Simulation of electromagnetic descriptor models using projectors

Electromagnetic descriptor models are models which lead to differential algebraic equations (DAEs). Some of these models mostly arise from electric circuit and power networks. The most frequently used modeling technique in the electric network design is the modified nodal analysis (MNA) which leads to differential algebraic equations in descriptor form. DAEs are known to be very difficult to solve numerically due to the sensitivity of their solutions to perturbations. We use the tractability index to measure this sensitivity since it can be computed numerically. Simulation of DAEs is a very difficult task especially for those with index greater than one. To solve higher-index DAEs, one needs to use multistep methods such as Backward difference formulas (BDFs). In this paper, we present an easier method of solving DAEs numerically using special projectors. This is done by first splitting the DAE system into differential and algebraic parts. We then use the existing numerical integration methods to approximate the solutions of the differential part and the solutions of the algebraic parts are computed explicitly. The desired solution of the DAE system is obtained by taking the linear combination of the solutions of the differential and algebraic parts. Our method is robust and efficient, and can be used on both small and very large systems

Index-aware model order reduction for differential-algebraic equations

We introduce a model order reduction procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. We implement numerically this procedure and show numerical evidence of its validity

Index-aware model order reduction for index-2 differential-algebraic equations

A model order reduction (MOR) method for index-2 differential-algebraic equations (DAEs) is introduced, which is based on the intrinsic differential equations contained in the starting system and on the remaining algebraic constraints. This extends the method introduced in a previous paper for index-1 DAEs. This procedure is implemented numerically and the results show numerical evidence of its robustness over the traditional methods

Index-aware model order reduction for index-2 differential-algebraic equations

A model order reduction (MOR) method for index-2 differential-algebraic equations (DAEs) is introduced, which is based on the intrinsic differential equations contained in the starting system and on the remaining algebraic constraints. This extends the method introduced in a previous paper for index-1 DAEs. This procedure is implemented numerically and the results show numerical evidence of its robustness over the traditional methods

Stress distribution during neck formation : an approximate theory

In this paper we investigate the effects of deformation of a metal specimen, which is either a plate or a cylindrical rod in our case. In particular we study neck formation in tensile loading of a plastic metal. We try to generalize the work of Bridgman, who considered a purely two-dimensional geometry, to an effective theory that takes into account some essential three dimensional characteristics. That extending the description of neck formation to three dimensions is necessary was illustrated by recent experimental findings of [1]. We have studied existing models from the literature that describe necking for plates and cylinders to identify the consequences of the crucial assumption of uniform in-plane stress. We also developed a new model that we have not yet been able to analyze. Finally, using work of [4] in which a power law relation between the von Mises stress and the effective strain is used, a perturbation analysis for a simple flat geometry was performed. The perturbation analysis offers a good starting point for generalizing the work of Bridgman to three dimensions. Keywords: Neck formation, von Mises stress, tensile pulling, plane stress assumptio

The mathematics of french fries

Although the act of cutting a single potato (Solanum tuberosum) into french fries may appear to be trivial, the questions concerning the efficiency of this process on an industrial scale are quite daunting. Therefore, many producers are looking for a rigorous method to evaluate the market potential of a given potato crop by predicting the number and parameters of the fries that can be cut from it. Applying the methods of geometry and numerical analysis our group was able to propose several algorithms that can be directly incorporated into the existing production process. Keywords: French fries, geometry, cutting, Finite Fry Method, simulations, histogram

O parlamento no ecrã: debate e conversação na televisão contemporânea

A televisão contemporânea caracteriza-se pelo grandíssimo destaque concedido às interacções discursivas. Com efeito, a saliência dos talk-shows e a programas de comentário, bem como rubricas de eminente partilha de opiniões em programas de outros géneros televisivos, confirmam esta incidência conversacional da televisão. Analisando o modo como uma discussão pública da experiência social ocorre, este artigo investiga o parlamento televisivo, isto é, essa tendência generalizada de discursivização ao mesmo tempo que sublinha as mutações positivas que ela impôs às audiências televisivas. Deste modo, e contrariamente à perspectiva convencional disfórica (audiências tendencialmente passivas, desinteressadas e apáticas), esboçar-se-á uma compreensão renovada das audiências televisivas que as coloca como participantes activas deste parlamento no ecrã. Com este objectivo, far-se-á uma breve caracterização do parlamento televisivo, descrever-se-á os seus fundamentos, e distinguir-se-ão os seus modos performativos.Parley on Screen – debate and conversation in contemporary television The contemporary television is characterized by the prominence accorded to discussion. Indeed, talk-shows and chatting programs successes, confirm this prevalence of a conversational dimension on television. Analyzing the way public discussion of social experience happens, this paper investigates the televised parley, i.e. this stress in conversation and dialogue, and, at the same time, underscores the positive change that it has imposed on television audiences. Thus, contrary to the conventional dysphoric perspective (audiences seen as passive, disinterested and apathetic), the paper sketches a renewed understanding of the television audience that put them as active participants on the parley television. With this objective, a brief characterization of the televised parley, its principles and performance modes, will be made.info:eu-repo/semantics/publishedVersio