Search results for: Thermal relaxation times.

Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

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As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Eric Costa, Sara Bragança, Rui Sousa, Anabela Alves

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This paper presents an application of the Single-Minute Exchange of Die (SMED) methodology to a turret punching machine in an elevators company, in Portugal. The work was developed during five months, in the ambit of a master thesis in Industrial Engineering and Management. The Lean Production tool SMED was applied to reduce setup times in order to improve the production flexibility of the machine. The main results obtained were a reduction of 64% in setup time (from 15.1 to 5.4min), 50% in work-in-process amount (from 12.8 to 6.4 days) and 99% in the distance traveled by the operator during the internal period (from 136.7 to 1.7m). These improvements correspond to gains of about €7,315.38 per year.

Keywords: Lean production, setup process, SMED.

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Authors: Aare Kuusik, E. Loigu, O. Sokk, Argo Kuusik

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This paper describes technological possibilities to enhance methane productionin the anaerobic stabilization of wastewater treatment plant excess sludge. This objective can be achieved by the addition of waste residues: crude glycerol from biodiesel production and residues from fishery. The addition ofglycerol in an amount by weight of 2 – 5% causes enhancement of methane production of about 250 – 400%. At the same time the percentage increase of total solids concentration in the outgoing sludge is ten or more times less. The containment of methane in biogas is higher in case of admixed substrate.

Keywords: Enhancement of methane production, fishery residues, waste glycerol

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Authors: Haroun A.K. Shahad, Nabeel Abdul-Hadi

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Experiments were carried out to evaluate the influence of the addition of hydrogen to the inlet air on the performance of a single cylinder direct injection diesel engine. Hydrogen was injected in the inlet manifold. The addition of hydrogen was done on energy replacement basis. It was found that the addition of hydrogen improves the combustion process due to superior combustion characteristics of hydrogen in comparison to conventional diesel fuels. It was also found that 10% energy replacement improves the engine thermal efficiency by about 40% and reduces the sfc by about 35% however the volumetric efficiency was reduced by about 35%.

Keywords: Hydrogen, Blended fuel, Manifold injection , Performance , Combustion

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Authors: S. Iffat, B. Bose

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Concrete as a construction material is versatile because it displays high degree of fire-resistance. Concrete’s inherent ability to combat one of the most devastating disaster that a structure can endure in its lifetime, can be attributed to its constituent materials which make it inert and have relatively poor thermal conductivity. However, concrete structures must be designed for fire effects. Structural components should be able to withstand dead and live loads without undergoing collapse. The properties of high-strength concrete must be weighed against concerns about its fire resistance and susceptibility to spalling at elevated temperatures. In this paper, the causes, effects and some remedy of deterioration in concrete due to fire hazard will be discussed. Some cost effective solutions to produce a fire resistant concrete will be conversed through this paper.

Keywords: Concrete, fire, spalling, temperature, compressive strength, density.

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Authors: Jian Yao, Chengwen Yan

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Solar shading designs are important for reduction of building energy consumption and improvement of indoor thermal environment. This paper carried out a number of building simulations for evaluation of the energy performance of different shading devices based on incremental costs. The results show that movable shading devices lower incremental costs by up to 50% compared with fixed ones for the same building energy efficiency for residential buildings, and wing panel shadings are much more suitable in commercial buildings than baring screen ones and overhangs for commercial buildings.

Keywords: Solar shading, Incremental costs, Building energy consumption.

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Authors: I. Restrepo, S. Solorzano

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This work was focused in to study the compatibility, dispersion and exfoliation of modified nanoclays in biodegradable polymers and evaluate its effect on the physical, mechanical and thermal properties on the biodegradable matrix used. The formulations have been developed with polylactic acid (PLA) and organically modified montmorillonite-type commercial nanoclays (Cloisite 15, Cloisite 20, and Cloisite 30B) in the presence of a plasticizer agent, specifically Polyethylene Glycol of low molecular weight. Different compositions were evaluated, in order to identify the influence of each nanoclayin the polymeric matrix. The mixtures were characterized by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), X-ray diffraction (DRX), transmission electron microscopy (TEM) and Tensile Test. These tests have allowed understanding the behavior of each of the mixtures developed.

