed enriched with coal. The presented paper includes the characteristics of the important phytotoxic areas and the methodology of their reclamation. The results are documented with the long term monitoring of physical, mineralogical, chemical and pedological parameters of rocks in the testing areas.

Keywords: Brown coal, dump, methodology, restoration.

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Authors: Md. Sharif Imam Ibne Amir, Mohammad Masud Kamal khan, Mohammad Golam Rasul, Raj H Sharma, Fatema Akram

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Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameters remaining stationary. However climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise are likely to change. To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: Climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment.

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Authors: A. Abdulkadir, Y. M. Bello, A. A. Okhimamhe, H. Ibrahim, M. B. Matazu, L. S. Barau

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The increasing volume of solid waste generated, collected and disposed daily complicate adequate management of solid waste by relevant agency like Niger State Environmental Protection Agency (NISEPA). In addition, the impacts of solid waste on the natural environment and human livelihood require identification of cost-effective ways for sustainable municipal waste management in Nigeria. These signal the need for identifying environment-friendly initiative and local solution to address the problem of municipal solid waste. A research field was secured at Pago, Minna, Niger State which is located in the guinea savanna belt of Nigeria, within longitude 60 361 4311 - 4511 and latitude 90 291 37.6111 - .6211 N. Poultry droppings, decomposed household waste manure and NPK treatments were used. The experimental field was divided into three replications and four (4) treatments on each replication making a total of twelve (12) plots. The treatments were allotted using Randomized Complete Block Design (RCBD) and Data collected was analyzed using SPSS software and RCBD. The result depicts variation in plant height and number of leaves at 50% flowering; Poultry dropping records the highest height while the number of leaves for waste manure competes fairly well with NPK treatment. Similarly, the varying treatments significantly increase vegetable yield, as the control (non-treatment) records the least yield for the three vegetable samples. Adoption of this organic manure for cultivation does not only enhance environment quality and attainment of food security but will contribute to local economic development, poverty alleviation as well as social inclusion.

Keywords: Environmental issues, food security, NISEPA, solid waste.

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Authors: Sumit Tiwari, Rohit Tripathi, G. N. Tiwari

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Present study focused on the utilization of solar energy by the help of photovoltaic greenhouse solar dryer under forced mode. A single slope photovoltaic greenhouse solar dryer has been proposed and thermal modelling has been developed. Various parameters have been calculated by thermal modelling such as greenhouse room temperature, cell temperature, crop temperature and air temperature at exit of greenhouse. Further cell efficiency, thermal efficiency, and overall thermal efficiency have been calculated for a typical day of May and November. It was found that system can generate equivalent thermal energy up to 7.65 kW and 6.66 kW per day for clear day of May and November respectively.

Keywords: Characteristics curve, Photovoltaic, Thermal modelling, Thermal efficiency.

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Authors: Ayse Yayla, Aynur Akar

Abstract:

Developments in scientific and technical area cause to use new methods and techniques in education, as is the case in all fields. Especially, the internet contributes a variety of new methods to design virtual and real time laboratory applications in education. In this study, a real time virtual laboratory is designed and implemented for analog and digital communications laboratory experiments by using Lab VIEW program for Marmara University Electronics-Communication Department. In this application, students can access the virtual laboratory web site and perform their experiments without any limitation of time and location so as the students can observe the signals by changing the parameters of the experiment and evaluate the results.

Keywords: Virtual laboratory, LabVIEW, ModulationTechniques

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Authors: S. K. Tiwari, Dinesh Kumar Shukla, R. Chandra

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Friction stir welding is a solid state joining process. High strength aluminum alloys are widely used in aircraft and marine industries. Generally, the mechanical properties of fusion welded aluminum joints are poor. As friction stir welding occurs in solid state, no solidification structures are created thereby eliminating the brittle and eutectic phases common in fusion welding of high strength aluminum alloys. In this review the process parameters, microstructural evolution, and effect of friction stir welding on the properties of weld specific to aluminum alloys have been discussed.

Keywords: Aluminum alloys, Friction stir welding (FSW), Microstructure, Properties.

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Authors: T. K. V. Iyengar, Punnamchandar Bitla

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The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.

Keywords: Pulsating flow, couple stress fluid, permeable beds, mass flux, shear stress.

