Search results for: Robert M. Field

Authors: Alexander L. Pyayt, Ilya I. Mokhov, Bernhard Lang, Valeria V. Krzhizhanovskaya, Robert J. Meijer

Abstract:

More and more natural disasters are happening every year: floods, earthquakes, volcanic eruptions, etc. In order to reduce the risk of possible damages, governments all around the world are investing into development of Early Warning Systems (EWS) for environmental applications. The most important task of the EWS is identification of the onset of critical situations affecting environment and population, early enough to inform the authorities and general public. This paper describes an approach for monitoring of flood protections systems based on machine learning methods. An Artificial Intelligence (AI) component has been developed for detection of abnormal dike behaviour. The AI module has been integrated into an EWS platform of the UrbanFlood project (EU Seventh Framework Programme) and validated on real-time measurements from the sensors installed in a dike.

Keywords: Early Warning System, intelligent environmentalmonitoring, machine learning, flood protection.

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Authors: G. Balogh, I. A. Szabó, P. Z. Kovács

Abstract:

Mechanical stress has a strong effect on the magnitude of the Barkhausen-noise in structural steels. Because the measurements are performed at the surface of the material, for a sample sheet, the full effect can be described by a biaxial stress field. The measured Barkhausen-noise is dependent on the orientation of the exciting magnetic field relative to the axis of the stress tensor. The sample inhomogenities including the residual stress also modifies the angular dependence of the measured Barkhausen-noise. We have developed a laboratory device with a cross like specimen for bi-axial bending. The measuring head allowed performing excitations in two orthogonal directions. We could excite the two directions independently or simultaneously with different amplitudes. The simultaneous excitation of the two coils could be performed in phase or with a 90 degree phase shift. In principle this allows to measure the Barkhausen-noise at an arbitrary direction without moving the head, or to measure the Barkhausen-noise induced by a rotating magnetic field if a linear superposition of the two fields can be assumed.

Keywords: Barkhausen-noise, Bi-axial stress, Stress dependency, Stress measuring.

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Authors: Shohei Nakai, Yasuhiro Yamada

Abstract:

Weed suppression and weeding are necessary measures for rice cultivation. Weed suppression precedes the process of weeding. It means suppressing the growth of young weeds and creating a weed-less environment. If we suppress the growth of weeds, we can reduce the number of weeds in a paddy field. This would result in a reduction of the weeding work load. In this paper, we will show how we developed a weed suppression robot for the purpose of reducing the weeding work load. The robot has a laser range finder for autonomous mobility and a robot arm for weed suppression. It travels along the rice rows without stepping on and injuring the rice plants in a paddy field. The robot arm applies force to the weed seedlings and thereby suppresses the growth of weeds. This paper will explain the methodology of the autonomous mobile, the experiment in weed suppression, and the method of controlling the robot’s posture on uneven ground.

Keywords: Mobile robot, Paddy field, Robot arm, Weed.

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Authors: Tatyana R. Radeva, Ivan S. Yatchev, Dimitar N. Karastoyanov, Nikolay I. Stoimenov, Stanislav D. Gyoshev

Abstract:

The paper presents coupled electromagnetic and thermal field analysis of busbar system (of rectangular cross-section geometry) submitted to short circuit conditions. The laboratory model was validated against both analytical solution and experimental observations. The considered problem required the computation of the detailed distribution of the power losses and the heat transfer modes. In this electromagnetic and thermal analysis, different definitions of electric busbar heating were considered and compared. The busbar system is a three phase one and consists of aluminum, painted aluminum and copper busbar. The solution to the coupled field problem is obtained using the finite element method and the QuickField™ program. Experiments have been carried out using two different approaches and compared with computed results.

Keywords: Busbar system, coupled problems, finite element method, short-circuit currents.

