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Quantification of stochastic or quantum systems by a joint probability density or wave function is a notoriously difficult computational problem, since the solution depends on all possible states (or realizations) of the system. Due to this combinatorial flavor, even a system containing as few as ten particles may yield as many as $10^{10}$ discretized states. None of even modern supercomputers are capable to cope with this curse of dimensionality straightforwardly, when the amount of quantum particles, for example, grows up to more or less interesting order of hundreds. A traditional approach for a long time was to avoid models formulated in terms of probabilistic functions, and simulate particular system realizations in a randomized process. Since different times in different communities, data-sparse methods came into play. Generally, they aim to define all data points indirectly, by a map from a low amount of representers, and recast all operations (e.g. linear system solution) from the initial data to the effective parameters. The most advanced techniques can be applied (at least, tried) to any given array, and do not rely explicitly on its origin. The current work contributes further progress to this area in the particular direction: tensor product methods for separation of variables. The separation of variables has a long history, and is based on the following elementary concept: a function of many variables may be expanded as a product of univariate functions. On the discrete level, a function is encoded by an array of its values, or a tensor. Therefore, instead of a huge initial array, the separation of variables allows to work with univariate factors with much less efforts. The dissertation contains a short overview of existing tensor representations: canonical PARAFAC, Hierarchical Tucker, Tensor Train (TT) formats, as well as the artificial tensorisation, resulting in the Quantized Tensor Train (QTT) approximation method. The contribution of the dissertation consists in both theoretical constructions and practical numerical algorithms for high-dimensional models, illustrated on the examples of the Fokker-Planck and the chemical master equations. Both arise from stochastic dynamical processes in multiconfigurational systems, and govern the evolution of the probability function in time. A special focus is put on time propagation schemes and their properties related to tensor product methods. We show that these applications yield large-scale systems of linear equations, and prove analytical separable representations of the involved functions and operators. We propose a new combined tensor format (QTT-Tucker), which descends from the TT format (hence TT algorithms may be generalized smoothly), but provides complexity reduction by an order of magnitude. We develop a robust iterative solution algorithm, constituting most advantageous properties of the classical iterative methods from numerical analysis and alternating density matrix renormalization group (DMRG) techniques from quantum physics. Numerical experiments confirm that the new method is preferable to DMRG algorithms. It is as fast as the simplest alternating schemes, but as reliable and accurate as the Krylov methods in linear algebra.

This dissertation concerns the model reduction of linear periodic descriptor systems both in continuous and discrete-time case. In this dissertation, mainly the projection based approaches are considered for model order reduction of linear periodic time varying descriptor systems. Krylov based projection method is used for large continuous-time periodic descriptor systems and balancing based projection technique is applied to large sparse discrete-time periodic descriptor systems to generate the reduce systems. For very large dimensional state space systems, both the techniques produce large dimensional solutions. Hence, a recycling technique is used in Krylov based projection methods which helps to compute low rank solutions of the state space systems and also accelerate the computational convergence. The outline of the proposed model order reduction procedure is given with more details. The accuracy and suitability of the proposed method is demonstrated through different examples of different orders. Model reduction techniques based on balance truncation require to solve matrix equations. For periodic time-varying descriptor systems, these matrix equations are projected generalized periodic Lyapunov equations and the solutions are also time-varying. The cyclic lifted representation of the periodic time-varying descriptor systems is considered in this dissertation and the resulting lifted projected Lyapunov equations are solved to achieve the periodic reachability and observability Gramians of the original periodic systems. The main advantage of this solution technique is that the cyclic structures of projected Lyapunov equations can handle the time-varying dimensions as well as the singularity of the period matrix pairs very easily. One can also exploit the theory of time-invariant systems for the control of periodic ones, provided that the results achieved can be easily re-interpreted in the periodic framework. Since the dimension of cyclic lifted system becomes very high for large dimensional periodic systems, one needs to solve the very large scale periodic Lyapunov equations which also generate very large dimensional solutions. Hence iterative techniques, which are the generalization and modification of alternating directions implicit (ADI) method and generalized Smith method, are implemented to obtain low rank Cholesky factors of the solutions of the periodic Lyapunov equations. Also the application of the solvers in balancing-based model reduction of discrete-time periodic descriptor systems is discussed. Numerical results are given to illustrate the effciency and accuracy of the proposed methods.

