Search results for: Bottom elevation

Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

The Maximum entropy principle in spectral analysis was used as an estimator of Direction of Arrival (DoA) of electromagnetic or acoustic sources impinging on an array of sensors, indeed the maximum entropy operator is very efficient when the signals of the radiating sources are ergodic and complex zero mean random processes which is the case for cosmic sources. In this paper, we present basic review of the maximum entropy method (MEM) which consists of rank one operator but not a projector, and we elaborate a new operator which is full rank and sum of all possible projectors. Two dimensional Simulation results based on Monte Carlo trials prove the resolution power of the new operator where the MEM presents some erroneous fluctuations.

Keywords: Maximum entropy, Cosmic source, Localization, operator, projector, azimuth, elevation, DoA, circular array.

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Authors: R. Abbasnia, F. Mohajeri Nav, S. Zahedifar, A. Tajik

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Recent years, adaptive pushover methods have been developed for seismic analysis of structures. Herein, the accuracy of the displacement-based adaptive pushover (DAP) method, which is introduced by Antoniou and Pinho [2004], is evaluated for Irregular buildings. The results are compared to the force-based procedure. Both concrete and steel frame structures, asymmetric in plan and elevation are analyzed and also torsional effects are taking into the account. These analyses are performed using both near fault and far fault records. In order to verify the results, the Incremental Dynamic Analysis (IDA) is performed.

Keywords: Pushover Analysis, DAP, IDA, Torsion.

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Authors: Abdullah H. Özcan, Dilara Hisar, Yetkin Sayar, Cem Ünsalan

Abstract:

In this study, an automated building and tree detection method is proposed using DSM data and true orthophoto image. A multiscale matched filtering is used on DSM data. Therefore, first watershed transform is applied. Then, Otsu’s thresholding method is used as an adaptive threshold to segment each watershed region. Detected objects are masked with NDVI to separate buildings and trees. The proposed method is able to detect buildings and trees without entering any elevation threshold. We tested our method on ISPRS semantic labeling dataset and obtained promising results.

Keywords: Building detection, tree detection, matched filtering, multiscale, local maximum filtering, watershed segmentation.

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Authors: Ya-Fen Lee, Yun-Yao Chi, Cing-Hong Hung

Abstract:

Because of the global warming and the rising sea level, residents living in southwestern coastland, Taiwan are faced with the submerged land and may move to higher elevation area. It is desirable to discuss the key consideration factor for selecting the migration location under five dimensions of ಯ security”, “health”, “convenience”, “comfort” and “socio-economic” based on the document reviews. This paper uses the Structural Equation Modeling (SEM) and the questionnaire survey. The analysis results show that the convenience is the most key factor for residents in Taiwan. 

Keywords: Global warming, migration, structural equation modelling, questionnaire survey.

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Authors: S. W. Lo, C.-H. Yu

Abstract:

A new design of aerostatic thrust bearing is proposed for high static stiffness. The bearing body, which is mead of polymer covered with metallic membrane, is held by a circular ring. Such a support helps form a concave air gap to grasp the air pressure. The polymer body, which can be made rapidly by either injection or molding is able to provide extra damping under dynamic loading. The smooth membrane not only serves as the bearing surface but also protects the polymer body. The restrictor is a capillary inside a silicone tube. It can passively compensate the variation of load by expanding the capillary diameter for more air flux. In the present example, the stiffness soars from 15.85 N/μm of typical bearing to 349.85 N/μm at bearing elevation 9.5 μm; meanwhile the load capacity also enhances from 346.86 N to 704.18 N.

Keywords: Aerostatic, bearing, polymer, static stiffness.

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Authors: A. G. Temnikov, O. S. Belova, L. L. Chernensky, T. K. Gerastenok, N. Y. Lysov, A. V. Orlov, D. S. Zhuravkova