Keywords: Biopolymers, Nanoclays, polylacticacid (PLA), polymer blends.

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Authors: S. N. Vijayan, S. Sendhil Kumar

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Recent years have an upward trend in the research of renewable energy sector, due to the low availability of resources and huge consumption of conventional energies. Considerable renewable energy can be achieved from the available solar power with the utilization of collecting systems. Parabolic trough concentrating collector systems are mostly used to utilize maximum availability of solar power. This paper reviews the contributing factors for the overall performance of parabolic trough collectors. Its performance depends on the operating parameters such as the type of receiver and the collector material, medium of heat transfer, type of application and various climatic conditions.

Keywords: Solar radiation, parabolic trough collector, thermal analysis, efficiency.

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Authors: S. H. Alwan, J. Jasni, M. Z. A. Ab Kadir, N. Aziz

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The aim of this paper is to present a parametric study to determine the major factors that influence the calculations of current rating for both air and underground cables. The current carrying capability of the power cables rely largely on the installation conditions and material properties. In this work, the influences on ampacity of conductor size, soil thermal resistivity and ambient soil temperature for underground installations are shown. The influences on the current-carrying capacity of solar heating (time of day effects and intensity of solar radiation), ambient air temperature and cable size for cables air are also presented. IEC and IEEE standards are taken as reference.

Keywords: Cable ampacity, underground cable, IEC standard, air cables.

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Authors: Benjawan Saengwichian, Alasdair E. Charles, Philip J. Hyde

Abstract:

Magnetically controlled growing rods (MCGRs) have been used to stabilise and correct spinal curvature in children to support non-invasive scoliosis adjustment. Although the encapsulated driving components are intended to be isolated from body fluid contact, in vivo corrosion was observed on these components due to sealing mechanism damage. Consequently, a corrosion circuit is created with the body fluids, resulting in malfunction of the lengthening mechanism. Particularly, the chloride ions in blood plasma or cerebrospinal fluid (CSF) may corrode the MCGR alloys, possibly resulting in metal ion release in long-term use. However, there is no data available on the corrosion resistance of spinal implant alloys in CSF. In this study, an in vitro immersion configuration was designed to simulate in vivo corrosion of 440C SS-Ti6Al4V couples. The 440C stainless steel (SS) was heat-treated to investigate the effect of tempering temperature on intergranular corrosion (IGC), while crevice and galvanic corrosion were studied by limiting the clearance of dissimilar couples. Tests were carried out in a neutral artificial cerebrospinal fluid (ACSF) and phosphate-buffered saline (PBS) under aeration and deaeration for 2 months. The composition of the passive films and metal ion release were analysed. The effect of galvanic coupling, pH, dissolved oxygen and anion species on corrosion rates and corrosion mechanisms are discussed based on quantitative and qualitative measurements. The results suggest that ACSF is more aggressive than PBS due to the combination of aggressive chlorides and sulphate anions, while phosphate in PBS acts as an inhibitor to delay corrosion. The presence of Vivianite on the SS surface in PBS lowered the corrosion rate (CR) more than 5 times for aeration and nearly 2 times for deaeration, compared with ACSF. The CR of 440C is dependent on passive film properties varied by tempering temperature and anion species. Although the CR of Ti6Al4V is insignificant, it tends to release more Ti ions in deaerated ACSF than under aeration, about 6 µg/L. It seems the crevice-like design has more effect on macroscopic corrosion than combining the dissimilar couple, whereas IGC is dominantly observed on sensitized microstructure.

Keywords: Cerebrospinal fluid, crevice corrosion, intergranular corrosion, magnetically controlled growing rods.

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Authors: Khairuddin Bin Osman, Ngo Boon Kiat, A. Hamid Bin hamidon, Khairul Azha Bin A. Aziz, Hazli Rafis Bin Abdul Rahman, Mazran Bin Esro

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Conventional industrial monitoring systems are tedious, inefficient and the at times integrity of the data is unreliable. The objective of this system is to monitor industrial processes specifically the fluid level which will measure the instantaneous fluid level parameter and respond by text messaging the exact value of the parameter to the user when being enquired by a privileged access user. The development of the embedded program code and the circuit for fluid level measuring are discussed as well. Suggestions for future implementations and efficient remote monitoring works are included.