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Authors: Nebojsa B. Raicevic, Slavoljub R. Aleksic, Sasa S. Ilic

Abstract:

A power cable is widely used for power supply in power distributing networks and power transmission lines. Due to limitations in the production, delivery and setting up power cables, they are produced and delivered in several separate lengths. Cable itself, consists of two cable terminations and arbitrary number of cable joints, depending on the cable route length. Electrical stress control is needed to prevent a dielectric breakdown at the end of the insulation shield in both the air and cable insulation. Reliability of cable joint depends on its materials, design, installation and operating environment. The paper describes design and performance results for new modeled cable joints. Design concepts, based on numerical calculations, must be correct. An Equivalent Electrodes Method/Boundary Elements Method-hybrid approach that allows electromagnetic field calculations in multilayer dielectric media, including inhomogeneous regions, is presented.

Keywords: Cable joints, deflector's cones, equivalent electrodemethod, electric field distribution

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Authors: S. A. Aytkeldiyeva, A. K. Sadanov, E. R. Faizulina, A. A. Kurmanbayev

Abstract:

15 strains of oil-destructing microorganisms were isolated from oil polluted soil of Western Kazakhstan. Strains 2-A and 41-3 with the highest oil-destructing activities were chosen from them. It was shown that these strains oxidized n-alkanes very well, but isoalkanes, isoparaffin, cycloparaffin and heavy aromatic compounds were destructed very slowly. These both strains were tested as preparations for bioremediation of oil-polluted soil in model and field experiments. The degree of utilizing of soil oil by this preparation was 79-84 % in field experiments.

Keywords: Bioremediation, n-alkanes, oil-polluted soil, oiloxidizingmicroorganisms.

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

Abstract:

In this research a comparison between k-epsilon and LES model for a deoiling hydrocyclone is conducted. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Potential of prediction for both methods of this complex swirl flow is discussed. Large eddy simulation method results have more similarity to experiment and its results are presented in figures from different hydrocyclone cross sections.

Keywords: Deoiling hydrocyclones, k-epsilon model, Largeeddy simulation, OpenFOAM

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Authors: Koudjo M. Koumadi, Kester Quist-Aphetsi, Robert A. Sowah, Amevi Acakpovi

Abstract:

Downlink/Uplink (DL/UL) time slot allocation (TSA) in time division duplex (TDD) systems is generally uniform for all the cells. This TSA however is not efficient in case of different traffic asymmetry ratios in different cells. We first propose a new 3-coordinate architecture to identify cells in an orthogonal frequency division multiple access (OFDMA) system where each cell is divided into three sectors. Then, this coordinate system is used to derive a TSA for symmetric traffic. Mathematical analysis and simulations are used to show that the proposed TSA outperforms the traditional all uniform type of TSA in terms of total intercellular interference, even under uniform symmetrical traffic. Two adaptation strategies are further proposed to adjust the proposed TSA to asymmetrical traffic with different DL/UL traffic ratios in different cells. Further simulation results show that the adaptation strategies also yield higher signal-to-interference ratio (SIR).

Keywords: Crossed TSA, different-entity interference, same-entity interference, uniform TSA

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Authors: M. Raciti Castelli, A. Castelli, E. Benini

Abstract:

The flow field over a flat roof model building has been numerically investigated in order to determine threedimensional CFD guidelines for the calculation of the turbulent flow over a structure immersed in an atmospheric boundary layer. To this purpose, a complete validation campaign has been performed through a systematic comparison of numerical simulations with wind tunnel experimental data. Wind tunnel measurements and numerical predictions have been compared for five different vertical positions, respectively from the upstream leading edge to the downstream bottom edge of the analyzed model. Flow field characteristics in the neighborhood of the building model have been numerically investigated, allowing a quantification of the capabilities of the CFD code to predict the flow separation and the extension of the recirculation regions. The proposed calculations have allowed the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and corresponding turbulence model for the prediction of the flow field over a three-dimensional roof architecture dominated by flow separation.

Keywords: CFD, roof, building, wind

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Authors: Isao Tomita

Abstract:

Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ~I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction.

Keywords: Electrical Conduction, Electron Phase Coherence, Polycrystalline Metal, Magnetic Field.