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Hypothesis of the lightning initiation on the arrays of large hydrometeors are in the consideration. There is no agreement about the form the hydrometeors that could be the best for the lightning initiation from the thundercloud. Artificial charged water aerosol clouds of the positive or negative polarity could help investigate the possible influence of the hydrometeor form on the peculiarities and the probability of the lightning discharge initiation between the thundercloud and the ground. Artificial charged aerosol clouds that could create the electric field strength in the range of 5-6 kV/cm to 16-18 kV/cm have been used in experiments. The array of the model hydrometeors of the volume and plate form has been disposed near the bottom cloud boundary. It was established that the different kinds of the discharge could be initiated in the presence of the model hydrometeors array – from the cloud discharges up to the diffuse and channel discharges between the charged cloud and the ground. It was found that the form of the model hydrometeors could significantly influence the channel discharge initiation from the artificial charged aerosol cloud of the negative or positive polarity correspondingly. Analysis and generalization of the experimental results have shown that the maximal probability of the channel discharge initiation and propagation stimulation has been observed for the artificial charged cloud of the positive polarity when the arrays of the model hydrometeors of the cylinder revolution form have been used. At the same time, for the artificial charged clouds of the negative polarity, application of the model hydrometeor array of the plate rhombus form has provided the maximal probability of the channel discharge formation between the charged cloud and the ground. The established influence of the form of the model hydrometeors on the channel discharge initiation and from the artificial charged water aerosol cloud and its following successful propagation has been related with the different character of the positive and negative streamer and volume leader development on the model hydrometeors array being near the bottom boundary of the charged cloud. The received experimental results have shown the possibly important role of the form of the large hail particles precipitated in thundercloud on the discharge initiation.

Keywords: Cloud and channel discharges, hydrometeor form, lightning initiation, negative and positive artificial charged aerosol cloud.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: A.S. Kipcak, N. Baran Acarali, S. Kolemen, N. Tugrul, E. Moroydor Derun, S. Piskin

Abstract:

Fly ash is one of the residues generated in combustion, and comprises the fine particles that rise with the flue gases. Ash which does not rise is termed bottom ash [1]. In our country, it is expected that will be occurred 50 million tons of waste ash per year until 2020. Released waste from the thermal power plants is caused very significant problems as known. The fly ashes can be evaluated by using as adsorbent material. The purpose of this study is to investigate the possibility of use of Tuncbilek fly ash like low-cost adsorbents for heavy metal adsorption. First of all, Tuncbilek fly ash was characterized. For this purpose; analysis such as sieve analysis, XRD, XRF, SEM and FT-IR were performed.

Keywords: Fly ash, heavy metal, sieve, adsorbent

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Authors: Md. Fazlul Karim, Esa Al-Islam

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This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: Cherdvong Saengsupavanich

Abstract:

The impact of a proposed pier on tidal current alteration was evaluated. The proposed pier location was in Salad Bay on Koa Kood Island, Trat province, Thailand, and was designed to accommodate passenger ships with a draft of less than 2 m. The study began with collecting necessary data, including bathymetric, water elevation and tidal current characteristics. The impact was assessed using a software package (MIKE21). Although the results showed that the pier would affect the existing current pattern, the change was determined to be insignificant, as the design of the piles for the pier provided sufficient spacing to let the current flow as freely as possible. Consequences of the altered current, such as seabed erosion, water stagnation, sediment deposition and navigational risk were assessed. Environmental mitigation measures might be necessary if the impacts were considered unacceptable.

Keywords: Environmental impact assessment, pier, tidal currentchange, coastal engineering and management

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Authors: S. W. Hong, Y. S. Choi, T. H. Chung, J. H. Song, H. S. Kim

Abstract:

Bio-electrical responses obtained from freshwater sediments by employing microbial fuel cell (MFC) technology were investigated in this experimental study. During the electricity generation, organic matter in the sediment was microbially oxidized under anaerobic conditions with an electrode serving as a terminal electron acceptor. It was found that the sediment organic matter (SOM) associated with electrochemically-active electrodes became more humified, aromatic, and polydispersed, and had a higher average molecular weight, together with the decrease in the quantity of SOM. The alteration of characteristics of the SOM was analogous to that commonly observed in the early stage of SOM diagenetic process (i.e., humification). These findings including an elevation of the sediment redox potential present a possibility of the MFC technology as a new soil/sediment remediation technique based on its potential benefits: non-destructive electricity generation and bioremediation.

Keywords: Anaerobic oxidation, microbial fuel cell, remediation, sediment.

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Authors: Parkpoom Ch., Narongkorn D.

Abstract:

This paper presents the system identification by physical-s law method and designs the controller for the Azimuth Angle Control of the Platform of the Multi-Launcher Rocket System (MLRS) by Root Locus technique. The plant mathematical model was approximated using MATLAB for simulation and analyze the system. The controller proposes the implementation of PID Controller using Programmable Logic Control (PLC) for control the plant. PID Controllers are widely applicable in industrial sectors and can be set up easily and operate optimally for enhanced productivity, improved quality and reduce maintenance requirement. The results from simulation and experiments show that the proposed a PID Controller to control the elevation angle that has superior control performance by the setting time less than 12 sec, the rise time less than 1.6 sec., and zero steady state. Furthermore, the system has a high over shoot that will be continue development.

