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Transformation Matrix (transformation + matrix)
Selected AbstractsA systematic method for the development of a three-phase transformer non-linear modelINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 8 2010Andreas D. Theocharis Abstract In this work, a novel three-phase transformer non-linear model is developed. The proposed model takes into account the magnetic core topology and the windings connections. The non-linear characteristic curve of the core material is introduced by its magnetization curve or by its hysteresis loop using the mathematical hysteresis model proposed by Tellinen or the macroscopic hysteresis model proposed by Jiles,Atherton. The eddy currents effects are included through non-linear resistors using Bertotti's work. The proposed model presents several advantages. An incremental linear circuit, having the same topology with the magnetic circuit of the core, is used in order to directly write the differential equations of the magnetic part of the transformer. The matrix Ld that describes the coupling between the windings of the transformer is systematically derived. The electrical equations of the transformer can be easily written for any possible connection of the primary and secondary windings using the unconnected windings equations and transformation matrices. The proposed methods for the calculation of the coupling between the windings, the representation of the eddy currents and the inclusion of the core material characteristic curve can be used to develop a transformer model appropriate for the EMTP/ATP-type programs. Copyright © 2009 John Wiley & Sons, Ltd. [source] Four-node semi-EAS element in six-field nonlinear theory of shellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2006J. Chró, cielewski Abstract We propose a new four-node C0 finite element for shell structures undergoing unlimited translations and rotations. The considerations concern the general six-field theory of shells with asymmetric strain measures in geometrically nonlinear static problems. The shell kinematics is of the two-dimensional Cosserat continuum type and is described by two independent fields: the vector field for translations and the proper orthogonal tensor field for rotations. All three rotational parameters are treated here as independent. Hence, as a consequence of the shell theory, the proposed element has naturally six engineering degrees of freedom at each node, with the so-called drilling rotation. This property makes the element suitable for analysis of shell structures containing folds, branches or intersections. To avoid locking phenomena we use the enhanced assumed strain (EAS) concept. We derive and linearize the modified Hu,Washizu principle for six-field theory of shells. What makes the present approach original is the combination of EAS method with asymmetric membrane strain measures. Based on literature, we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry. To gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element, we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches. Copyright © 2006 John Wiley & Sons, Ltd. [source] An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifactsMAGNETIC RESONANCE IN MEDICINE, Issue 6 2010Yuguang Meng Abstract An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. Magn Reson Med, 2010. © 2010 Wiley-Liss, Inc. [source] Mapping low- and high-density clouds in astrophysical nebulae by imaging forbidden line emission,MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009J. E. Steiner ABSTRACT Emission line ratios have been essential for determining physical parameters such as gas temperature and density in astrophysical gaseous nebulae. With the advent of panoramic spectroscopic devices, images of regions with emission lines related to these physical parameters can, in principle, also be produced. We show that, with observations from modern instruments, it is possible to transform images taken from density-sensitive forbidden lines into images of emission from high- and low-density clouds by applying a transformation matrix. In order to achieve this, images of the pairs of density-sensitive lines as well as the adjacent continuum have to be observed and combined. We have computed the critical densities for a series of pairs of lines in the infrared, optical, ultraviolet and X-rays bands, and calculated the pair line intensity ratios in the high- and low-density limit using a four- and five-level atom approximation. In order to illustrate the method, we applied it to Gemini Multi-Object Spectrograph (GMOS) Integral Field Unit (GMOS-IFU) data of two galactic nuclei. We conclude that this method provides new information of astrophysical interest, especially for mapping low- and high-density clouds; for this reason, we call it ,the ld/hd imaging method'. [source] Groupoid of orientational variantsACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2006Cyril Cayron Daughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants to be determined. These are algebraically identified with left cosets and their number is given by the Lagrange formula. A simple equation links the numbers of variants of the direct and inverse transitions. The equivalence classes on the transformations between variants are isomorphic to the double cosets (operators) and their number is given by the Burnside formula. The orientational variants and the operators constitute a groupoid whose composition table acts as a crystallographic signature of the transition. A general method that determines if two daughter variants can be inherited from more than one parent crystal is also described. A computer program has been written to calculate all these properties for any structural transition; some results are given for Burgers transitions and for martensitic transitions in steels. The complexity, irreversibility and entropy of fractal systems constituted by orientational variants generated by thermal cycling are briefly discussed. [source] Further developments in the new approach to boundary condition iteration in optimal controlTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2001Rein LuusArticle first published online: 3 SEP 2010 Abstract In solving the boundary value problem resulting from the use of Pontryagin's maximum principle, a transformation matrix is used to relate the sensitivity of the final state to the initial state. This avoids the need to solve the (n × n) differential equation to give the transition matrix, and yields very rapid convergence to the optimum. To ensure convergence, iterative dynamic programming (IDP) is used for a number of passes to yield good starting conditions for this boundary condition iteration procedure. Clipping technique is used to handle constraints on control. Five optimal control problems are used to illustrate and to test the procedure. Dans la résolution du problème de valeur limlte résultant de l'utilisation du principe maximum de Pontryagin, on utilise une matrice de transformation afin de relier la sensibilité de l'état final à l'état initial. Cela évite d'avoir à résoudre l'équation différentielle (n × n) pour obtenir la matrice de transition et permet une convergence trés rapide vers l'optimum. Pour assurer la convergence, on a recours à la programmation dynamique itérative (IDP) pour plusieurs passages afin de créer de bonnes conditions de démarrage pour cette méthode d'itération sur les conditions limites. On utilise la technique de l'écêtage pour manier les contraintes sur le contrôle. Cinq problèmes de contrôle optimal permettent d'illustrer et de vérifier la méthode. [source] | |||||||||||||