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Authors: L. Korpinen, R. Pääkkönen, F. Gobba

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There has been discussion if the use of mobile phones causes accidents. We studied workers’ accidents and near accidents related to the use of phones. This study is part of a large cross-sectional study that was carried out on 15,000 working-age Finns. We noticed that there were 4–5 times more close call situations than accidents connected to mobile phones and also work related accidents were fewer than leisure related. There are confusing parameters like the use of mobile phones at work, differences in work content between women and men.

Keywords: Blue-collar workers, accident, cell phone, close call situation.

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Authors: Sandeep Sharma, Sarabjit Singh, Meenakshi Sharma

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Load balancing is the process of improving the performance of a parallel and distributed system through a redistribution of load among the processors [1] [5]. In this paper we present the performance analysis of various load balancing algorithms based on different parameters, considering two typical load balancing approaches static and dynamic. The analysis indicates that static and dynamic both types of algorithm can have advancements as well as weaknesses over each other. Deciding type of algorithm to be implemented will be based on type of parallel applications to solve. The main purpose of this paper is to help in design of new algorithms in future by studying the behavior of various existing algorithms.

Keywords: Load balancing (LB), workload, distributed systems, Static Load balancing, Dynamic Load Balancing

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Authors: Farhat Hajer, Khir Tahar, Cherni Rafik, Dakhli Radhouen, Ammar Ben Brahim

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This paper presents the energy and exergy optimization of a real gas turbine power plant performance of 100 MW of power, installed in the South East of Tunisia. A simulation code is established using the EES (Engineering Equation Solver) software. The parameters considered are those of the actual operating conditions of the gas turbine thermal power station under study. The results show that thermal and exergetic efficiency decreases with the increase of the ambient temperature. Air excess has an important effect on the thermal efficiency. The emission of NOx rises in the summer and decreases in the winter. The obtained rates of NOx are compared with measurements results.

Keywords: Efficiency, exergy, gas turbine, temperature.

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Authors: B.-A. Behrens, H. J. Maier, A. Neumann, J. Moritz, S. Hübner, T. Gretzki, F. Nürnberger, A. Spiekermeier

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Press-hardened profiles are used e.g. for automotive applications in order to improve light weight construction due to the high reachable strength. The application of interior water-air spray cooling contributes to significantly reducing the cycle time in the production of heat-treated tubes. This paper describes a new manufacturing method for producing press-hardened hollow profiles by means of an additional interior cooling based on a water-air spray. Furthermore, this paper provides the results of thorough investigations on the properties of press-hardened tubes in dependence of varying spray parameters.

Keywords: 22MnB5, hollow profiles, press hardening, tubes, water-air spray cooling.

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Authors: Zhi-Wei Zheng, Zhong-Qi Liu, Jia-Ling Qiu, Shan-Qing Guo, Zhong-Wei Jia, Chun Hao

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Objectives: The purpose of this study was to understand and examine the association between diurnal mood variation and sexual/health-related status among men who have sex with men (MSM) using data from MSM Chinese Twitter messages. The study consists of 843,745 postings of 377,610 MSM users located in Guangdong that were culled from the MSM Chinese Twitter App. Positive affect, negative affect, sexual related behaviors, and health-related status were measured using the Simplified Chinese Linguistic Inquiry and Word Count. Emotions, including joy, sadness, anger, fear, and disgust were measured using the Weibo Basic Mood Lexicon. A positive sentiment score and a positive emotions score were also calculated. Linear regression models based on a permutation test were used to assess associations between affective states and sexual/health-related status. In the results, 5,871 active MSM users and their 477,374 postings were finally selected. MSM expressed positive affect and joy at 8 a.m. and expressed negative affect and negative emotions between 2 a.m. and 4 a.m. In addition, 25.1% of negative postings were directly related to health and 13.4% reported seeking social support during that sensitive period. MSM who were senior, educated, overweight or obese, self-identified as performing a versatile sex role, and with less followers, more followers, and less chat groups mainly expressed more negative affect and negative emotions. MSM who talked more about sexual-related behaviors had a higher positive sentiment score (β=0.29, p < 0.001) and a higher positive emotions score (β = 0.16, p < 0.001). MSM who reported more on their health status had a lower positive sentiment score (β = -0.83, p < 0.001) and a lower positive emotions score (β = -0.37, p < 0.001). The study concluded that psychological intervention based on an app for MSM should be conducted, as it may improve mental health.

Keywords: Affect, men who have sex with men, sexual-related behaviors, health-related status, social media.