Keywords: Azimuth angle control, PID Controller, The platform of Multi-Launcher Rocket System.

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we mainly analyze an automated parking system where the storage and retrieval requests are performed by a tower crane. In this parking system, the S/R crane which is located at the middle of the bottom of the cylinder parking area can rotate in both clockwise and counterclockwise and three kinds of movements can be done simultaneously. We develop some mathematical travel time models for the single command cycle under the random storage assignment using the characteristics of this system. Finally, we compare these travel models with discrete case and it is shown that these travel models display a good satisfactory performance.

Keywords: Parking system, travel time model, tower crane.

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Authors: Janis Šliseris, Karlis Rocens

Abstract:

Optimization of rational geometrical and mechanical parameters of panel with curved plywood ribs is considered in this paper. The panel consists of cylindrical plywood ribs manufactured from Finish plywood, upper and bottom plywood flange, stiffness diaphragms. Panel is filled with foam. Minimal ratio of structure self weight and load that could be applied to structure is considered as rationality criteria. Optimization is done, by using classical beam theory without nonlinearities. Optimization of discreet design variables is done by Genetic algorithm.

Keywords: Curved plywood ribs, genetic algorithm, rationalparameters of ribbed panel, structure optimization.

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Authors: E. G. Bautista, J. M. Reyes, O. Bautista, J. C. Arcos

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In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law distribution. We show that the spatial distribution of the waves in the varying cross-section is a function of a kinematic parameter,κ , and two geometrical parameters εh and w ε . The above spatial behavior of the surface elevation is modeled by an ordinary differential equation. The use of single formulas to model the varying cross sections or transitions considered in this work can be a useful approximation to natural or artificial geometrical configurations.

Keywords: Surface waves, Asymptotic solution, Power law function, Non-dispersive waves.

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Authors: Zhiqing Zhang, Xiangong Zhou, Zihan Zhou

Abstract:

Ground fissures can be seen in some cities all over the world. As a special urban geological disaster, ground fissures in Xi'an have caused great harm to infrastructure. Chang'an Road Interchange in Xi'an City is a bridge across ground fissures. The damage to Chang'an Road interchange is the most serious and typical. To study the influence of ground fissures on the bridge, we established a bridge monitoring system. The main monitoring items include elevation monitoring, structural displacement monitoring, etc. The monitoring results show that the typical failure is mainly reflected in the bridge deck damage caused by horizontal tension and vertical dislocation. For the construction of urban interchange spanning ground fissures, the interchange should be divided reasonably, a simple support structure with less restriction should be adopted, and the monitoring of supports should be strengthened to prevent the occurrence of beam falling.

Keywords: Bridge monitoring, ground fissures, typical disease, structural displacement.

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Authors: A. A. Purohit, M. M. Vaidya, M. D. Kudale

Abstract:

Among the various developing countries in the world like China, Malaysia, Korea etc., India is also developing its infrastructures in the form of Road/Rail/Airports and Waterborne facilities at an exponential rate. Mumbai, the financial epicenter of India is overcrowded and to relieve the pressure of congestion, Navi Mumbai suburb is being developed on the east bank of Thane creek near Mumbai. The government due to limited space at existing Mumbai Airports (domestic and international) to cater for the future demand of airborne traffic, proposes to build a new international airport near Panvel at Navi Mumbai. Considering the precedence of extreme rainfall on 26^th July 2005 and nearby townships being in a low-lying area, wherein new airport is proposed, it is inevitable to study this complex confluence area from a hydrodynamic consideration under both tidal and extreme events (predicted discharge hydrographs), to avoid inundation of the surrounding due to the proposed airport reclamation (1160 hectares) and to determine the safe grade elevation (SGE). The model studies conducted using the application of unstructured mesh to simulate the Panvel estuarine area (93 km²), calibration, validation of a model for hydraulic field measurements and determine the maxima water levels around the airport for various extreme hydrodynamic events, namely the simultaneous occurrence of highest tide from the Arabian Sea and peak flood discharges (Probable Maximum Precipitation and 26^th July 2005) from five rivers, the Gadhi, Kalundri, Taloja, Kasadi and Ulwe, meeting at the proposed airport area revealed that: (a) The Ulwe River flowing beneath the proposed airport needs to be diverted. The 120m wide proposed Ulwe diversion channel having a wider base width of 200 m at SH-54 Bridge on the Ulwe River along with the removal of the existing bund in Moha Creek is inevitable to keep the SGE of the airport to a minimum. (b) The clear waterway of 80 m at SH-54 Bridge (Ulwe River) and 120 m at Amra Marg Bridge near Moha Creek is also essential for the Ulwe diversion and (c) The river bank protection works on the right bank of Gadhi River between the NH-4B and SH-54 bridges as well as upstream of the Ulwe River diversion channel are essential to avoid inundation of low lying areas. The maxima water levels predicted around the airport keeps SGE to a minimum of 11m with respect to Chart datum of Ulwe Bundar and thus development is not only technologically-economically feasible but also sustainable. The unstructured mesh modeling is a promising tool to simulate complex extreme hydrodynamic events and provides a reliable solution to evolve optimal SGE of airport.

