Search results for: Vogel’s approximation method

Authors: Tatyana Rybitskaya, Alexandr Starostenko, Kseniya Ryabchenko

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Collector ring (CR) of FAIR project is a large acceptance storage ring and field quality plays a major role in the magnet design. The CR will use normal conducting dipole magnets. There will be 24 H-type sector magnets with a maximum field value of 1.6 T. The integrated over the length of the magnet field quality as a function of radius is ∆B.l/B.l = ±1x10⁻⁴. Below 1.6 T the value ∆B.l/B.l can be higher with a linear approximation up to ±2.5x10⁻⁴ at the field level of 0.8 T. An iron-dominated magnet with required field quality is produced with standard technology as the quality is dominated by the yoke geometry.

Keywords: conventional magnet, iron yoke dipole, harmonic terms, particle accelerators

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Authors: Mohammed Salem Alzahrani

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In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all program of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: admission process model, assignment problem, Hungarian Method, Least Cost Method, Northwest Corner Method, SAM

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Authors: A. Zitouni, S. Bentata, B. Bouadjemi, T. Lantri, W. Benstaali, A. Zoubir, S. Cherid, A. Sefir

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The structural, electronic, and magnetic properties of transition metal Co and Mn doped zinc-blende semiconductor CdTe were calculated using the density functional theory (DFT) with both generalized gradient approximation (GGA). We have analyzed the structural parameters, charge and spin densities, total and partial densities of states. We find that the Co and Mn doped zinc blende CdTe show half-metallic behavior with a total magnetic moment of 6.0 and 10.0 µB, respectively.The results obtained, make the Co and Mn doped CdTe a promising candidate for application in spintronics.

Keywords: first-principles, half-metallic, diluted magnetic semiconductor, magnetic moment

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Authors: J. S. Savier

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Real power is the component power which is converted into useful energy whereas reactive power is the component of power which cannot be converted to useful energy but it is required for the magnetization of various electrical machineries. If the reactive power is compensated at the consumer end, the need for reactive power flow from generators to the load can be avoided and hence the overall power loss can be reduced. In this scenario, this paper presents a succinct method called JSS method for allocation of reactive power losses to consumers connected to radial distribution networks in a deregulated environment. The proposed method has the advantage that no assumptions are made while deriving the reactive power loss allocation method.

Keywords: deregulation, reactive power loss allocation, radial distribution systems, succinct method

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Authors: S. Mousavian, A. Abedianpour, A. Khanmohammadi, S. Hematian, Gh. Eidi Veisi

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Distillation is one of the most important and utilized separation methods in the industrial practice. There are different ways to design of distillation column. One of these ways is short cut method. In short cut method, material balance and equilibrium are employed to calculate number of tray in distillation column. There are different methods that are classified in short cut method. One of these methods is Fenske-Underwood-Gilliland method. In this method, minimum reflux ratio should be calculated by underwood equation. Underwood proposed an equation that is useful for simple distillation column with one feed and one top and bottom product. In this study, underwood method is developed to predict minimum reflux ratio for column with one side stream upper than feed. The result of this model compared with McCabe-Thiele method. The result shows that proposed method able to calculate minimum reflux ratio with very small error.

Keywords: minimum reflux ratio, side stream, distillation, Underwood’s method

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Authors: Nicolay Zarutskiy, Roman Bulkin

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The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: automation, calibration, calibration device, calibration method, force-torque sensors

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Authors: Hari Prasad Nepal

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Research on lecture method issues confirm that this teaching method has been practiced from the very beginnings of schooling. Many teachers, lecturers and professors are convinced that lecture still represents main tool of contemporary instructional process. The central purpose of this study is to uncover the extent of using lecture method in the higher education. The study was carried out in Nepalese context with employing mixed method research design. To obtain the primary data this study employed a questionnaire involving items with close and open answers. 120 teachers, lecturers and professors participated in this study. The findings indicated that 75 percent of the respondents use the lecture method in their classroom teaching. The study reveals that there are advantages of using lecture method such as easy to practice, less time to prepare, high pass rate, high students’ satisfaction, little comments on instructors, appropriate to large classes and high level students. In addition, the study divulged the instructors’ reflections and measures to improve the lecture method. This research concludes that the practice of lecture method is still significantly applicable in colleges and universities in Nepalese contexts. So, there are no significant changes in the application of lecture method in the higher education classroom despite the emergence of new learning approaches and strategies.