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Authors: Shaun Cox, Michael Oakes, Stefan Wermter, Maurice Hawthorne

Abstract:

We report on the results of a pilot study in which a data-mining tool was developed for mining audiology records. The records were heterogeneous in that they contained numeric, category and textual data. The tools developed are designed to observe associations between any field in the records and any other field. The techniques employed were the statistical chi-squared test, and the use of self-organizing maps, an unsupervised neural learning approach.

Keywords: Audiology, data mining, chi-squared, self-organizing maps

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Authors: Carmen D. Pricinâ, E. Corina Cipu, Victor Ţigoiu

Abstract:

The flow of a third grade fluid in an orthogonal rheometer is studied. We employ the admissible velocity field proposed in [5]. We solve the problem and obtain the velocity field as well as the components for the Cauchy tensor. We compare the results with those from [9]. Some diagrams concerning the velocity and Cauchy stress components profiles are presented for different values of material constants and compared with the corresponding values for a linear viscous fluid.

Keywords: Non newtonian fluid flow, orthogonal rheometer, third grade fluid.

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Authors: Ravinesh C. Deo

Abstract:

This article reviews the role of nozzle-exit conditions on the flow field of a plane jet. The jet issuing from a sharp-edged orifice plate at a Reynolds number (Re=18000) with nozzle aspect ratio (AR=72) exhibits the greatest shear-layer instabilities, highest entrainment and jet-spreading rates compared to the radially contoured nozzle. The growth rate of the shear-layer is the highest for the orifice-jet although this property could be amplified for larger Re or AR. A local peak in turbulent energy is found at x»10h. The peak appears to be elevated for an orifice-jet with lower Re or AR. The far-field energy sustained by the orifice-jet exceeds the contoured case although a higher Re and AR may enhance this value. The spectra demonstrated the largest eddy structures for the contoured nozzle. However, the frequency of coherent eddies is higher for the orifice-jet, with a larger magnitude achievable for lower Re and AR. 

Keywords: Plane jet, Reynolds number, nozzle-exit conditions, nozzle geometry, aspect ratio.

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Authors: M. A. Meslem

Abstract:

For precise geoid determination, we use a reference field to subtract long and medium wavelength of the gravity field from observations data when we use the remove-compute-restore technique. Therefore, a comparison study between considered models should be made in order to select the optimal reference gravity field to be used. In this context, two recent global geopotential models have been selected to perform this comparison study over Northern Algeria. The Earth Gravitational Model (EGM2008) and the Global Gravity Model (GECO) conceived with a combination of the first model with anomalous potential derived from a GOCE satellite-only global model. Free air gravity anomalies in the area under study have been used to compute residual data using both gravity field models and a Digital Terrain Model (DTM) to subtract the residual terrain effect from the gravity observations. Residual data were used to generate local empirical covariance functions and their fitting to the closed form in order to compare their statistical behaviors according to both cases. Finally, height anomalies were computed from both geopotential models and compared to a set of GPS levelled points on benchmarks using least squares adjustment. The result described in details in this paper regarding these two models has pointed out a slight advantage of GECO global model globally through error degree variances comparison and ground-truth evaluation.

Keywords: Quasigeoid, gravity anomalies, covariance, GGM.

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Authors: H.A. Ashorynejad, M. Farhadi, K.Sedighi, A.Hasanpour

Abstract:

We report the results of an lattice Boltzmann simulation of magnetohydrodynamic damping of sidewall convection in a rectangular enclosure filled with a porous medium. In particular we investigate the suppression of convection when a steady magnetic field is applied in the vertical direction. The left and right vertical walls of the cavity are kept at constant but different temperatures while both the top and bottom horizontal walls are insulated. The effects of the controlling parameters involved in the heat transfer and hydrodynamic characteristics are studied in detail. The heat and mass transfer mechanisms and the flow characteristics inside the enclosure depended strongly on the strength of the magnetic field and Darcy number. The average Nusselt number decreases with rising values of the Hartmann number while this increases with increasing values of the Darcy number.