Keywords: Airport, hydrodynamics, hydrographs, safe grade elevation, tides.

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Authors: L. Bartonová, D. Juchelková, Z. Klika, B. Cech

Abstract:

Work is focused to the study of unburned carbon in ash from coal (and wastes) combustion in 8 combustion tests at 3 fluidised-bed power station, at co-combustion of coal and wastes (also at fluidized bed) and at bench-scale unit simulating coal combustion in small domestic furnaces. The attention is paid to unburned carbon contents in bottom ashes and fly ashes at these 8 combustion tests and to morphology of unburned carbons. Specific surface area of coals, unburned carbons and ashes and the relation of specific surface area of unburned carbon and the content of volatile combustibles in coal were studied as well.

Keywords: Coal combustion, emissions, toxic elements, unburned carbon.

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Authors: M. Khal, Ab. Algouti, A. Algouti

Abstract:

Water erosion is the major cause of the erosion that shapes the earth's surface. Modeling water erosion requires the use of software and GIS programs, commercial or closed source. The very high prices for commercial GIS licenses, motivates users and researchers to find open source software as relevant and applicable as the proprietary GIS. The objective of this study is the modeling of water erosion and the hydrogeological and morphophysical characterization of the Oued M'Goun watershed (southern flank of the Central High Atlas) developed by free programs of GIS. The very pertinent results are obtained by executing tasks and algorithms in a simple and easy way. Thus, the various geoscientific and geostatistical analyzes of a digital elevation model (SRTM 30 m resolution) and their combination with the treatments and interpretation of satellite imagery information allowed us to characterize the region studied and to map the area most vulnerable to water erosion.

Keywords: Central High-Atlas, hydrogeology, M’Goun watershed, OpenGIS, water erosion.

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Authors: Abu Bakar Sambah, Fusanori Miura

Abstract:

Remote sensing image processing, spatial data analysis through GIS approach, and analytical hierarchy process were introduced in this study for assessing the vulnerability area and inundation area due to tsunami hazard in the area of Rikuzentakata, Iwate Prefecture, Japan. Appropriate input parameters were derived from GSI DEM data, ALOS AVNIR-2, and field data. We used the parameters of elevation, slope, shoreline distance, and vegetation density. Five classes of vulnerability were defined and weighted via pairwise comparison matrix. The assessment results described that 14.35km² of the study area was under tsunami vulnerability zone. Inundation areas are those of high and slightly high vulnerability. The farthest area reached by a tsunami was about 7.50km from the shoreline and shows that rivers act as flooding strips that transport tsunami waves into the hinterland. This study can be used for determining a priority for land-use planning in the scope of tsunami hazard risk management.

Keywords: AHP, GIS, remote sensing, tsunami vulnerability.

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Authors: S. Atabay, T. A. Ali, Md. M. Mortula

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This paper presents the results and findings from a parametric study on the water surface elevation at upstream of bridge constriction for subcritical flow. In this study, the influence of Manning's Roughness Coefficient of main channel (nmc) and floodplain (nfp), and bridge opening (b) flow rate (Q), contraction (kcon) and expansion coefficients (kexp) were investigated on backwater level. The DECK bridge models with different span widths and without any pier were investigated within the two stage channel having various roughness conditions. One of the most commonly used commercial one-dimensional HEC-RAS model was used in this parametric study. This study showed that the effects of main channel roughness (nmc) and flow rate (Q) on the backwater level are much higher than those of the floodplain roughness (nfp). Bridge opening (b) with contraction (kcon) and expansion coefficients (kexp) have very little effect on the backwater level within this range of parameters.

