Search results for: revised weighting method

Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Ophir Nave

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In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

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Authors: Diana Santiago, Tania Lisboa, Sophie Lee, Alexander P. Demos, Monica C. S. Vasconcelos

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Memorization has long been recognized as an arduous and anxiety-evoking task for musicians, and yet, it is an essential aspect of performance. Research shows that musicians are often not taught how to memorize. While memorization and practice strategies of professionals have been studied, little research has been done to examine how student musicians learn to practice and memorize music in different cultural settings. We present the process of developing and testing a questionnaire of music memorization and musical practice for student musicians in the UK and Brazil. A survey was developed for a cross-cultural research project aiming at examining how young orchestral musicians (aged 7–18 years) in different learning environments and cultures engage in instrumental practice and memorization. The questionnaire development included members of a UK/US/Brazil research team of music educators and performance science researchers. A pool of items was developed for each aspect of practice and memorization identified, based on literature, personal experiences, and adapted from existing questionnaires. Item development took the varying levels of cognitive and social development of the target populations into consideration. It also considered the diverse target learning environments. Items were initially grouped in accordance with a single underlying construct/behavior. The questionnaire comprised three sections: a demographics section, a section on practice (containing 29 items), and a section on memorization (containing 40 items). Next, the response process was considered and a 5-point Likert scale ranging from ‘always’ to ‘never’ with a verbal label and an image assigned to each response option was selected, following effective questionnaire design for children and youths. Finally, a pilot study was conducted with young orchestral musicians from diverse learning environments in Brazil and the United Kingdom. Data collection took place in either one-to-one or group settings to facilitate the participants. Cognitive interviews were utilized to establish response process validity by confirming the readability and accurate comprehension of the questionnaire items or highlighting the need for item revision. Internal reliability was investigated by measuring the consistency of the item groups using the statistical test Cronbach’s alpha. The pilot study successfully relied on the questionnaire to generate data about the engagement of young musicians of different levels and instruments, across different learning and cultural environments, in instrumental practice and memorization. Interaction analysis of the cognitive interviews undertaken with these participants, however, exposed the fact that certain items, and the response scale, could be interpreted in multiple ways. The questionnaire text was, therefore, revised accordingly. The low Cronbach’s Alpha scores of many item groups indicated another issue with the original questionnaire: its low level of internal reliability. Several reasons for each poor reliability can be suggested, including the issues with item interpretation revealed through interaction analysis of the cognitive interviews, the small number of participants (34), and the elusive nature of the construct in question. The revised questionnaire measures 78 specific behaviors or opinions. It can be seen to provide an efficient means of gathering information about the engagement of young musicians in practice and memorization on a large scale.

Keywords: cross-cultural, memorization, practice, questionnaire, young musicians

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Authors: Jina Hong, Seongeun Ryu, Sungeun You

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Suicide rate among homeless people are much higher than one in the general population. The purpose of this study was to examine the mediating effect of PTSD and aggression in the relationship between childhood physical abuse and suicidal behavior among homeless people. One hundred one homeless were recruited from street and shelters in Korea. Face-to-face interviews were conducted by master’s level graduate students or facility employees of shelters. All participants completed the Suicidal Behaviors Questionnaire-Revised (SBQ-R), Life History of Aggression Questionnaire (LHAQ), Primary Care PTSD (PC-PTSD), and Traumatic Life Events Questionnaire (TLEQ). The average age of homeless people participated in the study was 55.2 years (SD = 10.7) with the age range of 30 to 87. Results indicated that PTSD symptoms and aggression fully mediated the relationship between childhood physical abuse and suicidal behavior among the homeless. These findings suggest the need for trauma-informed care for the homeless, and warrant the need for psychological services for PTSD and aggression in order to reduce suicide risk among homeless people.