Keywords: instructors, learning approaches, learning strategies, lecture method

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Authors: Iftikhar U. Sikder

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This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

Keywords: concept approximation, granular computing, reducts, rough set theory, rule induction

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Authors: Lin Huo, Xianwei Liu, Jingxiong Zhou

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Recently, due to the existence of semantic gap between image visual features and human concepts, the semantic of image auto-annotation has become an important topic. Firstly, by extract low-level visual features of the image, and the corresponding Hash method, mapping the feature into the corresponding Hash coding, eventually, transformed that into a group of binary string and store it, image auto-annotation by search is a popular method, we can use it to design and implement a method of image semantic auto-annotation. Finally, Through the test based on the Corel image set, and the results show that, this method is effective.

Keywords: image auto-annotation, color correlograms, Hash code, image retrieval

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Authors: S. Boria

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In the last years, the crashworthiness of an automotive body structure can be improved, since the beginning of the design stage, thanks to the development of specific optimization tools. It is well known how the finite element codes can help the designer to investigate the crashing performance of structures under dynamic impact. Therefore, by coupling nonlinear mathematical programming procedure and statistical techniques with FE simulations, it is possible to optimize the design with reduced number of analytical evaluations. In engineering applications, many optimization methods which are based on statistical techniques and utilize estimated models, called meta-models, are quickly spreading. A meta-model is an approximation of a detailed simulation model based on a dataset of input, identified by the design of experiments (DOE); the number of simulations needed to build it depends on the number of variables. Among the various types of meta-modeling techniques, Kriging method seems to be excellent in accuracy, robustness and efficiency compared to other ones when applied to crashworthiness optimization. Therefore the application of such meta-model was used in this work, in order to improve the structural optimization of a bumper for a racing car in composite material subjected to frontal impact. The specific energy absorption represents the objective function to maximize and the geometrical parameters subjected to some design constraints are the design variables. LS-DYNA codes were interfaced with LS-OPT tool in order to find the optimized solution, through the use of a domain reduction strategy. With the use of the Kriging meta-model the crashworthiness characteristic of the composite bumper was improved.

Keywords: composite material, crashworthiness, finite element analysis, optimization

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Authors: Anton A. Larenkov, Alesya Ya Maruk

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In the present study, highly effective iTLC single strip method for the determination of radiochemical purity (RCP) of ⁶⁸Ga-BCA-peptides was developed (with no double-developing, changing of eluents or other additional manipulation). In this method iTLC-SG strips and commonly used eluent TFA_aq. (3-5 % (v/v)) are used. The method allows determining each of the key radiochemical forms of ⁶⁸Ga (colloidal, bound, ionic) separately with the peaks separation being no less than 4 σ. Rf = 0.0-0.1 for ⁶⁸Ga-colloid; Rf = 0.5-0.6 for ⁶⁸Ga-BCA-peptides; Rf = 0.9-1.0 for ionic ⁶⁸Ga. The method is simple and fast: For developing length of 75 mm only 4-6 min is required (versus 18-20 min for pharmacopoeial method). The method has been tested on various compounds (including ⁶⁸Ga-DOTA-TOC, ⁶⁸Ga-DOTA-TATE, ⁶⁸Ga-NODAGA-RGD₂ etc.). The cross-validation work for every specific form of ⁶⁸Ga showed good correlation between method developed and control (pharmacopoeial) methods. The method can become convenient and much more informative replacement for pharmacopoeial methods, including HPLC.

Keywords: DOTA-TATE, 68Ga, quality control, radiochemical purity, radiopharmaceuticals, TLC

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Hyun-Koo Kim, Yonghun Kim, Yong-Hoon Kim, Ju Hee Lee, Myungho Song

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In this paper, we have described an efficient stereo matching method and pedestrian detection method using stereo types LWIR camera. We compared with three types stereo camera algorithm as block matching, ELAS, and SGM. For pedestrian detection using stereo LWIR camera, we used that SGM stereo matching method, free space detection method using u/v-disparity, and HOG feature based pedestrian detection. According to testing result, SGM method has better performance than block matching and ELAS algorithm. Combination of SGM, free space detection, and pedestrian detection using HOG features and SVM classification can detect pedestrian of 30m distance and has a distance error about 30 cm.

Keywords: advanced driver assistance system, pedestrian detection, stereo matching method, stereo long-wave IR camera

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Authors: J. Shiue, I. H. Chen, S. W. Y. Chiu, Y. L. Wang

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In this work, we present a nondestructive method to characterize bacteria in a TEM system. Unlike the conventional TEM specimen preparation method, which needs to thin the specimen in a destructive way, or spread the samples on a tiny millimeter sized carbon grid, our method is easy to operate without the need of sample pretreatment. With a specially designed transparent chip that allows the electron beam to pass through, and a custom made chip holder to fit into a standard TEM sample holder, the bacteria specimen can be easily prepared on the chip without any pretreatment, and then be observed under TEM. The centimeter-sized chip is covered with Au nanoparticles in the surface as the markers which allow the bacteria to be observed easily on the chip. We demonstrate the success of our method by using E. coli as an example, and show that high-resolution TEM images of E. coli can be obtained with the method presented. Some E. coli morphology characteristics imaged using this method are also presented.