L’industrie de métallurgie est demandeuse de propriétés thermophysiques essentielles pour la modélisation et l’optimisation des procédés d’élaborations.Les propriétés thermophysiques des métaux et des alliages métalliques à l’état liquide sont mal connues. Ces propriétés dépendent de la température et sont difficiles à mesurer surtout à haute température. A l’état liquide, le métal est réactif et facilement polluable. Dans les années 1980, Egry a développé un lévitateur électromagnétique TEMPUS pour mesurer en apesanteur sans contact matériel les propriétés thermophysiques des métaux et alliages en fusion. Dans l’espace, les effets du brassage électromagnétique et de la déformation des échantillons fondus sont beaucoup plus faibles que sur terre.L’emploi de cet outil spatial est coûteux. C’est pour, à terme, diminuer les coûts tout en maintenant voire améliorant la qualité des mesures, que nous avons souhaité remplacer la microgravité par un champ magnétique continu.Les travaux réalisés dans cette thèse consistent à mesurer les propriétés thermiques des métaux par procédé électromagnétique en utilisant une méthode de calorimétrie modulée.Elle comporte deux parties.-Une partie numérique dans laquelle nous avons simulé d’une part le lévitateur spatial TEMPUS et d’autre part le lévitateur terrestre AEXAM.La simulation du lévitateur spatial TEMPUS a pour but de déterminer l’effet de la superposition de courants inducteurs de fréquences différentes (courants de chauffage et de centrage) sur les comportements hydrodynamique et thermique de la goutte. Les résultats des calculs nous ont montré que le courant de centrage est susceptible d’agir sur les mesures.La simulation du lévitateur terrestre AEXAM consiste à déterminer la fréquence d’oscillation verticale de la goutte, la puissance Joule dissipée dans celle-ci, les champs de vitesse et de température. La goutte prend la forme d’une poire et elle oscille à une fréquence de 7 Hz. La puissance Joule dissipée dans la charge est maximale vers le bas de la charge dans les premiers millimètres à mi-hauteur entre l’équateur et le pôle. Elle diminue en pénétrant dans la charge et est nul sur l’axe de symétrie. La convection dans la goutte crée un brassage électromagnétique et homogénéise le champ de température.-Une partie expérimentale dans laquelle le lévitateur AEXAM a été placé dans un champ magnétique continu horizontal pour amortir l’oscillation verticale et le brassage électro-magnétique de la goutte mentionnée dans les calculs. Ceci nous a permis la mise en œuvre d’un protocole de mesure original sur un métal liquide. Ce protocole est un programme de traitement des donnés basé sur le comportement du champ de température lorsque les sources thermiques internes à l’échantillon sont instationnaires. Dans ce programme, nous avons utilisé une fonction d’identification qui permet d’obtenir un modèle mathématique à partir de mesures. Pour obtenir un modèle mathématique consistant, il est important d'exciter le système avec toutes les fréquences de sa plage de fonctionnement. C’est ce que nous faisons quand nous appliquons un bruit blanc sur la consigne d’entrée du générateur. Nous avons précédemment validé le protocole sur du solide en remontant aux valeurs de la capacité calorifique et de la conductivité thermique.Pour optimiser les pertes de masse, les instabilités sur les mesures du courant inducteur et la bonne reproductivité des mesures sur une goutte, nous avons choisi une masse initiale de 3,5 g pour faire les mesures avec modulation du courant inducteur dans un champ magnétique continu de 1 Tesla. Nous avons obtenu les valeurs de la capacité calorifique et de la conductivité thermique de la goutte. Celles-ci sont voisines des valeurs données par la littérature. Ce qui nous a permis de valider en partie le protocole de traitement des mesures.Dans le futur, ce protocole peut être appliqué sur des alliages métalliques. / The metal industry is requesting essential thermophysical properties for modeling and optimizing elaboration processes.Thermophysical properties of metals and metal alloys in liquid state are well known. These properties depend on the temperature and are difficult to measure especially at high temperature. In the liquid state, the metal is reactive and easily contaminated .In the 1980s, Egry developed an electromagnetic levitator TEMPUS developed an electromagnetic levitator TEMPUS to measure thermophysical properties of molten metals and alloys using a contactless technique under microgravity conditions. In space, the effects of electromagnetic stirring and deformation in molten samples are much lower than on Earth.The use of this space tool is expensive. In order to reduce the cost while maintaining or even improving the quality of measurements, we wanted to replace microgravity by a continuous magnetic field.The work in this thesis includes measuring the thermal properties of metals by electromagnetic method using a modulated calorimetry technique.The work has been divided in two parts:-The first consisted in the numerical simulation of space levitator TEMPUS and a terrestrial levitator AEXAM.The numerical simulation of space levitator TEMPUS aims to determine the effect of the superposition currents of different induction frequencies (heating currents and centering) on the hydrodynamic and thermal behavior of the drop. Calculation results showed that in some cases the centering current is likely to act on the measures and therefore it should be taking into account.The numerical simulation of terrestrial levitator AEXAM was destined to determine the vertical oscillation frequency of the drop, the power dissipated, the velocity fields developed inside and temperature. The drop takes the form of a pear and oscillates at a frequency of 7 Hz. The Joule power dissipated in the load is maximum on the lower part of the drop and decreases towards the interior of the drop vanishing at the center. Convection in the drop creates an electromagnetic stirring and homogenizing the temperature field.