Keywords: aggression, homeless, PTSD, suicidal behavior

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Authors: Mesut BALIBEY, Serpil TÜRKYILMAZ

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A popular topic in the econometrics and time series area is the cointegrating relationships among the components of a nonstationary time series. Engle and Granger’s least squares method and Johansen’s conditional maximum likelihood method are the most widely-used methods to determine the relationships among variables. Furthermore, a method proposed to test a unit root based on the periodogram ordinates has certain advantages over conventional tests. Periodograms can be calculated without any model specification and the exact distribution under the assumption of a unit root is obtained. For higher order processes the distribution remains the same asymptotically. In this study, in order to indicate advantages over conventional test of periodograms, we are going to examine a possible relationship between tourism and economic growth during the period 1999:01-2010:12 for Turkey by using periodogram method, Johansen’s conditional maximum likelihood method, Engle and Granger’s ordinary least square method.

Keywords: cointegration, economic growth, periodogram ordinate, tourism

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: Abouzar Kaboudian, Boo Cheong Khoo

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The Ghost Solid Method (GSM) based algorithms have been extensively used for numerical calculation of wave propagation in the limit of abrupt changes in materials. In this work, we present a unified version of the GSMs that can be successfully applied to both abrupt as well as smooth changes of the material properties in a medium. The application of this method enables us to use the previously-matured numerical algorithms which were developed to be applied to homogeneous mediums, with only minor modifications. This method is developed for one-dimensional settings and its extension to multi-dimensions is briefly discussed. Various numerical experiments are presented to show the applicability of this unified GSM to wave propagation problems in sharply as well as smoothly varying mediums.

Keywords: elastic solid, functionally graded material, ghost solid method, solid-solid interaction

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Tomas Barnak, Libor Matejka

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The aim of this study is to create a standard application using multi-criteria evaluation in the field of forensic engineering. This situation can occur in the professional assessment in several cases such as when it is necessary to consider more criteria variant of the structural subsystems, more variants according to several criteria based on a court claim, which requires expert advice. A problematic situation arises when it is necessary to clearly determine the ranking of the options according to established criteria, and reduce subjective evaluation. For the procurement in the field of construction which is based on the prepared text of the law not only economic criteria but also technical, technological and environmental criteria will be determined. This fact substantially changes the style of evaluation of individual bids. For the above-mentioned needs of procurement, the unification of expert’s decisions and the use of multi-criteria assessment seem to be a reasonable option. In the case of experimental verification when using multi-criteria evaluation of alternatives construction subsystem the economic, technical, technological and environmental criteria will be compared. The core of the solution is to compare a selected number of set criteria, application methods and evaluation weighting based on the weighted values assigned to each of the criteria to use multi-criteria evaluation methods. The sequence of individual variations is determined by the evaluation of the importance of the values of corresponding criteria concerning expertise in the problematic of outside wall constructional subsystems.

Keywords: criteria, expertise, multi-criteria evaluation, outside wall subsystems

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: Shadi Motamedighazvini, Roohollah Taherkhani, Mahdi Mahdikhani, Najme Hashempour

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Nowadays, green building rating systems are an inevitable necessity for managing environmental considerations to achieve green buildings. The aim of this paper is to deliver a detailed recognition of what has been the focus of green building policymakers around the world; It is important to conduct this study in a way that can provide a context for researchers who intend to establish or upgrade existing rating systems. In this paper, fifteen rating systems including four worldwide well-known plus eleven local rating systems which have been selected based on the answers to the questionnaires were examined. Their similarities and differences in mandatory and prerequisite clauses, highest and lowest scores for each criterion, the most frequent criteria, and most frequent sub-criteria are determined. The research findings indicated that although the criteria of energy, water, indoor quality (except Homestar), site and materials (except GRIHA) were common core criteria for all rating systems, their sub-criteria were different. This research, as a roadmap, eliminates the lack of a comprehensive reference that encompasses the key criteria of different rating systems. It shows the local systems need to be revised to be more comprehensive and adaptable to their own country’s conditions such as climate.