Keywords: bacteria, chip, nanoparticles, TEM

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Authors: Takuya Suzuki, Atsushi Shirai, Takashi Seki

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Acupuncture therapy is one of the treatments in traditional Chinese medicine. Recently, some reports have shown the effectiveness of acupuncture. However, its full acceptance has been hindered by the lack of understanding on mechanism of the therapy. Acupuncture applied to Zusanli (ST-36) enhances blood flow volume in superior mesenteric artery (SMA), yielding peripheral vascular resistance – regulated blood flow of SMA dominated by the parasympathetic system and inhibition of sympathetic system. In this study, a lumped-parameter approximation model of blood flow in the systemic arteries was developed. This model was extremely simple, consisting of the aorta, carotid arteries, arteries of the four limbs and SMA, and their peripheral vascular resistances. Here, the individual artery was simplified to a tapered tube and the resistances were modelled by a linear resistance. We numerically investigated contribution of the peripheral vascular resistance of SMA to the systemic blood distribution using this model. In addition to the upstream end of the model, which correlates with the left ventricle, two types of boundary condition were applied; mean left ventricular pressure which correlates with blood pressure (BP) and mean cardiac output which corresponds to cardiac index (CI). We examined it to reproduce the experimentally obtained hemodynamic change, in terms of the ratio of the aforementioned hemodynamic parameters from their initial values before the acupuncture, by regulating the peripheral vascular resistances and the upstream boundary condition. First, only the peripheral vascular resistance of SMA was changed to show contribution of the resistance to the change in blood flow volume in SMA, expecting reproduction of the experimentally obtained change. It was found, however, this was not enough to reproduce the experimental result. Then, we also changed the resistances of the other arteries together with the value given at upstream boundary. Here, the resistances of the other arteries were changed simultaneously in the same amount. Consequently, we successfully reproduced the hemodynamic change to find that regulation of the upstream boundary condition to the value experimentally obtained after the stimulation is necessary for the reproduction, though statistically significant changes in BP and CI were not observed in the experiment. It is generally known that sympathetic and parasympathetic tones take part in regulation of whole the systemic circulation including the cardiac function. The present result indicates that stimulation to ST-36 could induce vasodilation of peripheral circulation of SMA and vasoconstriction of that of other arteries. In addition, it implies that experimentally obtained small changes in BP and CI induced by the acupuncture may be involved in the therapeutic response.

Keywords: acupuncture, hemodynamics, lumped-parameter approximation, modeling, systemic vascular resistance

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Jing Zhang, Daniel Nikovski

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We propose an approximation algorithm called LINKUMP to compute the Pan Matrix Profile (PMP) under the unnormalized l∞ distance (useful for value-based similarity search) using double-ended queue and linear interpolation. The algorithm has comparable time/space complexities as the state-of-the-art algorithm for typical PMP computation under the normalized l₂ distance (useful for shape-based similarity search). We validate its efficiency and effectiveness through extensive numerical experiments and a real-world anomaly detection application.

Keywords: pan matrix profile, unnormalized euclidean distance, double-ended queue, discord discovery, anomaly detection

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Lamia Bourdache, Amar Djema

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The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: Kais Ben-Ahmed, Mhamed Ali-El-Aroui

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This paper develops a Local Generalized Linear Spatial Model (LGLSM) to describe the spatial variation of Visceral Leishmaniasis (VL) infection risk in northern and central Tunisia. The response from each region is a number of affected children less than five years of age recorded from 1996 through 2006 from Tunisian pediatric departments and treated as a poison county level data. The model includes climatic factors, namely averages of annual rainfall, extreme values of low temperatures in winter and high temperatures in summer to characterize the climate of each region according to each continentality index, the pluviometric quotient of Emberger (Q2) to characterize bioclimatic regions and component for residual extra-poison variation. The statistical results show the progressive increase in the number of affected children in regions with high continentality index and low mean yearly rainfull. On the other hand, an increase in pluviometric quotient of Emberger contributed to a significant increase in VL incidence rate. When compared with the original GLSM, Bayesian locally modeling is improvement and gives a better approximation of the Tunisian VL risk estimation. According to the Bayesian approach inference, we use vague priors for all parameters model and Markov Chain Monte Carlo method.

