Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while using a minimal amount of material. Computer modeling and analysis of thin and slender structures has its own set of problems stemming from assumptions made when deriving the equations modeling their behavior from the theory of continuum mechanics. In this thesis we consider two kinds of thin elastic structures; threads and plates. Real-time simulation of threads are of interest in various types of virtual simulations such as surgery simulation for instance. In the first paper of this thesis we develop a thread model for use in interactive applications. By viewing the thread as a continuum rather than a truly one dimensional object existing in three dimensional space we derive a thread model that naturally handles both bending, torsion and inertial effects. We apply a corotational framework to simulate large deformation in real-time. On the fly adaptive resolution is used to minimize corotational artifacts. Plates are flat elastic structures only allowing deflection in the normal direction. In the second paper in this thesis we propose a family of finite elements for approximating solutions to the Kirchhoff-Love plate equation using a continuous piecewise linear deflection field. We reconstruct a discontinuous piecewise quadratic deflection field which is applied in a discontinuous Galerkin method. Given a criterion on the reconstruction operator we prove a priori estimates in energy and L2 norms. Numerical results for the method using three possible reconstructions are presented.

Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted meshes. The arbitrary Lagrangian- Eulerian (ALE) approach is a way to overcome this difficulty. Numerical simulations of convection-dominated problems have for long been the subject to many researchers. Galerkin formulations, which yield the best approximations for differential equations with high diffusivity, tend to induce spurious oscillations in the numerical solution of convection dominated equations. Though such spurious oscillations can be avoided by adaptive meshing, which is computationally very expensive on ne grids. Alternatively, stabilization methods can be used to suppress the spurious oscillations. In this work, the considered equation is designed within the framework of ALE formulation. In the first part, Streamline Upwind Petrov-Galerkin (SUPG) finite element method with conservative ALE formulation is proposed. Further, the first order backward Euler and the second order Crank-Nicolson methods are used for the temporal discretization. It is shown that the stability of the semi-discrete (continuous in time) ALE-SUPG equation is independent of the mesh velocity, whereas the stability of the fully discrete problem is unconditionally stable for implicit Euler method and is only conditionally stable for Crank-Nicolson time discretization. Numerical results are presented to support the stability estimates and to show the influence of the SUPG stabilization parameter in a time-dependent domain. In the second part of this work, SUPG stabilization method with non-conservative ALE formulation is proposed. The implicit Euler, Crank-Nicolson and backward difference methods are used for the temporal discretization. At the discrete level in time, the ALE map influences the stability of the corresponding discrete scheme with different time discretizations, and it leads to schemes where conservative and non-conservative formulations are no longer equivalent. The stability of the fully discrete scheme, irrespective of the temporal discretization, is only conditionally stable. It is observed from numerical results that the Crank-Nicolson scheme induces high oscillations in the numerical solution compare to the implicit Euler and the backward difference time discretiza-tions. Moreover, the backward difference scheme is more sensitive to the stabilization parameter k than the other time discretizations. Further, the difference between the solutions obtained with the conservative and non-conservative ALE forms is significant when the deformation of domain is large, whereas it is negligible in domains with small deformation. Finally, the local projection stabilization (LPS) and the higher order dG time stepping scheme are studied for convection dominated problems. The analysis is based on the quadrature formula for approximating the integrals in time. We considered the exact integration in time, which is impractical to implement and the Radau quadrature in time, which can be used in practice. The stability and error estimates are shown for the mathematical basis of considered numerical scheme with both time integration methods. The numerical analysis reveals that the proposed stabilized scheme with exact integration in time is unconditionally stable, whereas Radau quadrature in time is conditionally stable with time-step restriction depending on the ALE map. The theoretical estimates are illustrated with appropriate numerical examples with distinct features. The second order dG(1) time discretization is unconditionally stable while Crank-Nicolson gives the conditional stable estimates only. The convergence order for dG(1) is two which supports the error estimate.

This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.

We analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency. / text

Dans ce mémoire, nous étudions un système prédateur-proie de Gause généralisé avec une récolte de proie contrôlée et une fonction de réponse de Holling de type III généralisée. Nous introduisons une fonction de récolte contrôlée sur les proies tenant compte du nombre de proies et dépendant d'un seuil de récolte. Ceci permet de rendre le système réaliste, d'optimiser la récolte, et de prévenir la possibilité d'extinction des espèces que le système avec récolte constante pouvait avoir pour toutes valeurs de paramètres. Ce type de fonction de récolte implique a priori la manipulation d'un système discontinu: nous étudions donc des techniques de lissage de ces discontinuités par régularisation. Nous faisons d'abord un retour sur les systèmes sans et avec récolte de proie constante en traçant les diagrammes de bifurcations exacts et les portraits de phase de ces systèmes. Ensuite, nous étudions le système discontinu et les méthodes de régularisation afin de choisir la plus optimale. Finalement, nous assemblons le tout avec l'étude du système avec récolte de proie régularisé, en passant par l'étude complète du système avec approvisionnement de proie, et donnons les différents effets sur les portraits de phase selon les conditions initiales. / In this master thesis, we study a generalized Gause predator-prey system with controlled prey harvest and a generalized Holling response function of type III. We introduce a controlled prey harvesting function taking into account the number of preys with a harvesting threshold. This makes the system realistic, it optimizes the harvesting, and it prevents the possibility of species' extinction which exists in the system with constant harvest for all parameters. This type of harvesting function a priori implies handling a discontinuous system : therefore we study smoothing techniques of such discontinuities by regularization. We first return on systems without and with constant harvest by drawing the exact bifurcation diagrams and phase portraits of those systems. Then, we study the discontinuous system and the regularization methods in order to choose the optimal one. Finally, we put together everything by studying the regularized prey harvesting system through a complete study of the prey stocking system, and we highlight the different effects on the phase portraits under the initial conditions.

