Search results for: generalised linear modelling.

Authors: Dimitrios J. Dimitriou

Abstract:

Airport’s serving a tourist destination are an essential counterpart of the tourist demand supply chain, and their productivity is related to the region’s attractiveness and is enhanced by the air transport business. In this paper, the evaluation framework of the scheduled flights between two tourist airports is taken into consideration. By adopting a systemic approach, the arrivals from an airport that its connectivity heavily depended on the departures of another major airport are reviewed. The methodology framework, based on inventory control theory and the numerical example, promotes the use of the modelling formulation. The results would be essential for comparison and exercising to other similar cases.

Keywords: Airport connectivity, inventory control, optimization, optimum allocation.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

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Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: D. Vijayakumar, R. K. Nema

Abstract:

Over Current Relays (OCRs) and Directional Over Current Relays (DOCRs) are widely used for the radial protection and ring sub transmission protection systems and for distribution systems. All previous work formulates the DOCR coordination problem either as a Non-Linear Programming (NLP) for TDS and Ip or as a Linear Programming (LP) for TDS using recently a social behavior (Particle Swarm Optimization techniques) introduced to the work. In this paper, a Modified Particle Swarm Optimization (MPSO) technique is discussed for the optimal settings of DOCRs in power systems as a Non-Linear Programming problem for finding Ip values of the relays and for finding the TDS setting as a linear programming problem. The calculation of the Time Dial Setting (TDS) and the pickup current (Ip) setting of the relays is the core of the coordination study. PSO technique is considered as realistic and powerful solution schemes to obtain the global or quasi global optimum in optimization problem.

Keywords: Directional over current relays, Optimization techniques, Particle swarm optimization, Power system protection.

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: K. S. Sivakumaran, Bo Chen

Abstract:

The floor beams of steel buildings, cold-formed steel floor joists in particular, often require large web openings, which may affect their shear capacities. A cost effective way to mitigate the detrimental effects of such openings is to weld/fasten reinforcements. A difficulty associated with an experimental investigation to establish suitable reinforcement schemes for openings in shear zone is that moment always coexists with the shear, and thus, it is impossible to create pure shear state in experiments, resulting in moment influenced results. However, Finite Element Method (FEM) based analysis can be conveniently used to investigate the pure shear behaviour of webs including webs with reinforced openings. This paper presents the details associated with the finite element analysis of thick/thin-plates (representing the web of hot-rolled steel beam, and the web of a cold-formed steel member) having a large reinforced opening. The study considered simply-supported rectangular plates subjected to in-plane shear loadings until failure (including post-buckling behaviour). The plate was modelled using geometrically non-linear quadrilateral shell elements, and non-linear stress-strain relationship based on experiments. Total Langrangian with large displacement/small strain formulation was used for such analyses. The model also considered the initial geometric imperfections. This study considered three reinforcement schemes, namely, flat, lip, and angle reinforcements. This paper discusses the modelling considerations and presents the results associated with the various reinforcement schemes under consideration.

Keywords: Cold-formed steel, finite element analysis, opening, reinforcement, shear resistance.

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Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: C. Pislaru, A. Shebani

Abstract:

This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: System identification, Nonlinear system, Neural networks, RBF neural network.

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Authors: A. Zare Bazghaleh, M. R. Naghashan, H. Mahmoudimanesh, M. R. Meshkatoddini

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Linear induction motors are used in various industries but they have some specific phenomena which are the causes for some problems. The most important phenomenon is called end effect. End effect decreases efficiency, power factor and output force and unbalances the phase currents. This phenomenon is more important in medium and high speeds machines. In this paper a factor, EEF , is obtained by an accurate equivalent circuit model, to determine the end effect intensity. In this way, all of effective design parameters on end effect is described. Accuracy of this equivalent circuit model is evaluated by two dimensional finite-element analysis using ANSYS. The results show the accuracy of the equivalent circuit model.

Keywords: Linear induction motor, end effect, equivalent circuitmodel, finite-element method.

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Authors: Jin Zhang, Wing Lon Ng

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In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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Authors: Roozbeh Molavi, Davood A. Khaburi

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The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.

Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).

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Authors: A. Ben Abdallah, H. Essabbah, M. H. Bedoui

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The myocardial sintigraphy is an imaging modality which provides functional informations. Whereas, coronarography modality gives useful informations about coronary arteries anatomy. In case of coronary artery disease (CAD), the coronarography can not determine precisely which moderate lesions (artery reduction between 50% and 70%), known as the “gray zone", are haemodynamicaly significant. In this paper, we aim to define the relationship between the location and the degree of the stenosis in coronary arteries and the observed perfusion on the myocardial scintigraphy. This allows us to model the impact evolution of these stenoses in order to justify a coronarography or to avoid it for patients suspected being in the gray zone. Our approach is decomposed in two steps. The first step consists in modelling a coronary artery bed and stenoses of different location and degree. The second step consists in modelling the left ventricle at stress and at rest using the sphercical harmonics model and myocardial scintigraphic data. We use the spherical harmonics descriptors to analyse left ventricle model deformation between stress and rest which permits us to conclude if ever an ischemia exists and to quantify it.