Keywords: Lattice Boltzmann method , Natural convection , Magnetohydrodynamic , Porous medium

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Authors: Akhilesh Khapre, Basudeb Munshi

Abstract:

A computational fluid dynamics simulation is done for non-Newtonian fluid in a baffled stirred tank. The CMC solution is taken as non-Newtonian shear thinning fluid for simulation. The Reynolds Average Navier Stocks equation with steady state multi reference frame approach is used to simulate flow in the stirred tank. The turbulent flow field is modelled using realizable k-ε turbulence model. The simulated velocity profiles of Rushton turbine is validated with literature data. Then, the simulated flow field of CD-6 impeller is compared with the Rushton turbine. The flow field generated by CD-6 impeller is less in magnitude than the Rushton turbine. The impeller global parameter, power number and flow number, and entropy generation due to viscous dissipation rate is also reported.

Keywords: Computational fluid dynamics, non-Newtonian, Rushton turbine, CD-6 impeller, power number, flow number, viscous dissipation rate.

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Authors: Rekha V. Dundur , M.V.Latte, S.Y. Kulkarni, M.K.Venkatesha

Abstract:

The advent of multi-million gate Field Programmable Gate Arrays (FPGAs) with hardware support for multiplication opens an opportunity to recreate a significant portion of the front end of a human cochlea using this technology. In this paper we describe the implementation of the cochlear filter and show that it is entirely suited to a single device XC3S500 FPGA implementation .The filter gave a good fit to real time data with efficiency of hardware usage.

Keywords: Cochlea, FPGA, IIR (Infinite Impulse Response), Multiplier.

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Authors: Diako Azizi, Hosein Heydari, Ahmad Gholami

Abstract:

Today with the rapid growth of telecommunications equipment, electronic and developing more and more networks of power, influence of electromagnetic waves on one another has become hot topic discussions. So in this article, this issue and appropriate mechanisms for EMC operations have been presented. First, impact of high voltage lines on the surrounding environment especially on the control room has been investigated, then to reduce electromagnetic radiation, various methods of shielding are provided and shielding effectiveness of them has been compared. It should be expressed that simulations have been done by the finite element method (FEM).

Keywords: Electrical field, EMC, field distribution, finite element method

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Authors: V. Chitra, R. S. Prabhakar

Abstract:

Because of the low maintenance and robustness induction motors have many applications in the industries. The speed control of induction motor is more important to achieve maximum torque and efficiency. Various speed control techniques like, Direct Torque Control, Sensorless Vector Control and Field Oriented Control are discussed in this paper. Soft computing technique – Fuzzy logic is applied in this paper for the speed control of induction motor to achieve maximum torque with minimum loss. The fuzzy logic controller is implemented using the Field Oriented Control technique as it provides better control of motor torque with high dynamic performance. The motor model is designed and membership functions are chosen according to the parameters of the motor model. The simulated design is tested using various tool boxes in MATLAB. The result concludes that the efficiency and reliability of the proposed speed controller is good.

Keywords: Induction motor, Field Oriented Control, Fuzzy logic controller, Maximum torque, Membership function.

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Authors: Sunil Dehipawala, Todd Holden, E. Cheung, Robert Regan, P. Schneider, G. Tremberger Jr, D. Lieberman, T. Cheung

Abstract:

The zinc and iron environments in different growth stages have been studied with EXAFS and XANES with Brookhaven Synchrotron Light Source. Tissue samples included meat, organ, vegetable, leaf, and yeast. The project studied the EXAFS and XANES of tissue samples using Zn and Fe K-edges. Duck embryo samples show that brain and intestine would contain shorter EXFAS determined Zn-N/O bond; as with the cases of fresh yeast versus reconstituted live yeast and green leaf versus yellow leaf. The XANES Fourier transform characteristic-length would be useful as a functionality index for selected types of tissue samples in various physical states. The extension to the development of functional synchrotron imaging for tissue engineering application based on spectroscopic technique is discussed.