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Authors: Mohammad Hosseini

Abstract:

Ultrafast transistor laser investigated here has the graded index separate confinement heterostructure (GRIN-SCH) in its base region. Resonance-free optical frequency response with -3 dB bandwidth of more than 26 GHz has been achieved for a single quantum well transistor laser by using graded index layers of AlξGa1-ξAs (ξ: 0.1→0) in the left side of quantum well and AlξGa1-ξAs (ξ: 0.05→0) in the right side of quantum well. All required parameters, including quantum well and base transit time, optical confinement factor and spontaneous recombination lifetime, have been calculated using a self-consistent charge control model.

Keywords: Transistor laser, ultrafast, GRIN-SCH, -3db optical bandwidth, AlξGa1-ξAs.

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Authors: Boukelkoul Lahcen

Abstract:

The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: Cost, finite state, Markov model, operation, maintenance.

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Authors: Y. Si Youcef, M. Chemrouk

Abstract:

The present work presents a method of calculating the ductility of rectangular sections of beams considering nonlinear behavior of concrete and steel. This calculation procedure allows us to trace the curvature of the section according to the bending moment, and consequently deduce ductility. It also allowed us to study the various parameters that affect the value of the ductility. A comparison of the effect of maximum rates of tension steel, adopted by the codes, ACI [1], EC8 [2] and RPA [3] on the value of the ductility was made. It was concluded that the maximum rate of steels permitted by the ACI [1] codes and RPA [3] are almost similar in their effect on the ductility and too high. Therefore, the ductility mobilized in case of an earthquake is low, the inverse of code EC8 [2]. Recommendations have been made in this direction.

Keywords: Ductility, beam, reinforced concrete, seismic code, relationship, time bending, resistance, non-linear behavior.

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Authors: Farzaneh Tahmoorian, Bijan Samali, John Yeaman

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Road networks are increasingly expanding all over the world. The construction and maintenance of the road pavements require large amounts of aggregates. Considerable usage of various natural aggregates for constructing roads as well as the increasing rate at which solid waste is generated have attracted the attention of many researchers in the pavement industry to investigate the feasibility of the application of some of the waste materials as alternative materials in pavement construction. Among various waste materials, construction and demolition wastes, including Recycled Construction Aggregate (RCA) constitute a major part of the municipal solid wastes in Australia. Creating opportunities for the application of RCA in civil and geotechnical engineering applications is an efficient way to increase the market value of RCA. However, in spite of such promising potentials, insufficient and inconclusive data and information on the engineering properties of RCA had limited the reliability and design specifications of RCA to date. In light of this, this paper, as a first step of a comprehensive research, aims to investigate the feasibility of the application of RCA obtained from construction and demolition wastes for the replacement of part of coarse aggregates in asphalt mixture. As the suitability of aggregates for using in asphalt mixtures is determined based on the aggregate characteristics, including physical and mechanical properties of the aggregates, an experimental program is set up to evaluate the physical and mechanical properties of RCA. This laboratory investigation included the measurement of compressive strength and workability of RCA, particle shape, water absorption, flakiness index, crushing value, deleterious materials and weak particles, wet/dry strength variation, and particle density. In addition, the comparison of RCA properties with virgin aggregates has been included as part of this investigation and this paper presents the results of these investigations on RCA, basalt, and the mix of RCA/basalt.

Keywords: Asphalt, basalt, pavement, recycled aggregate.

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Authors: Abd Elrahman Elgamala, N. Darwish, I. Bondouk, Sh. Hamada

Abstract:

Available experimental angular distributions for ⁶Li elastically scattered from ¹⁶O nucleus in the energy range 13.0–50.0 MeV are investigated and reanalyzed using optical model of the conventional phenomenological potential and also using double folding optical model of different interaction models: DDM3Y1, CDM3Y1, CDM3Y2, and CDM3Y3. All the involved models of interaction are of M3Y Paris except DDM3Y1 which is of M3Y Reid and the main difference between them lies in the different values for the parameters of the incorporated density distribution function F(ρ). We have extracted the renormalization factor N_R for ⁶Li+¹⁶O nuclear system in the energy range 13.0–50.0 MeV using the aforementioned interaction models.

Keywords: Elastic scattering, optical model, folding potential, density distribution.

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Authors: Arash Azizi-Mazreah, Mohammad T. Manzuri Shalmani, Hamid Barati, Ali Barati

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The energy consumption and delay in read/write operation of conventional SRAM is investigated analytically as well as by simulation. Explicit analytical expressions for the energy consumption and delay in read and write operation as a function of device parameters and supply voltage are derived. The expressions are useful in predicting the effect of parameter changes on the energy consumption and speed as well as in optimizing the design of conventional SRAM. HSPICE simulation in standard 0.25μm CMOS technology confirms precision of analytical expressions derived from this paper.