Keywords: Industrial monitoring system, text messaging, embedded programming.

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Authors: T. B. Karu Jayasundara

Abstract:

The Earth’s gravity is not uniform. The satellite imageries of the Earth’s surface from NASA reveal a number of different gravity anomaly regions all over the globe. When the moon rotates around the earth, its gravity has a major physical influence on a number of regions on the earth. This physical change can be seen by the tides. The tides make sea levels high and low in coastal regions. During high tide, the gravitational force of the Moon pulls the Earth’s gravity so that the total gravitational intensity of Earth is reduced; it is further reduced in the low gravity regions of Earth. This reduction in gravity helps keep the suspended particles such as dust in the atmosphere, sand grains in the sea water for longer. Dramatic differences can be seen from the floating dust in the low gravity regions when compared with other regions. The above phenomena can be demonstrated from experiments. The experiments have to be done in high and low gravity regions of the earth during high and low tide, which will assist in comparing the final results. One of the experiments that can be done is by using a water filled cylinder about 80 cm tall, a few particles, which have the same density and same diameter (about 1 mm) and a stop watch. The selected particles were dropped from the surface of the water in the cylinder and the time taken for the particles to reach the bottom of the cylinder was measured using the stop watch. The times of high and low tide charts can be obtained from the regional government authorities. This concept is demonstrated by the particle drop times taken at high and low tides. The result of the experiment shows that the particle settlement time is less in low tide and high in high tide. The experiment for dust particles in air can be collected on filters, which are cellulose ester membranes and using a vacuum pump. The dust on filters can be used to make slides according to the NOHSC method. Counting the dust particles on the slides can be done using a phase contrast microscope. The results show that the concentration of dust is high at high tide and low in low tide. As a result of the high tides, a high concentration of heavy minerals deposit on placer deposits and dust particles retain in the atmosphere for longer in low gravity regions. These conditions are remarkably exhibited in the lowest low gravity region of the earth, mainly in the regions of India, Sri Lanka and in the middle part of the Indian Ocean. The biggest heavy mineral placer deposits are found in coastal regions of India and Sri Lanka and heavy dust particles are found in the atmosphere of India, particularly in the Delhi region.

Keywords: Dust particles, high and low tides, heavy minerals. low gravity.

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Authors: Widi Astuti, Agus Prasetya, Endang Tri Wahyuni, I Made Bendiyasa

Abstract:

Coal fly ash (CFA) generated by coal-based thermal power plants is mainly composed of quartz, mullite, and unburned carbon. In this study, the effect of unburned carbon on CFA toward its adsorption capacity was investigated. CFA with various carbon content was obtained by refluxing it with sulfuric acid having various concentration at various temperature and reflux time, by heating at 400-800°C, and by sieving into 100-mesh in particle size. To evaluate the effect of unburned carbon on CFA toward its adsorption capacity, adsorption of methyl violet solution with treated CFA was carried out. The research shows that unburned carbon leads to adsorption capacity decrease. The highest adsorption capacity of treated CFA was found 5.73 x 10-4mol.g-1.

Keywords: CFA, carbon, methyl violet, adsorption capacity.

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Authors: A. Aydarous, M. El Ghazaly

Abstract:

The purpose of this study was to investigate the response of the newly released Gafchromic HD-V2 film for alpha particle of 5.5 MeV. Gafchromic HD-V2 was exposed to alpha particles of energy 5 MeV from 241Am for different durations. Then the films were scanned with a flatbed scanner. The dose response curve up to 2200 Gy has been achieved. The film’s reproducibility and sensitivity were evaluated. The results obtained show that the net optical density increases almost exponentially with the increase in the exposure time, and it becomes saturated after prolonged exposure times. The red channel shows the highest sensitivity, with a value of 4 x 10-3 Gy-1 at netOD of 0.4. The inter-film reproducibility was measured and the relative uncertainty found was 1.7 %, 2.1 % and 2.3 % for grey, red and green channels, respectively.

Keywords: Alpha dosimetry, 241Am, Gafchromic film.