Keywords: generalized linear spatial model, local model, extra-poisson variation, continentality index, visceral leishmaniasis, Tunisia

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Authors: Olgha Giorgishvili

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The work is mainly concerned with the determination of modulus of deformation by laboratory method. It is known that a modulus of deformation is defining by laboratory and field methods. By laboratory method the modulus of deformation is defined in the compressive devices. Our goal is to conduct experiments by both methods and finally make to interpret the obtained results. In this article is considered the definition by new offered laboratory method of deformation modulus that is closer to the real deformation modulus. Finally, the obtained results gives the possibility to us to raise the issue of change the state norms for determining ground by laboratory method.

Keywords: building, soil mechanic, deformation moulus, compression methods

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

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This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: aeroacoustics, fluid-structure coupling, inverse methods, naval, turbulent flow

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Authors: Adnan A. Y. Mustafa

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In this paper we present a quick technique to measure the similarity between binary images. The technique is based on a probabilistic mapping approach and is fast because only a minute percentage of the image pixels need to be compared to measure the similarity, and not the whole image. We exploit the power of the Probabilistic Matching Model for Binary Images (PMMBI) to arrive at an estimate of the similarity. We show that the estimate is a good approximation of the actual value, and the quality of the estimate can be improved further with increased image mappings. Furthermore, the technique is image size invariant; the similarity between big images can be measured as fast as that for small images. Examples of trials conducted on real images are presented.

Keywords: big images, binary images, image matching, image similarity

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Authors: Hossain Samani, Mohammad Ehteram

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In this paper, we consider finite volume method (FVM) in water hammer. We will simulate these techniques on a looped network with complex boundary conditions. After comparing methods, we see the FVM method as the best method. We compare the results of FVM with experimental data. Finite volume using staggered grid is applied for solving water hammer equations.

Keywords: hydraulic transient, water hammer, interpolation, non-liner interpolation

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Authors: Sidrah Ahmed

Abstract:

The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Osama Terra, Hatem Hussein

Abstract:

Calibration of Optical Time Domain Reflectometer (OTDR) is crucial for the accurate determination of loss budget for long optical fiber links. In this paper, the calibration of the attenuation scale of an OTDR using two different techniques is discussed and implemented. The first technique is the external modulation method (EM). A setup is proposed to calibrate an OTDR over a dynamic range of around 15 dB based on the EM method. Afterwards, the OTDR is calibrated using two standard reference fibers (SRF). Both SRF are calibrated using cut-back technique; one of them is calibrated at our home institute (the National Institute of Standards – NIS) while the other at the National Physical Laboratory (NPL) of the United Kingdom to confirm our results. In addition, the parameters contributing the calibration uncertainty are thoroughly investigated. Although the EM method has several advantages over the SRF method, the uncertainties in the SRF method is found to surpass that of the EM method.

Keywords: optical time domain reflectometer, fiber attenuation measurement, OTDR calibration, external source method

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Authors: Amir T. Payandeh Najafabadi

Abstract:

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: T. S. Almutairi, Paul May, Neil Allan

Abstract:

The geometrical, electronic and magnetic properties of the neutral Mg center and MgN₃ cluster in diamond have been studied theoretically in detail by means of an HSE06 Hamiltonian that includes a fraction of the exact exchange term; this is important for a satisfactory picture of the electronic states of open-shell systems. Another batch of the calculations by GGA functionals have also been included for comparison, and these support the results from HSE06. The local perturbations in the lattice by introduced Mg defect are restricted in the first and second shell of atoms before eliminated. The formation energy calculated with HSE06 and GGA of single Mg agrees with the previous result. We found the triplet state with C₃ᵥ is the ground state of Mg center with energy lower than the singlet with C₂ᵥ by ~ 0.1 eV. The recent experimental ZPL (557.4 nm) of Mg center in diamond has been discussed in the view of present work. The analysis of the band-structure of the MgN₃ cluster confirms that the MgN₃ defect introduces a shallow donor level in the gap lying within the conduction band edge. This observation is supported by the EMM that produces n-type levels shallower than the P donor level. The formation energy of MgN₂ calculated from a 2NV defect (~ 3.6 eV) is a promising value from which to engineer MgN₃ defects inside the diamond. Ion-implantation followed by heating to about 1200-1600°C might induce migration of N related defects to the localized Mg center. Temperature control is needed for this process to restore the damage and ensure the mobilities of V and N, which demands a more precise experimental study.

Keywords: empirical marker method, generalised gradient approximation, Heyd–Scuseria–Ernzerhof screened hybrid functional, zero phono line

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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