-The second part present the experiments performed using the levitator AEXAM placed in a horizontal continuous magnetic field for dampening the vertical oscillation and the turbulence produced by the effect of the electromagnetic stirring as it was mentioned in the calculations.This allowed us the implementation of a new protocol for measuring thermal properties in liquid metals.The protocol is a post processing program based on the temperature field variation resulting from unsteady joule power dissipation in the charge. An implemented identification function provides a mathematical model based on performed measurements. The use of a wide range of system frequencies was required to obtain a robust mathematical model. This was achieved by using pseudo-white noise perturbation at the generator inlet. The program has been validated successfully on solid matter by reverse determination of thermal conductivity and heat capacity.The preliminary studies under continuous magnetic field without modulation have mounted for a maximum initial weight of 3.5, we have less mass loss and improved measurement stability of the inductor current, as well as the reproductivity of the measurements.The protocol was validated successfully on the liquid charge using modulated perturbation under a continuous magnetic field of 1 Tesla. The obtained values of the heat capacity and thermal conductivity were comparable to the values given by the literature which partially validates the protocol.As a perspective, this protocol can be applied to a wide range of metal alloys.

This dissertation analyses various kinds of the orthographical exercises in the second grade of the primary school. The dissertation focuses on the question of orthography in the theoretical part, after that it focuses on a short view of orthography in the Czech history or its division into lexical, morphological and syntactical orthography. We find here a short description of the orthography and a view of orthographical's effects in the teaching of Czech language in the primary school or meeting with orthographical guides. The goal of the practical part of this dissertation is a deeper typological description of these exercises, we will primarily focus on examples of rewriting, orthographical analysis, refilling and alternating exercises and dictations.

L'intérêt de l'échantillonnage compressé dans l'imagerie ultrasonore a été récemment évalué largement par plusieurs équipes de recherche. Suite aux différentes configurations d'application, il a été démontré que les données RF peuvent être reconstituées à partir d'un faible nombre de mesures et / ou en utilisant un nombre réduit d'émission d'impulsions ultrasonores. Selon le modèle de l'échantillonnage compressé, la résolution des images ultrasonores reconstruites à partir des mesures compressées dépend principalement de trois aspects: la configuration d'acquisition, c.à.d. l'incohérence de la matrice d'échantillonnage, la régularisation de l'image, c.à.d. l'a priori de parcimonie et la technique d'optimisation. Nous nous sommes concentrés principalement sur les deux derniers aspects dans cette thèse. Néanmoins, la résolution spatiale d'image RF, le contraste et le rapport signal sur bruit dépendent de la bande passante limitée du transducteur d'imagerie et du phénomène physique lié à la propagation des ondes ultrasonores. Pour surmonter ces limitations, plusieurs techniques de traitement d'image en fonction de déconvolution ont été proposées pour améliorer les images ultrasonores. Dans cette thèse, nous proposons d'abord un nouveau cadre de travail pour l'imagerie ultrasonore, nommé déconvolution compressée, pour combiner l'échantillonnage compressé et la déconvolution. Exploitant une formulation unifiée du modèle d'acquisition directe, combinant des projections aléatoires et une convolution 2D avec une réponse impulsionnelle spatialement invariante, l'avantage de ce cadre de travail est la réduction du volume de données et l'amélioration de la qualité de l'image. Une méthode d'optimisation basée sur l'algorithme des directions alternées est ensuite proposée pour inverser le modèle linéaire, en incluant deux termes de régularisation exprimant la parcimonie des images RF dans une base donnée et l'hypothèse statistique gaussienne généralisée sur les fonctions de réflectivité des tissus. Nous améliorons les résultats ensuite par la méthode basée sur l'algorithme des directions simultanées. Les deux algorithmes sont évalués sur des données simulées et des données in vivo. Avec les techniques de régularisation, une nouvelle approche basée sur la minimisation alternée est finalement développée pour estimer conjointement les fonctions de réflectivité des tissus et la réponse impulsionnelle. Une investigation préliminaire est effectuée sur des données