Keywords: Spherical harmonics model, vascular bed, 3D reconstruction, left ventricle, myocardial scintigraphy.

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Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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Authors: Mehdi Ghayoumi

Abstract:

We have applied new accelerated algorithm for linear discriminate analysis (LDA) in face recognition with support vector machine. The new algorithm has the advantage of optimal selection of the step size. The gradient descent method and new algorithm has been implemented in software and evaluated on the Yale face database B. The eigenfaces of these approaches have been used to training a KNN. Recognition rate with new algorithm is compared with gradient.

Keywords: lda, adaptive, svm, face recognition.

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: Dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming.

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observations as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use quasi-likelihood estimation approach to estimate the parameters of the model. Under-dispersion parameter is estimated to be 2.14 justifying the appropriateness of Com-Poisson distribution in modelling under-dispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, quasi-likelihood estimation

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Authors: Job H. Domingo, Carolina Bancayrin-Baguio

Abstract:

The Sphere Method is a flexible interior point algorithm for linear programming problems. This was developed mainly by Professor Katta G. Murty. It consists of two steps, the centering step and the descent step. The centering step is the most expensive part of the algorithm. In this centering step we proposed some improvements such as introducing two or more initial feasible solutions as we solve for the more favorable new solution by objective value while working with the rigorous updates of the feasible region along with some ideas integrated in the descent step. An illustration is given confirming the advantage of using the proposed procedure.

Keywords: Interior point, linear programming, sphere method, initial feasible solution, feasible region, centering and descent steps, optimal solution.

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Authors: Mohammed Salahat, Steve Wade

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This paper presents an application of a “Systematic Soft Domain Driven Design Framework” as a soft systems approach to domain-driven design of information systems development. The framework use SSM as a guiding methodology within which we have embedded a sequence of design tasks based on the UML leading to the implementation of a software system using the Naked Objects framework. This framework have been used in action research projects that have involved the investigation and modelling of business processes using object-oriented domain models and the implementation of software systems based on those domain models. Within this framework, Soft Systems Methodology (SSM) is used as a guiding methodology to explore the problem situation and to develop the domain model using UML for the given business domain. The framework is proposed and evaluated in our previous works, and a real case study “Information Retrieval System for academic research” is used, in this paper, to show further practice and evaluation of the framework in different business domain. We argue that there are advantages from combining and using techniques from different methodologies in this way for business domain modelling. The framework is overviewed and justified as multimethodology using Mingers multimethodology ideas.

Keywords: SSM, UML, domain-driven design, soft domaindriven design, naked objects, soft language, information retrieval, multimethodology.

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Authors: Kazuyoshi Mori, Keisuke Hashimoto

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In this paper, we consider the two-stage compensator designs of SISO plants. As an investigation of the characteristics of the two-stage compensator designs, which is not well investigated yet, of SISO plants, we implement three dimensional visualization systems of output signals and optimization system for SISO plants by the parametrization of stabilizing controllers based on the two-stage compensator design. The system runs on Mathematica by using “Three Dimensional Surface Plots,” so that the visualization can be interactively manipulated by users. In this paper, we use the discrete-time LTI system model. Even so, our approach is the factorization approach, so that the result can be applied to many linear models.

Keywords: Linear systems, visualization, optimization, two-Stage compensator design, Mathematica.

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

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This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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Authors: Yang Weiping, Zhang Zhilong, Zhang Yan, Chen Zengping

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Infrared focal plane arrays (IRFPA) sensors, due to their high sensitivity, high frame frequency and simple structure, have become the most prominently used detectors in military applications. However, they suffer from a common problem called the fixed pattern noise (FPN), which severely degrades image quality and limits the infrared imaging applications. Therefore, it is necessary to perform non-uniformity correction (NUC) on IR image. The algorithms of non-uniformity correction are classified into two main categories, the calibration-based and scene-based algorithms. There exist some shortcomings in both algorithms, hence a novel non-uniformity correction algorithm based on non-linear fit is proposed, which combines the advantages of the two algorithms. Experimental results show that the proposed algorithm acquires a good effect of NUC with a lower non-uniformity ratio.

Keywords: Non-uniformity correction, non-linear fit, two-point correction, temporal Kalman filter.

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Authors: Inta Volodko, Valentina Koliskina

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Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Takashi Kaburagi, Takamasa Komura, Yosuke Kurihara

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Absolute pitch is the ability to identify a musical note without a reference tone. Training for absolute pitch often occurs in preschool education. It is necessary to clarify how well the trainee can make use of synesthesia in order to evaluate the effect of the training. To the best of our knowledge, there are no existing methods for objectively confirming whether the subject is using synesthesia. Therefore, in this study, we present a method to distinguish the use of color-auditory synesthesia from the separate use of color and audition during absolute pitch training. This method measures blood volume in the prefrontal cortex using functional Near-infrared spectroscopy (fNIRS) and assumes that the cognitive step has two parts, a non-linear step and a linear step. For the linear step, we assume a second order ordinary differential equation. For the non-linear part, it is extremely difficult, if not impossible, to create an inverse filter of such a complex system as the brain. Therefore, we apply a method based on a self-organizing map (SOM) and are guided by the available data. The presented method was tested using 15 subjects, and the estimation accuracy is reported.