Keywords: environmental assessment, green buildings, green building criteria, green building rating systems, sustainability, rating tools

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Authors: Kunya Bowornchockchai

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The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins method, Holt’s method, mean absolute percentage error (MAPE), exchange rate

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Authors: David Lindström

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We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

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Authors: Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The discontinuities is characterized using a hybrid spectral/numerical technique. This structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore, the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method proposed.

Keywords: segmentation, s parameters, simulation, optimization

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Authors: Madiha Zahid, Afifa Khanam

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The present study aims to investigate the effect of reflective teaching practices on prospective teachers’ performance. Reflective teaching practice helps teachers to plan, implement and improve their performance by rethinking about their strengths and weaknesses. An action research was conducted by the researcher. All prospective teachers of sixth semester in a women university’s teacher education program were the population of the study. From 40 students, 20 students were taken as experimental group, and the rest of 20 students were taken as control group. During the action research a cyclic process of producing a module, training teachers for the reflective practices and then observing them during their class for reflective practice was done by the researchers. The research used a set of rubrics and checklists for assessing prospective teachers’ performance during their class. Finally, the module was modified with the help of findings. It was found that the training has improved the performance of teachers as they revised and modified their teaching strategies through reflective practice. However, they were not able to train their students for reflective practice as per expectation. The study has implications for teacher training programs to include reflective practice modules as part of their course work for making them better teachers.

Keywords: reflective practices, prospective teacher, effect, performance

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Authors: Ashish Ankus Yerunkar, Ravi Terkar

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Study aimed at evaluating the best process environment which could simultaneously satisfy requirements of both quality as well as productivity with special emphasis on reduction of cutting tool flank wear, because reduction in flank wear ensures increase in tool life. The predicted optimal setting ensured minimization of surface roughness. Purpose of this paper is focused on the analysis of optimum cutting conditions to get lowest surface roughness in turning SCM 440 alloy steel by Taguchi method. Design for the experiment was done using Taguchi method and 18 experiments were designed by this process and experiments conducted. The results are analyzed using ANOVA method. Taguchi method has depicted that the depth of cut has significant role to play in producing lower surface roughness followed by feed. The Cutting speed has lesser role on surface roughness from the tests. The vibrations of the machine tool, tool chattering are the other factors which may contribute poor surface roughness to the results and such factors ignored for analyses. The inferences by this method will be useful to other researches for similar type of study and may be vital for further research on tool vibrations, cutting forces etc.

Keywords: surface roughness (ra), machining, dry turning, taguchi method, turning process, anova method, mahr perthometer

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Authors: Daniel A. Montoya, Marta L. Tostes

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This investigation aims at analyzing and determining the relation between two very important variables in the human resource management: The organizational climate and the performance assessment. This study aims at contributing with knowledge in the search of the relation between the mentioned variables because the literature still does not provide solid evidence to this respect and the cases revised are incipient to reach conclusions enabling a typology about this relation.To this regard, a correlational and cross-sectional perspective was adopted in which quantitative and qualitative techniques were chosen with the total of the workers of the tourist service company PTS Peru. In order to measure the organizational climate, the OCQ (Organization Climate Questionnaire) from was used; it has 50 items and measures 9 dimensions of the Organizational Climate. Also, to assess performance, a questionnaire with 21 items and 6 dimensions was designed. As a means of assessment, a focus group was prepared and was applied to a worker in every area of the company. Additionally, interviews to human resources experts were conducted. The results of the investigation show a clear relation between the organizational climate and the personnel performance assessment as well as a relation between the nine dimensions of the organizational climate and the work performance in general and with some of its dimensions.