Keywords: EXAFS, Fourier Transform, metalloproteins, XANES

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Authors: Liv Gingnell, Evelina Ericsson, Joakim Lilliesköld, Robert Langerström

Abstract:

In recent years, an increased competition and lower profit margins have necessitated a focus on improving the performance of the product development process, an area that traditionally have been excluded from detailed steering and evaluation. A systematic improvement requires a good understanding of the current performance, wherefore the interest for product development performance measurement has increased dramatically. This paper presents a case study that evaluates the performance of the product development performance measurement system used in a Swedish company that is a part of a global corporate group. The study is based on internal documentation and eighteen in-depth interviews with stakeholders involved in the product development process. The results from the case study includes a description of what metrics that are in use, how these are employed, and its affect on the quality of the performance measurement system. Especially, the importance of having a well-defined process proved to have a major impact on the quality of the performance measurement system in this particular case.

Keywords: Outcome metric, Performance driver, Performance measurement, Product development process.

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Authors: Matheus Müller, Delma Vidal

Abstract:

The present paper aims to expose two techniques of dewatering for sludge, analyzing its operations and dewatering processes, aiming at improving the conditions of disposal of residues with high liquid content. It describes the field tests performed on two geotextile systems, a closed geotextile tube and an open geotextile drying bed, both of which are submitted to two filling cycles. The sludge used in the filling cycles for the field trials is from the water treatment plant of the Technological Center of Aeronautics – CTA, in São José dos Campos, Brazil. Data about volume and height abatement due to the dewatering and consolidation were collected per time, until it was observed constancy. With the laboratory analysis of the sludge allied to the data collected in the field, it was possible to perform a critical comparative study between the observed and the scientific literature, in this way, this paper expresses the data obtained and compares them with the bibliography. The tests were carried out on three fronts: field tests, including the filling cycles of the systems with the sludge from CTA, taking measurements of filling time per cycle and maximum filling height per cycle, heights against the abatement by dewatering of the systems over time; tests carried out in the laboratory, including the characterization of the sludge and removal of material samples from the systems to ascertain the solids content within the systems per time and; comparing the data obtained in the field and laboratory tests with the scientific literature. Through the study, it was possible to perceive that the process of densification of the material inside a closed system, such as the geotextile tube, occurs faster than the observed in the drying bed system. This process of accelerated densification can be brought about by the pumping pressure of the sludge in its filling and by the confinement of the residue through the permeable geotextile membrane (allowing water to pass through), accelerating the process of densification and dewatering by its own weight after the filling with sludge.

Keywords: Consolidation, dewatering, geotextile drying bed, geotextile tube.

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Authors: Rafal Michalski, Jakub Zygadlo

Abstract:

We present the concept and scientific methods and algorithms of our computation system called ATOMIC MATTERS. This is the first presentation of the new computer package, that allows its user to describe physical properties of atomic localized electron systems subject to electromagnetic interactions. Our solution applies to situations where an unclosed electron 2p/3p/3d/4d/5d/4f/5f subshell interacts with an electrostatic potential of definable symmetry and external magnetic field. Our methods are based on Crystal Electric Field (CEF) approach, which takes into consideration the electrostatic ligands field as well as the magnetic Zeeman effect. The application allowed us to predict macroscopic properties of materials such as: Magnetic, spectral and calorimetric as a result of physical properties of their fine electronic structure. We emphasize the importance of symmetry of charge surroundings of atom/ion, spin-orbit interactions (spin-orbit coupling) and the use of complex number matrices in the definition of the Hamiltonian. Calculation methods, algorithms and convention recalculation tools collected in ATOMIC MATTERS were chosen to permit the prediction of magnetic and spectral properties of materials in isostructural series.

Keywords: Atomic matters, crystal electric field, spin-orbit coupling, localized states, electron subshell, fine electronic structure.

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Authors: Gh. Saeidifar, F. Raeiszadeh

Abstract:

BRI-STARS (BRIdge Stream Tube model for Alluvial River Simulation) program was used to investigate the scour depth around bridge piers in some of the major river systems in Iran. Model calibration was performed by collecting different field data. Field data are cataloged on three categories, first group of bridges that their rivers bed are formed by fine material, second group of bridges that their rivers bed are formed by sand material, and finally bridges that their rivers bed are formed by gravel or cobble materials. Verification was performed with some field data in Fars Province. Results show that for wide piers, computed scour depth is more than measured one. In gravel bed streams, computed scour depth is greater than measured scour depth, the reason is due to formation of armor layer on bed of channel. Once this layer is eroded, the computed scour depth is close to the measured one.