Keywords: Bridge backwater, parametric study and waterways.

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Authors: T. Zalabsky, P. Bezousek, T. Shejbal

Abstract:

The paper describes new concept of the ribbon beam antenna for RFID technology. Antenna is located near to railway lines to monitor tags situated on trains. Antenna works at 2.45 GHz and it is fabricated by microstrip technology. Antenna contains two same mirrored parts having the same radiation patterns. Each part consists of three dielectric layers. The first layer has on one side radiation elements. The second layer is only for mechanical construction and it sets optimal electromagnetic field for each radiating elements. The third layer has on its top side a ground plane and on the bottom side a microstrip circuit used for individual radiation elements feeding.

Keywords: RFID, cosecant radiation pattern, ribbon beam, patch antenna, microstrip.

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Authors: Xing Li, Chengqing Zong

Abstract:

This paper presents an effective framework for Chinesesyntactic parsing, which includes two parts. The first one is a parsing framework, which is based on an improved bottom-up chart parsingalgorithm, and integrates the idea of the beam search strategy of N bestalgorithm and heuristic function of A* algorithm for pruning, then get multiple parsing trees. The second is a novel evaluation model, which integrates contextual and partial lexical information into traditional PCFG model and defines a new score function. Using this model, the tree with the highest score is found out as the best parsing tree. Finally,the contrasting experiment results are given. Keywords?syntactic parsing, PCFG, pruning, evaluation model.

Keywords: syntactic parsing, PCFG, pruning, evaluation model.

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Authors: S. P. Koko, K. Kusakana, H. J. Vermaak

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Standalone micro-hydrokinetic river (MHR) system is one of the promising technologies to be used for remote rural electrification. It simply requires the flow of water instead of elevation or head, leading to expensive civil works. This paper demonstrates an economic benefit offered by a standalone MHR system when compared to the commonly used standalone systems such as solar, wind and diesel generator (DG) at the selected study site in Kwazulu Natal. Wind speed and solar radiation data of the selected rural site have been taken from national aeronautics and space administration (NASA) surface meteorology database. The hybrid optimization model for electric renewable (HOMER) software was used to determine the most feasible solution when using MHR, solar, wind or DG system to supply 5 rural houses. MHR system proved to be the best cost-effective option to consider at the study site due to its low cost of energy (COE) and low net present cost (NPC).

Keywords: Economic analysis, Micro-hydrokinetic system, Rural-electrification, Stand-alone system.

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Authors: Dhananjayulu Avula, Ratnesh Kumar Raj Singh, D.K.Dwivedi, N.K.Mehta

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This study demonstrates the feasibility of joining the commercial pure copper plates by friction stir welding (FSW). Microstructure, microhardness and tensile properties in terms of the joint efficiency were found 94.03 % compare to as receive base material (BM). The average hardness at the top was higher than bottom. Hardness of weld zone was higher than the base material. Different microstructure zones were revealed by optical microscopy and scanning electron microscopy. The stirred zone (SZ) exhibited primary two phases namely, recrystallized grains and fine precipitates in matrix of copper.

Keywords: Welding; FSW, Commercial Copper, Mechanical properties

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Authors: M.Devakar, T.K.V.Iyengar

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In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

Keywords: Couple stress fluid, Generalized Stokes’ problems, Laplace transform, Numerical inversion

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Authors: Mohammad Moeini, Mehrdad Ghyabi, Kiarash Mohtasham Dolatshahi

Abstract:

This paper investigates seismic soil-pile interaction using the Beam on Nonlinear Winkler Foundation (BNWF) approach. Three soil types are considered to cover all the possible responses, as well as nonlinear site response analysis using finite element method in OpenSees platform. Excitations at each elevation that are output of the site response analysis are used as the input excitation to the soil pile system implementing multi-support excitation method. Spectral intensities of acceleration show that the extent of the response in sand is more severe than that of clay, in addition, increasing the PGA of ground strong motion will affect the sandy soil more, in comparison with clayey medium, which is an indicator of the sensitivity of soil-pile systems in sandy soil.

Keywords: Beam on nonlinear Winkler foundation method, multi-support excitation, nonlinear site response analysis, seismic soil-pile interaction.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: Monomial form, rectangular surfaces, CAGD curves, monomial matrix applications.

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Authors: Norihan Md Arifin, Norfifah Bachok

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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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