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Authors: A.Hasanpour, M. Farhadi, H.R. Ashorynejad

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In this paper a numerical technique is used to predict the metal temperature of a gas turbine vane. The Rising combustor exit temperatures in gas turbine engines necessitate active cooling for the downstream turbine section to avoid thermal failure. This study is performed the solution of external flow, internal convection, and conduction within the metal vane. Also the trade-off between the cooling performances in four different hole shapes and configurations is performed. At first one of the commonly used cooling hole geometry is investigated; cylindrical holes and then two other configurations are simulated. The average temperature magnitude in mid-plan section of each configuration is obtained and finally the lower temperature value is selected such as best arrangement.

Keywords: Forced Convection, Gas Turbine Blade, Hole Configuration

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Authors: Y. Bentoutou, A.M. Si Mohammed

Abstract:

This paper presents a review of an 8-year study on radiation effects in commercial memory devices operating within the main on-board computer system OBC386 of the Algerian microsatellite Alsat-1. A statistical analysis of single-event upset (SEU) and multiple-bit upset (MBU) activity in these commercial memories shows that the typical SEU rate at alsat-1's orbit is 4.04 × 10-7 SEU/bit/day, where 98.6% of these SEUs cause single-bit errors, 1.22% cause double-byte errors, and the remaining SEUs result in multiple-bit and severe errors.

Keywords: Radiation effects, error detection and correction, satellite computer, small satellite mission.

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Authors: M. Kito, M. Takezaki, T. Shakouchi, K. Tsujimoto, T. Ando

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Impinging jets are widely used in industrial cooling systems for their high heat transfer characteristics at stagnation points. However, the heat transfer characteristics are low in the downstream direction. In order to improve the heat transfer coefficient further downstream, investigations introducing ribs on jet-cooled flat plates have been conducted. Most studies regarding the heat-transfer enhancement using a rib-roughened wall have dealt with the rib pitch. In this paper, we focused on the rib spacing and demonstrated that the rib spacing must be more than 6 times the nozzle width to improve heat transfer at Reynolds number Re=5.0×103 because it is necessary to have enough space to allow reattachment of flow behind the first rib.

Keywords: Forced convection, heat transfer, impinging jet cooling, rib roughened wall

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Authors: A. Hellany, M.Nagrial, M. Nassereddine, J. Rizk

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As new challenges emerge in power electrical workplace safety, it is the responsibility of the systems designer to seek out new approaches and solutions that address them. Design decisions made today will impact cost, safety and serviceability of the installed systems for 40 or 50 years during the useful life for the owner. Studies have shown that this cost is an order of magnitude of 7 to 10 times the installed cost of the power distribution equipment. This paper reviews some aspects of earthing system design in power substation surrounded by residential houses. The electrical potential rise and split factors are discussed and a few recommendations are provided to achieve a safety voltage in the area beyond the boundary of the substation.

Keywords: EPR, Split Factor, Earthing Design

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

Abstract:

The tree structured approach of non-uniform filterbank (NUFB) is normally used in perfect reconstruction (PR). The PR is not always feasible due to certain limitations, i.e, constraints in selecting design parameters, design complexity and some times output is severely affected by aliasing error if necessary and sufficient conditions of PR is not satisfied perfectly. Therefore, there has been generalized interest of researchers to go for near perfect reconstruction (NPR). In this proposed work, an optimized tree structure technique is used for the design of NPR non-uniform filterbank. Window functions of Blackman family are used to design the prototype FIR filter. A single variable linear optimization is used to minimize the amplitude distortion. The main feature of the proposed design is its simplicity with linear phase property.

Keywords: Tree structure, NUFB, QMF, NPR.

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Authors: Raed A. Amro

Abstract:

Standard packaging and interconnection technologies of power devices have difficulties meeting the increasing thermal demands of new application fields of power electronics devices. Main restrictions are the decreasing reliability of bond-wires and solder layers with increasing junction temperature. In the last few years intensive efforts have been invested in developing new packaging and interconnection solutions which may open a path to future application of power devices. In this paper, the main failure mechanisms of power devices are described and principle of new packaging and interconnection concepts and their power cycling reliability are presented.