Keywords: BRI-STARS, local scour, bridge, computer modeling

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Authors: Robert Setekera, Luuk Tiemeijer, Ramses van der Toorn

Abstract:

In this paper an extensive verification of the extraction method (published earlier) that consistently accounts for self-heating and Early effect to accurately extract both base and thermal resistance of bipolar junction transistors is presented. The method verification is demonstrated on advanced RF SiGe HBTs were the extracted results for the thermal resistance are compared with those from another published method that ignores the effect of Early effect on internal base-emitter voltage and the extracted results of the base resistance are compared with those determined from noise measurements. A self-consistency of our method in the extracted base resistance and thermal resistance using compact model simulation results is also carried out in order to study the level of accuracy of the method.

Keywords: Avalanche, Base resistance, Bipolar transistor, Compact modeling, Early voltage, Thermal resistance, Self-heating, parameter extraction.

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Authors: T. Parra, R. Z. Szasz, C. Duwig, R. Pérez, V. Mendoza, F. Castro

Abstract:

The POD makes possible to reduce the complete high-dimensional acoustic field to a low-dimensional subspace where different modes are identified and let reconstruct in a simple way a high percentage of the variance of the field.

Rotating modes are instabilities which are commonly observed in swirling flows. Such modes can appear under both cold and reacting conditions but that they have different sources: while the cold flow rotating mode is essentially hydrodynamic and corresponds to the wellknown PVC (precessing vortex core) observed in many swirled unconfined flows, the rotating structure observed for the reacting case inside the combustion chamber might be not hydrodynamically but acoustically controlled. The two transverse acoustic modes of the combustion chamber couple and create a rotating motion of the flame which leads to a self-sustained turning mode which has the features of a classical PVC but a very different source (acoustics and not hydrodynamics).

Keywords: Acoustic field, POD, swirling flames.

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Authors: Elisabeth Brandenburg, Robert Woll, Rainer Stark

Abstract:

This paper presents how smart glasses and voice commands can be used for improving the maintenance process of industrial gas turbines. It presents the process of inspecting a gas turbine’s combustion chamber and how it is currently performed using a set of paper-based documents. In order to improve this process, a portable hands-free process assistance system has been conceived. In the following, it will be presented how the approach of user-centered design and the method of paper prototyping have been successfully applied in order to design a user interface and a corresponding workflow model that describes the possible interaction patterns between the user and the interface. The presented evaluation of these results suggests that the assistance system could help the user by rendering multiple manual activities obsolete, thus allowing him to work hands-free and to save time for generating protocols.

Keywords: Paper prototyping, smart glasses, turbine maintenance, user centered design.

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Authors: A. Movaghar, R. A. Mahdavinejad

Abstract:

To analyze the effect of various parameters of fluid on the material properties such as surface and depth defects and/or cracks, it is possible to determine the affection of pressure field on these specifications. Stress tensor analysis is also able to determine the points in which the probability of defection creation is more. Besides, from pressure field, it is possible to analyze the affection of various fluid specifications such as viscosity and density on defect created in the material. In this research, the concerned boundary conditions are analyzed first. Then the solution network and stencil used are mentioned. With the determination of relevant equation on the fluid flow between notch and matrix and their discretion according to the governed boundary conditions, these equations can be solved. Finally, with the variation creations on fluid parameters such as density and viscosity, the affection of these variations can be determined on pressure field. In this direction, the flowchart and solution algorithm with their results as vortex and current function contours for two conditions with most applications in pressing process are introduced and discussed.

Keywords: Pressing, notch, matrix, flow function, vortex.

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Authors: Vikas Kumar

Abstract:

The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. The results thus obtained are presented numerically and graphically in the paper.

Keywords: Axi-symmetric, ferrofluid, magnetic field, porous rotating disk.

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Authors: Betül Gezer, Hacer Özden, Ahmet Tekcan, Osman Bizim

Abstract:

Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves.

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