simulées. / The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small number of measurements and/or using a reduced number of ultrasound pulse emissions. According to the model of compressive sampling, the resolution of reconstructed ultrasound images from compressed measurements mainly depends on three aspects: the acquisition setup, i.e. the incoherence of the sampling matrix, the image regularization, i.e. the sparsity prior, and the optimization technique. We mainly focused on the last two aspects in this thesis. Nevertheless, RF image spatial resolution, contrast and signal to noise ratio are affected by the limited bandwidth of the imaging transducer and the physical phenomenon related to Ultrasound wave propagation. To overcome these limitations, several deconvolution-based image processing techniques have been proposed to enhance the ultrasound images. In this thesis, we first propose a novel framework for Ultrasound imaging, named compressive deconvolution, to combine the compressive sampling and deconvolution. Exploiting an unified formulation of the direct acquisition model, combining random projections and 2D convolution with a spatially invariant point spread function, the benefit of this framework is the joint data volume reduction and image quality improvement. An optimization method based on the Alternating Direction Method of Multipliers is then proposed to invert the linear model, including two regularization terms expressing the sparsity of the RF images in a given basis and the generalized Gaussian statistical assumption on tissue reflectivity functions. It is improved afterwards by the method based on the Simultaneous Direction Method of Multipliers. Both algorithms are evaluated on simulated and in vivo data. With regularization techniques, a novel approach based on Alternating Minimization is finally developed to jointly estimate the tissue reflectivity function and the point spread function. A preliminary investigation is made on simulated data.

A presente pesquisa centra-se no estudo das relações entre memória de curto prazo, memória de trabalho, velocidade de processamento, processamento visuoespacial, funções executivas, atenção seletiva e alternada e desempenho matemático, uma vez que essas relações podem esclarecer as diferenças entre os alunos na aprendizagem da matemática. O trabalho teve como objeto de observação crianças da 2ª série do ensino fundamental. Consiste em um estudo com base correlacional e comparativa. A amostra desta pesquisa é composta por 40 alunos, com idade entre 8 e 9 anos. A investigação envolvendo o funcionamento neuropsicológico e o desempenho cognitivo na aprendizagem matemática é relevante, pois para desenvolver habilidades de cálculo matemático é fundamental que o aluno tenha construído o conceito de número e esta construção está vinculada ao desenvolvimento das funções neuropsicológicas. O desempenho matemático é avaliado através da Prova de Aritmética de Capovilla, Montiel e Capovilla (2007) e as funções neuropsicológicas, através de quatro subtestes da Escala Wechsler WISCIII, que são: Memória de Curto Prazo – teste de Dígitos de Ordem Direta; Memória de Trabalho – Dígitos de Ordem Inversa; Velocidade de Processamento - Procurar Símbolos e Códigos; Percepção Visuoespacial – teste de Cubos. A Função Executiva é avaliada através do Teste das Trilhas de Montiel e Capovilla (2007) e a Atenção, através do Teste de Atenção por Cancelamento de Montiel e Capovilla (2007). Observa-se uma correlação significativa entre Desempenho Matemático e Memória de Curto Prazo, Velocidade de Processamento, Função Executiva e Atenção. Neste estudo, não se encontrou uma correlação estatisticamente significativa entre as funções Memória de Trabalho e Processamento Visuoespacial. / This paper approaches the relationship amongst neuropsychological functions –Short Term Memory (STM), Working Memory (WM), Speed Processing (SP), Visual Spatial Perception (VSP), Executive Functions (EF), Attention (A) and Math Performance (MP) in 2nd grade children at a public Elementary School from Porto Alegre. It is a comparative and correlation study. The sample of this research is composed for 40 pupils with are between 8 and 9 years. Research involving neuropsychological functioning and cognitive performance in mathematics is pertinent, for it is essential that the student build the notion of number in order to develop mathematical skills and such construction relies on the expansion of neuropsychological functions. The mathematical performance is measured by the Arthmetic Test of Capovilla, Montiel and Capovilla (2007) and the neuropsychological functions are verified by subtests Wechsler WIS CIII; Short Term Memory is assessed by the Digits in Direct Order, while the Working Memory is established by the Digits in Reverse Order. The speed processing is assessed through the use of Find Symbols and Codes activities, and spatial perception is confirmed by the utilization of cubes. The Executive Function is assessed by the Trail Making of Montiel and Capovilla (2007) and attention is assessed by the Attention Test for Cancellation of Montiel and Capovilla (2007). There is a momentous correlation amid math performance and Short-Term Memory, speed processing, executive function and attention. This study one did not mett, however, the establishment of a statistically significant correlation between the Working Memory functions and the Visual Spatial Processing.