Keywords: Read energy consumption, write energy consumption, read delay, write delay.

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Authors: A. Nour Eddine, D. Chalet, L. Aixala, P. Chessé, X. Faure, N. Hatat

Abstract:

Thermal power technology such as the TEG (Thermo-Electric Generator) arouses significant attention worldwide for waste heat recovery. Despite the potential benefits of marine application due to the permanent heat sink from sea water, no significant studies on this application were to be found. In this study, a test rig has been designed and built to test the performance of the TEG on engine operating points. The TEG device is built from commercially available materials for the sake of possible economical application. Two types of commercial TEM (thermo electric module) have been studied separately on the test rig. The engine data were extracted from a commercial Diesel engine since it shares the same principle in terms of engine efficiency and exhaust with the marine Diesel engine. An open circuit water cooling system is used to replicate the sea water cold source. The characterization tests showed that the silicium-germanium alloys TEM proved a remarkable reliability on all engine operating points, with no significant deterioration of performance even under sever variation in the hot source conditions. The performance of the bismuth-telluride alloys was 100% better than the first type of TEM but it showed a deterioration in power generation when the air temperature exceeds 300 °C. The temperature distribution on the heat exchange surfaces revealed no useful combination of these two types of TEM with this tube length, since the surface temperature difference between both ends is no more than 10 °C. This study exposed the perspective of use of TEG technology for marine engine exhaust heat recovery. Although the results suggested non-sufficient power generation from the low cost commercial TEM used, it provides valuable information about TEG device optimization, including the design of heat exchanger and the types of thermo-electric materials.

Keywords: Internal combustion engine application, Seebeck, thermo-electricity, waste heat recovery.

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Authors: Saeed AL-Rashdy, Qing Guo

Abstract:

The IEEE802.16 standard which has emerged as Broadband Wireless Access (BWA) technology, promises to deliver high data rate over large areas to a large number of subscribers in the near future. This paper analyze the effect of overheads over capacity of downlink (DL) of orthogonal frequency division multiple access (OFDMA)–based on the IEEE802.16e mobile WiMAX system with and without overheads. The analysis focuses in particular on the impact of Adaptive Modulation and Coding (AMC) as well as deriving an algorithm to determine the maximum numbers of subscribers that each specific WiMAX sector may support. An analytical study of the WiMAX propagation channel by using Cost- 231 Hata Model is presented. Numerical results and discussion estimated by using Matlab to simulate the algorithm for different multi-users parameters.

Keywords: BWA, mobile WiMAX, capacity, AMC , overheads.

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Authors: G. B. Hong, H. W. Chen

Abstract:

Liquid-Liquid Equilibrium (LLE) data are measured for the ternary mixtures of water + 1-butanol + butyl acetate and quaternary mixtures of water + 1-butanol + butyl acetate + glycerol at atmospheric pressure at 313.15 K. In addition, isothermal vapor–liquid–liquid equilibrium (VLLE) data are determined experimentally at 333.15 K. The region of heterogeneity is found to increase as the hydrophilic agent (glycerol) is introduced into the aqueous mixtures. The experimental data are correlated with the NRTL model. The predicted results from the solution model with the model parameters determined from the constituent binaries are also compared with the experimental values.

Keywords: LLE, VLLE, hydrophilic agent, NRTL.

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Authors: Ermanu A. Hakim, Adi Soeprijanto, Mauridhi H.P

Abstract:

This paper presents PSS (Power system stabilizer) design based on optimal fuzzy PID (OFPID). OFPID based PSS design is considered for single-machine power systems. The main motivation for this design is to stabilize or to control low-frequency oscillation on power systems. Firstly, describing the linear PID control then to combine this PID control with fuzzy logic control mechanism. Finally, Fuzzy PID parameters (Kp. Kd, KI, Kupd, Kui) are tuned by Genetic Algorthm (GA) to reach optimal global stability. The effectiveness of the proposed PSS in increasing the damping of system electromechanical oscillation is demonstrated in a one-machine-infinite-bus system

Keywords: Fuzzy PID, Genetic Algorithm, power system stabilizer.