Keywords: Power electronics devices, Reliability, Power Cycling, Low-temperature joining technique (LTJT)

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Authors: K. J. Chung, C.C.Chiang, Y.M. Liu, N. W. Pu, M. D. Ger

Abstract:

Fabrication and efficiency enhancement of non-mercury, high efficiency and green field emission lamps using carbon nano-materials such as carbon nanotubes as cathode field emitters was studied. Phosphor was coated on the ITO glass or metal substrates as the anode. The luminescence efficiency enhancement was carried out by upgrading the uniform of the emitters, improving electron and thermal conductivity of the phosphor and the optimization of the design of different cathode/anode configurations. After evaluation of the aforementioned parameters, the luminescence efficiency of the field emission lamps was raised.

Keywords: Field emission lamps, carbon nano-materials, luminescence efficiency

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Authors: Sylvia Encheva

Abstract:

Students in high education are presented with new terms and concepts in nearly every lecture they attend. Many of them prefer Web-based self-tests for evaluation of their concepts understanding since they can use those tests independently of tutors- working hours and thus avoid the necessity of being in a particular place at a particular time. There is a large number of multiple-choice tests in almost every subject designed to contribute to higher level learning or discover misconceptions. Every single test provides immediate feedback to a student about the outcome of that test. In some cases a supporting system displays an overall score in case a test is taken several times by a student. What we still find missing is how to secure delivering of personalized feedback to a user while taking into consideration the user-s progress. The present work is motivated to throw some light on that question.

Keywords: Clustering, rough sets, many valued logic, predictions

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Authors: Tomáš Melichar, Jiří Bydžovský, Vít Černý

Abstract:

In this article our research focused on study of basic physical and mechanical parameters of polymer-cement repair materials is presented. Namely the influence of applied aggregates in combination with active admixture is specially considered. New formulas which were exposed in ambient with temperature even to 1000°C were suggested. Subsequently densities and strength characteristics including their changes were evaluated. Selected samples were analyzed using electron microscope. The positive influence of porous aggregates based on sintered ash was definitely demonstrated. Further it was found than in terms of thermal resistance the effective micro silica amount represents 5% to 7.5% of cement weight.

Keywords: Aggregate, ash, high, lightweight, microsilica, mortar, polymer-cement, repair, temperature.

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Authors: É. Vincze

Abstract:

Demand on plant oils has increased to an enormous extent that is due to the change of human nutrition habits on the one hand, while on the other hand to the increase of raw material demand of some industrial sectors, just as to the increase of biofuel production. Besides the determining importance of sunflower in Hungary the production area, just as in part the average yield amount of rapeseed has increased among the produced oil crops. The variety/hybrid palette has changed significantly during the past decade. The available varieties’/hybrids’ palette has been extended to a significant extent. It is agreed that rapeseed production demands professionalism and local experience. Technological elements are successive; high yield amounts cannot be produced without system-based approach. The aim of the present work was to execute the complex study of one of the most critical production technology element of rapeseed production, that was sowing technology. Several sowing technology elements are studied in this research project that are the following: biological basis (the hybrid Arkaso is studied in this regard), sowing time (sowing time treatments were set so that they represent the wide period used in industrial practice: early, optimal and late sowing time) plant density (in this regard reaction of rare, optimal and too dense populations) were modelled. The multifactorial experimental system enables the single and complex evaluation of rapeseed sowing technology elements, just as their modelling using experimental result data. Yield quality and quantity have been determined as well in the present experiment, just as the interactions between these factors. The experiment was set up in four replications at the Látókép Plant Production Research Site of the University of Debrecen. Two different sowing times were sown in the first experimental year (2014), while three in the second (2015). Three different plant densities were set in both years: 200, 350 and 500 thousand plants ha-1. Uniform nutrient supply and a row spacing of 45 cm were applied. Winter wheat was used as pre-crop. Plant physiological measurements were executed in the populations of the Arkaso rapeseed hybrid that were: relative chlorophyll content analysis (SPAD) and leaf area index (LAI) measurement. Relative chlorophyll content (SPAD) and leaf area index (LAI) were monitored in 7 different measurement times.

Keywords: Inner quality, plant density, rapeseed, sowing time.