A presente pesquisa centra-se no estudo das relações entre memória de curto prazo, memória de trabalho, velocidade de processamento, processamento visuoespacial, funções executivas, atenção seletiva e alternada e desempenho matemático, uma vez que essas relações podem esclarecer as diferenças entre os alunos na aprendizagem da matemática. O trabalho teve como objeto de observação crianças da 2ª série do ensino fundamental. Consiste em um estudo com base correlacional e comparativa. A amostra desta pesquisa é composta por 40 alunos, com idade entre 8 e 9 anos. A investigação envolvendo o funcionamento neuropsicológico e o desempenho cognitivo na aprendizagem matemática é relevante, pois para desenvolver habilidades de cálculo matemático é fundamental que o aluno tenha construído o conceito de número e esta construção está vinculada ao desenvolvimento das funções neuropsicológicas. O desempenho matemático é avaliado através da Prova de Aritmética de Capovilla, Montiel e Capovilla (2007) e as funções neuropsicológicas, através de quatro subtestes da Escala Wechsler WISCIII, que são: Memória de Curto Prazo – teste de Dígitos de Ordem Direta; Memória de Trabalho – Dígitos de Ordem Inversa; Velocidade de Processamento - Procurar Símbolos e Códigos; Percepção Visuoespacial – teste de Cubos. A Função Executiva é avaliada através do Teste das Trilhas de Montiel e Capovilla (2007) e a Atenção, através do Teste de Atenção por Cancelamento de Montiel e Capovilla (2007). Observa-se uma correlação significativa entre Desempenho Matemático e Memória de Curto Prazo, Velocidade de Processamento, Função Executiva e Atenção. Neste estudo, não se encontrou uma correlação estatisticamente significativa entre as funções Memória de Trabalho e Processamento Visuoespacial. / This paper approaches the relationship amongst neuropsychological functions –Short Term Memory (STM), Working Memory (WM), Speed Processing (SP), Visual Spatial Perception (VSP), Executive Functions (EF), Attention (A) and Math Performance (MP) in 2nd grade children at a public Elementary School from Porto Alegre. It is a comparative and correlation study. The sample of this research is composed for 40 pupils with are between 8 and 9 years. Research involving neuropsychological functioning and cognitive performance in mathematics is pertinent, for it is essential that the student build the notion of number in order to develop mathematical skills and such construction relies on the expansion of neuropsychological functions. The mathematical performance is measured by the Arthmetic Test of Capovilla, Montiel and Capovilla (2007) and the neuropsychological functions are verified by subtests Wechsler WIS CIII; Short Term Memory is assessed by the Digits in Direct Order, while the Working Memory is established by the Digits in Reverse Order. The speed processing is assessed through the use of Find Symbols and Codes activities, and spatial perception is confirmed by the utilization of cubes. The Executive Function is assessed by the Trail Making of Montiel and Capovilla (2007) and attention is assessed by the Attention Test for Cancellation of Montiel and Capovilla (2007). There is a momentous correlation amid math performance and Short-Term Memory, speed processing, executive function and attention. This study one did not mett, however, the establishment of a statistically significant correlation between the Working Memory functions and the Visual Spatial Processing.