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Authors: C. Bisu, M. Zapciu, A. Gérard

Abstract:

This paper proposes a method to vibration analysis in order to on-line monitoring and predictive maintenance during the milling process. Adapting envelope method to diagnostics and the analysis for milling tool materials is an important contribution to the qualitative and quantitative characterization of milling capacity and a step by modeling the three-dimensional cutting process. An experimental protocol was designed and developed for the acquisition, processing and analyzing three-dimensional signal. The vibration envelope analysis is proposed to detect the cutting capacity of the tool with the optimization application of cutting parameters. The research is focused on Hilbert transform optimization to evaluate the dynamic behavior of the machine/ tool/workpiece.

Keywords: diagnostics, envelope, milling, vibration

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Authors: Hai-Qing Xie, Yun Zeng, Yong-Hong Yan, Guo-Liang Zhang, Tai-Hong Wang

Abstract:

We propose photo-BJMOSFET (Bipolar Junction Metal-Oxide-Semiconductor Field Effect Transistor) fabricated on SOI film. ITO film is adopted in the device as gate electrode to reduce light absorption. I-V characteristics of photo-BJMOSFET obtained in dark (dark current) and under 570nm illumination (photo current) are studied furthermore to achieve high photo-to-dark-current contrast ratio. Two variables in the calculation were the channel length and the thickness of the film which were set equal to six different values, i.e., L=2, 4, 6, 8, 10, and 12μm and three different values, i.e., dsi =100, 200 and 300nm, respectively. The results indicate that the greatest photo-to-dark-current contrast ratio is achieved with L=10μm and dsi=200 nm at VGK=0.6V.

Keywords: Photo-to-dark-current contrast ratio, Photo-current, Dark-current, Process parameter

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Authors: Liyana Zahid, Mohd Fareq Abd Malek, Ee Meng Cheng, Wei Wen Liu, Yeng Seng Lee, Muhammad Nadeem Iqbal, Fwen Hoon Wee, Farrah Salwani Abdullah

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One of the parameters that affect the performance of microwave absorbers is the shape of the absorbers. This paper shows the performance (reflection loss) of truncated pyramidal and truncated wedge microwave absorbers in the range frequency between 8.2 to 12.4 GHz (X-Band) in simulation. The material used is sugarcane bagasse (SCB) which is one of the new materials that used to fabricate the microwave absorber. The complex permittivity was measured using Agilent dielectric probe technique. The designs were simulated using CST Microwave Studio Software. The reflection losses between these two shapes were compared.

Keywords: Microwave Absorber, Reflection Loss, Sugarcane Bagasse (SCB), X- Band.

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Authors: Abdullah Al Faruque, Ram Balachandar

Abstract:

Series of laboratory tests were carried out to study the extent of scour caused by a three-dimensional wall jets exiting from a square cross-section nozzle and into a non-cohesive sand beds. Previous observations have indicated that the effect of the tail water depth was significant for densimetric Froude number greater than ten. However, the present results indicate that the cut off value could be lower depending on the value of grain size-to-nozzle width ratio. Numbers of equations are drawn out for a better scaling of numerous scour parameters. Also suggested the empirical prediction of scour to predict the scour centre line profile and plan view of scour profile at any particular time.

Keywords: Densimetric Froude Number, Jets, Nozzle, Sand, Scour, Tailwater, Time.

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Authors: Abdussamad Ismail, Dong-Sheng Jeng

Abstract:

A self-evolution algorithm for optimizing neural networks using a combination of PSO and JPSO is proposed. The algorithm optimizes both the network topology and parameters simultaneously with the aim of achieving desired accuracy with less complicated networks. The performance of the proposed approach is compared with conventional back-propagation networks using several synthetic functions, with better results in the case of the former. The proposed algorithm is also implemented on slope stability problem to estimate the critical factor of safety. Based on the results obtained, the proposed self evolving network produced a better estimate of critical safety factor in comparison to conventional BPN network.

Keywords: Neural networks, Topology evolution, Particle swarm optimization.

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Authors: Ozlem Faydasicok, Sabri Arik

Abstract:

This paper derives some new sufficient conditions for the stability of a class of neutral-type neural networks with discrete time delays by employing a suitable Lyapunov functional. The obtained conditions can be easily verified as they can be expressed in terms of the network parameters only. It is shown that the results presented in this paper for neutral-type delayed neural networks establish a new set of stability criteria, and therefore can be considered as the alternative results to the previously published literature results. A numerical example is also given to demonstrate the applicability of our proposed stability criterion.

Keywords: Stability Analysis, Neutral-Type Neural Networks, Time Delay Systems, Lyapunov Functionals.

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