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Authors: Abdelghani Dendouga, Nour-Eddine Bouguechal, Souhil Kouda, Samir Barra

Abstract:

A behavioral model of a second order switchedcapacitor Sigma-Delta modulator is presented. The purpose of this work is the presentation of a behavioral model of a second order switched capacitor ΣΔ modulator considering (Error due to Clock Jitter, Thermal noise Amplifier Noise, Amplifier Slew-Rate, Non linearity of amplifiers, Gain error, Charge Injection, Clock Feedthrough, and Nonlinear on-resistance). A comparison between the use of MOS switches and the use transmission gate switches use is analyzed.

Keywords: Charge injection, clock feed through, Sigma Deltamodulators, Sigma Delta non-idealities, switched capacitor.

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Authors: N. Kekelidze, B. Kvirkvelia, E. Khutsishvili, T. Qamushadze, D. Kekelidze, R. Kobaidze, Z. Chubinishvili, N. Qobulashvili, G. Kekelidze

Abstract:

On the basis of InAs, InP and their InP_xAs_1-x solid solutions, the technologies were developed and materials were created where the electron concentration and optical and thermoelectric properties do not change under the irradiation with Ф = 2∙10¹⁸ n/cm² fluences of fast neutrons high-energy electrons (50 MeV, Ф = 6·10¹⁷ e/cm²) and 3 MeV electrons with fluence Ф = 3∙10¹⁸ e/cm². The problem of obtaining such material has been solved, in which under hard irradiation the mobility of the electrons does not decrease, but increases. This material is characterized by high thermal stability up to T = 700 °C. The complex process of defects formation has been analyzed and shown that, despite of hard irradiation, the essential properties of investigated materials are mainly determined by point type defects.

Keywords: InAs, InP, solid solutions, irradiation.

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Authors: Thomas Jin-Chee Liu, Ji-Fu Tseng, Yu-Shen Chen

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This paper investigates the thermo-electric effects around the crack and notch tips under the electric current load. The research methods include the finite element analysis and thermal imaging experiment. The finite element solutions show that the electric current density field concentrates at the crack tip. Due to the Joule heating, this electric concentration causes the hot spot at the tip zone. From numerical and experimental results, this hot spot is identified. The temperature of the hot spot is affected by the electric load, operation time and geometry of the sample.

Keywords: Thermo-electric, Joule heating, crack tip, notch tip.

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Authors: Jinkyu Park, Yungjin Kim, Byungdeok In, Sangki Park, Kihyung Lee

Abstract:

Internal combustion engines rejects 30-40% of the energy supplied by fuel to the environment through exhaust gas. thus, there is a possibility for further significant improvement of efficiency with the utilization of exhaust gas energy and its conversion to mechanical energy or electrical energy. The Thermo-Electric Generator (TEG) will be located in the exhaust system and will make use of an energy flow between the warmer exhaust gas and the external environment. Predict to th optimum position of temperature distribution and the performance of TEG through numerical analysis. The experimental results obtained show that the power output significantly increases with the temperature difference between cold and hot sides of a thermoelectric generator.

Keywords: Thermoelectric generator, Numerical analysis, Seebeck coefficient, Figure of merit

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Authors: Arkadiusz Biernacki

Abstract:

In this paper we present a statistical analysis of Voice over IP (VoIP) packet streams produced by the G.711 voice coder with voice activity detection (VAD). During telephone conversation, depending whether the interlocutor speaks (ON) or remains silent (OFF), packets are produced or not by a voice coder. As index of dispersion for both ON and OFF times distribution was greater than one, we used hyperexponential distribution for approximation of streams duration. For each stage of the hyperexponential distribution, we tested goodness of our fits using graphical methods, we calculated estimation errors, and performed Kolmogorov-Smirnov test. Obtained results showed that the precise VoIP source model can be based on the five-state Markov process.

Keywords: VoIP source modelling, distribution approximation, hyperexponential distribution.

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Authors: Norihan Md Arifin, Norfifah Bachok

Abstract:

The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the internal heating, depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with internal heating are studied in detail.

Keywords: Linear stability, Marangoni convection, Internal Heatgeneration.

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