Submitted to the Department of Electrical Engineering in Fulfilment of the Requirements for the Magister Technologiae in Electrical Engineering at the Cape Peninsula University of Technology SUPERVISOR: E. VOSS NOVEMBER 2013 / The reluctance synchronous machine (RSM) operates on the principle of magnetic reluctance, which is produced through a careful selection of rotor flux barriers and cut-outs. Magnetic reluctivity is the resistance to magnetic flux and can be directly related to the principles of Ohm’s law in electrical circuits. Although reluctance motors have been known for more than 150 years, researchers lost interest when Nikola Tesla’s induction machine (IM) was introduced to industry. Over the last few decades, however, RSMs have shown a lot of potential. They are cheap, robust, reliable, and their rotors can also be used in the stators of IMs. The disadvantage of these machines is an inherently high torque ripple, being the result of its rotor geometry, but the biggest advantage is having a significant reduction in copper losses after the rotor cage has been removed. This advantage drove engineers to investigate, optimise and modify the performance and structure of this machine, which led to the usage of electronic drive systems. The recent advances in technology have allowed researchers to further investigate and modify the design and performance of this special type of machine, with the integration of Finite Element Analysis (FEA) software also making a contribution to the development of the RSM’s current driven systems. The voltage-fed RSM, driven direct-on-line (DOL) from the utility supply, was left in the shadows as the current-fed RSM took reign, but still is, in the author’s opinion, not yet fully analysed. This thesis practically investigates the performance characteristics of the cageless, voltage-fed 3kW RSM in its steady-state operation, under various loads. These performance characteristics are also compared to a RSM driven from a sensorless vector drive (current-fed) to investigate the advantages and disadvantages between the two. Experiments performed on the test bench immediately reveal a limitation to the voltage-fed RSM’s ability to drive higher loads. While the current-fed RSM conveniently reaches 150% of its full-load, the voltage-fed RSM, due to its cageless structure, only reaches 110% of its full-load power. Despite this discovery, the voltage-fed RSM proves to have a lower core loss, harmonic content and torque ripple. Using a FE software package with an integrated source-code, additional parameters such as the dq-axis inductances and currents are also compared and analysed in terms of its reaction to an increase in load. The eddy-current, hysteresis and excess losses are also analysed as well as the harmonic components caused by the geometry of the RSM. For academic purposes, a fair amount of emphasis is placed on the approach to the problem. The preparation for the FE simulation is explained in detail, providing insight into the FE mathematical model as well as parameter acquisition. These parameters include current angle, friction and windage losses, stator resistance, end-winding leakage reactance, core loss and inertia. The results obtained by the FE model are compared to that of the measured results and is found to have an error of only 0.52%. Furthermore, this study attempts to find the feasibility of the voltage-fed RSM’s practicality in modern-day industry. The conclusion is drawn that the voltage-fed RSM could be used as a more elegant alternative to an otherwise over-complicated and over-priced installation.

This dissertation presents an application of Virtual and Augmented Reality, having as main focus the study of the magnetic field created by a single-phase engine of induction during its functioning. Virtual Reality and Augmented Reality potentially emerges every days, due increasing number of its applications in the most varied areas of the knowledge. One of the most benefited is Education. Therefore, these technologies becomes supporting tools for education, for assisting in the perception and interaction of the students in diverses subjects. The visualization of the magnetic field is related to strategies of use of ferromagnetic elements. Such fields, the example of others (Electric Field, Gravitational Field) have threedimensional characteristics. Since great part of the referring images to this physical phenomenon is static what most of the time it finishes making it difficult the learning of this subject. In this work, the Magnetic Field could be visualized, for the user, with use of Virtual Reality or Augmented Reality. The study element will be the Magnetic Field that is generated in an electric engine (of single-phase induction). It is intended, by means of this boarding, to identify the advantages of if using the techniques of Virtual Reality and Augmented Reality in relation the other forms of visualization of the magnetic field. / Esta dissertação apresenta uma aplicação de Realidade Virtual e Aumentada, tendo como foco principal o estudo do campo magnético criado por um motor de indução monofásico durante o seu funcionamento. A Realidade Virtual e a Realidade Aumentada a cada dia vêm se destacando, devido ao surgimento de suas inúmeras aplicações nas mais variadas áreas do conhecimento, e uma das mais beneficiadas é a educação. Portanto estas tecnologias vêm se tornando ferramentas de apoio ao ensino, auxiliando a percepção e interação dos alunos em assuntos diversos. A visualização do campo magnético está relacionada com estratégias de utilização de elementos ferromagnéticos. Tais campos, a exemplo de outros (Campo Elétrico, Campo Gravitacional) têm características tridimensionais. Sendo que grande parte das imagens referentes a este fenômeno físico é estática o que na maioria das vezes acaba dificultando ao aprendizado deste tema. Neste trabalho, o Campo Magnético poderá ser visualizado, pelo usuário, com uso de Realidade Virtual ou Realidade Aumentada. O elemento de estudo será o Campo Magnético que é gerado em um motor elétrico (de indução monofásico). Pretende-se, por meio desta abordagem, identificar as vantagens de se utilizar as técnicas de Realidade Virtual e Realidade Aumentada em relação à outras formas de visualização do campo magnético. / Mestre em Ciências