Keywords: Absolute pitch, functional near-infrared spectroscopy, prefrontal cortex, synesthesia.

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Authors: K. V. Geetha, N. R. Mangalambal

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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: Kutubuddin Ansari, Malay Mukul, Sridevi Jade

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We used high-precision Global Positioning System (GPS) to geodetically constrain the motion of stations in the Darjiling-Sikkim Himalayan (DSH) wedge and examine the deformation at the Indian-Tibetan plate boundary using IGS (International GPS Service) fiducial stations. High-precision GPS based displacement and velocity field was measured in the DSH between 1997 and 2009. To obtain additional insight north of the Indo-Tibetan border and in the Darjiling-Sikkim-Tibet (DaSiT) wedge, published velocities from four stations J037, XIGA, J029 and YADO were also included in the analysis. India-fixed velocities or the back-slip was computed relative to the pole of rotation of the Indian Plate (Latitude 52.97 ± 0.22º, Longitude - 0.30 ± 3.76º, and Angular Velocity 0.500 ± 0.008º/ Myr) in the DaSiT wedge. Dislocation modelling was carried out with the back-slip to model the best possible solution of a finite rectangular dislocation or the causative fault based on dislocation theory that produced the observed back-slip using a forward modelling approach. To find the best possible solution, three different models were attempted. First, slip along a single thrust fault, then two thrust faults and in finally, three thrust faults were modelled to simulate the back-slip in the DaSiT wedge. The three-fault case bests the measured displacements and is taken as the best possible solution.

Keywords: Global Positioning System, Darjiling-Sikkim Himalaya, Dislocation modelling.

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Authors: Arkady Bolotin

Abstract:

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.

Keywords: Categorization, Uncertain medical categories, Binomial regression model, Fuzzy dependent variable, Robustness.

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Authors: S. K. Satpathy, S. Panda, K. K. Nagwanshi, C. Ardil

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This paper proposes a new technique based on nonlinear Minmax Detector Based (MDB) filter for image restoration. The aim of image enhancement is to reconstruct the true image from the corrupted image. The process of image acquisition frequently leads to degradation and the quality of the digitized image becomes inferior to the original image. Image degradation can be due to the addition of different types of noise in the original image. Image noise can be modeled of many types and impulse noise is one of them. Impulse noise generates pixels with gray value not consistent with their local neighborhood. It appears as a sprinkle of both light and dark or only light spots in the image. Filtering is a technique for enhancing the image. Linear filter is the filtering in which the value of an output pixel is a linear combination of neighborhood values, which can produce blur in the image. Thus a variety of smoothing techniques have been developed that are non linear. Median filter is the one of the most popular non-linear filter. When considering a small neighborhood it is highly efficient but for large window and in case of high noise it gives rise to more blurring to image. The Centre Weighted Mean (CWM) filter has got a better average performance over the median filter. However the original pixel corrupted and noise reduction is substantial under high noise condition. Hence this technique has also blurring affect on the image. To illustrate the superiority of the proposed approach, the proposed new scheme has been simulated along with the standard ones and various restored performance measures have been compared.

Keywords: Filtering, Minmax Detector Based (MDB), noise, centre weighted mean filter, PSNR, restoration.

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Authors: Ion Smeureanu, Adriana Reveiu, Marian Dardala, Titus Felix Furtuna, Roman Kanala

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This paper proposes a linear model for optimizing domestic energy consumption in Romania. The particularity of the model is that it is putting in competition both tangible technologies and thermal insulation projects with different financing modes. The model is optimizing the energy system by minimizing the global discounted cost in household sector, by integrating residential lighting, space heating, hot water, combined space heating – hot water, as well as space cooling, in a monolithic model. Another demand sector included is the passenger transport. This paper focuses on space heating part, analyzing technical and economic issues related to investment decisions to envelope and insulate buildings, in order to minimize energy consumption.

Keywords: Consumer behavior, energy modelling, Open Source Energy Modeling System (OSeMOSYS), MARKAL/TIMES Romanian energy model.

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Authors: V. Geza, J. Vencels, G. Zageris, S. Pavlovs

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One of the most perspective methods to produce SoG-Si is refinement via metallurgical route. The most critical part of this route is refinement from boron and phosphorus. Therefore, a new approach could address this problem. We propose an approach of creating surface waves on silicon melt’s surface in order to enlarge its area and accelerate removal of boron via chemical reactions and evaporation of phosphorus. A two dimensional numerical model is created which includes coupling of electromagnetic and fluid dynamic simulations with free surface dynamics. First results show behaviour similar to experimental results from literature.

Keywords: Numerical modelling, silicon refinement, surface waves, VOF method.

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Authors: Ivan Yatchev, Ewen Ritchie

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Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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