Keywords: job performance, job satisfaction, organization climate, performance assessment

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Authors: T. Arshad

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A correlation study was done to explore the relationship of intrusiveness, appraisal and thought control strategies in patients with Obsessive Compulsive Disorder. Theoretical frame work for the present study was Salkovskis (1985) cognitive model of obsessive compulsive disorder. Sample of 100 patients (men=48, women=52) of age 14-62 years (M=32.13, SD=10.37) was recruited from hospitals of Lahore, Pakistan. Revised Obsessional Intrusion Inventory, Stress Appraisal Measure, Thought Control Questionnaire and Symptoms Checklist-R were self-administered. Findings revealed that intrusiveness is correlated with appraisals (controllable by self, controllable by others, uncontrollable, stressfulness) and thought control strategy (punishment). Furthermore, appraisals (uncontrollable, stressfulness, controllable by others) were emerged as strong predictors for different through control strategies (distraction, punishment and social control). Moreover, men have higher frequency of intrusion, whereas women were frequently using social control as thought control strategy. Results implied that intrusiveness, appraisals (controllable by others, uncontrollable, stressfulness) and thought control strategy (punishment) are related which maintains the disorder.

Keywords: appraisal, intrusiveness, obsessive compulsive disorder, thought control strategies

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Authors: M. Barański

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The article presents a new vibration diagnostic method designed to (PM) machines with permanent magnets. Those devices are commonly used in small wind and water systems or vehicles drives. The author’s method is very innovative and unique. Specific structural properties of PM machines are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical PM machines and there was no method found to determine the technical condition of such machine basing on their own signals. In this article, the method genesis, the similarity of machines with permanent magnet to vibration sensor and simulation and laboratory tests results will be discussed. The method of determination the technical condition of electrical machine with permanent magnets basing on its own signals is the subject of patent application No P.405669, and it is the main thesis of author’s doctoral dissertation.

Keywords: vibrations, generator, permanent magnet, traction drive, electrical vehicle

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Bashara Want

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One of the key factors limiting the performance of magnetic memory is that the coercivity has a distribution with finite width, and the reversal starts at the weakest link in the distribution. So one must first know the distribution of coercivities in order to learn how to reduce the width of distribution and increase the coercivity field to obtain a system with narrow width. First Order Reversal Curve (FORC) method characterizes a system with hysteresis via the distribution of local coercivities and, in addition, the local interaction field. The method is more versatile than usual conventional major hysteresis loops that give only the statistical behaviour of the magnetic system. The FORC method will be presented and discussed at the conference.

Keywords: magnetic materials, hysteresis, first-order reversal curve method, nanostructures

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Authors: A.R. Eskandari, M.R. Eskandari

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A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.

Keywords: inverse scattering, microwave imaging, two-dimensional objects, Linear Sampling Method (LSM)

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Authors: Peng Li, Chuanri Li, Tao Li

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Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method and gives concrete processes on determining the factor set, the factor weight set, judgment set, and multi-grade fuzzy comprehensive evaluation. To determine the weight of factor set, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in the fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: reliability allocation, fuzzy arithmetic, allocation weight, linear programming

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: Claudio D'Alonzo

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According to recent tendencies, progress on resource efficiency is possible and it will lead to economic, environmental, and social benefits. The passage to a circular economy system, in which all the materials and energy will maintain their value for as long as possible, waste is reduced and only a few resources are used, is one of the most relevant parts of the European Union's environmental policy to develop a sustainable, competitive and low-carbon economy. A definition of circular economy can be found in Decision 1386/2013/EU of the European Parliament and of the Council on a General Union Environment Action Programme to 2020 named “Living well, within the limits of our planet”. The purpose of renewing waste management systems in the UE and making the European model one of the most effective in the world, a revised waste legislative framework entered into force in July 2018. Regarding the Italian legislation, the laws to be modified are the Legislative Decree 3 April 2006, n. 152 and the laws ruling waste management, end-of-waste, by-products and, the regulatory principles regarding circular economy. European rules on end-of-waste are not fully harmonised and so there are legal challenges. The target to be achieved is full consistency between the laws implementing waste and chemicals policies. Only in this way, materials will be safe, fit-for-purpose and designed for durability; additionally, they will have a low environmental impact.

Keywords: circular economy, end-of-waste, legislation, secondary raw materials

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Authors: Aymen Laadhari, Gábor Székely

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This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: finite element method, implicit, level set, membrane, Newton method

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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