Le travail effectué au cours de cette thèse consiste à étudier et développer des techniques innovantes de modulation de largeurs d'impulsions (MLI) qui visent à optimiser les chaînes de traction électriques embarquées dans des véhicules hybrides ou électriques. La MLI joue un rôle stratégique au coeur des variateurs de vitesse, elle influe sur le comportement général de la chaîne de traction et sur sa performance. La MLI présente des degrés de liberté qui peuvent contribuer avantageusement à redimensionner les composants du variateur tels que le circuit de refroidissement, le filtre EMI et le condensateur du bus continu. Les véhicules hybrides constituent une étape naturelle dans la transition énergétique entre les véhicules thermiques et les véhicules électriques. Notre étude contribue à l'optimisation des variateurs de vitesse en général et ceux au coeur des véhicules hybrides ou électriques en particulier. Notre apport consiste à proposer une MLI performante afin de rendre le variateur plus léger et plus compacte tout en garantissant les fonctionnalités traditionnelles. La compétitivité de ces variateurs et par conséquent des véhicules hybrides ou électriques devient alors accessible. Les véhicules hybrides ou électriques utilisent généralement une machine de traction à courant alternatif en raison de nombreux avantages que celle ci présente par rapport à une machine à courant continu. La source d’alimentation au bord d'un véhicule est une batterie, il est donc nécessaire d'utiliser un onduleur pour transformer la tension continue en tension alternative à amplitude et fréquence variables. Le contrôle de cet onduleur est réalisé par des techniques de modulation de largeurs d'impulsions (MLI) ce qui permet ainsi de réguler le couple de la machine. Les techniques MLI produisent une composante basse fréquence, le fondamental qui est le signal désiré et des composantes hautes fréquences appelées harmoniques de commutation qui sont indésirables. Dans les véhicules modernes, il y a de plus en plus de charges mécaniques pilotées par des machines électriques et des systèmes électroniques. Il est impératif d'éliminer le risque d'interférences électromagnétiques entre ces différents systèmes pour éviter le dysfonctionnement ou la défaillance. Il faut donc filtrer ces harmoniques indésirables pour qu'elles ne perturbent pas les calculateurs et autres circuits électroniques de faibles niveaux de tensions. Il existe des techniques de modulation aléatoire (RPWM) qui permettent d'étaler les harmoniques à la fréquence de commutation et ses multiples. Dans cette étude, notre choix s’est porté sur la technique de modulation vectorielle aléatoire (RSVM) qui présente plusieurs avantages par rapport à la MLI intersective. Les machines pilotées par une MLI produisent des tensions de mode commun dites « shaft voltage », qui peuvent provoquer des courants à travers les roulements de la machine, ces derniers pouvant être destructifs. Nous avons pu développer une technique MLI vectorielle basée sur un choix judicieux des vecteurs nuls pour réduire cette tension de mode commun. La chaleur produite par les pertes dans les convertisseurs à commutation dure lors de l'ouverture et de la fermeture des interrupteurs doit être évacuée rapidement, ce qui réduit le stress thermique, évite la défaillance et augmente la durée de vie des interrupteurs. Une technique utilisée pour réduire ces pertes par commutation est la modulation discontinue (DPWM) ; une amélioration est apportée à cette technique dans ce travail. Cette amélioration est présentée sous forme d'une technique discontinue évolutive (EDSVM) qui s'adapte au régime du moteur pour minimiser les pertes. Grâce à cette technique une meilleure distribution du stress thermique sur les différents bras de l'onduleur est rendue possible et permet ainsi d'augmenter la durée de vie de l'onduleur. (...) / The dissertation documents research work carried out on Pulse Width Modulation (PWM) strategies for hard switched Voltage Source Inverters (VSI) for variable speed electric drives. This research is aimed at Hybrid Electric Vehicles (HEV). PWM is at the heart of all variable speed electric drives; they have a huge influence on the overall performance of the system and may also help eventually give us an extra degree of freedom in the possibility to rethink the inverter design including the re-dimensioning of the inverter components.HEVs tend to cost more than conventional internal combustion engine (ICE) vehicles as they have to incorporate two traction systems, which is the major discouraging factor for consumers and in turn for manufacturers. The two traction system increases the maintenance cost of the car as well. In addition the electric drives not only cost extra money but space too, which is already scarce with an ICE under the hood. An all-electric car is not yet a viable idea as the batteries have very low energy density compared with petrol or diesel and take considerable time to charge. One solution could be to use bigger battery packs but these add substantially to the price and weight of the vehicle and are not economically viable. To avoid raising the cost of such vehicles to unreasonably high amounts, autonomy has to be compromised. However hybrid vehicles are an important step forward in the transition toward all-electric cars while research on better batteries evolves. The objective of this research is to make electric drives suitable for HEVs i.e. lighter, more compact and more efficient -- requiring less maintenance and eventually at lower cost so that the advantages, such as low emissions and better fuel efficiency, would out-weigh a little extra cost for these cars. The electrical energy source in a vehicle is a battery, a DC Voltage source, and the traction motor is generally an AC motor owing to the various advantages it offers over a DC motor. Hence the need for a VSI, which is used to transform the DC voltage into AC voltage of desired amplitude and frequency. Pulse width modulation techniques are used to control VSI to ensure that the required/calculated voltage is fed to the machine, to produce the desired torque/speed. PWM techniques are essentially open loop systems where no feedback is used and the instantaneous values differ from the required voltage, however the same average values are obtained. Pulse width modulated techniques produce a low frequency signal (desired average value of the switched voltage) also called the fundamental component, along with unwanted high frequency harmonics linked to the carrier signal frequency or the PWM period. In modern cars we see more and more mechanical loads driven by electricity through digital processors. It is very important to eliminate the risk of electromagnetic interference between these systems to avoid failure or malfunction. Hence these unwanted harmonics have to be filtered so that they do not affect the electronic control unit or other susceptible components placed in the vicinity. Randomised modulation techniques (RPWM) are used to dither these harmonics at the switching frequency and its multiple. In this thesis a random modulator based on space vector modulation is presented which has additional advantages of SVM. Another EMI problem linked to PWM techniques is that they produce common mode voltages in the load. For electric machines, common mode voltage produces shaft voltage which in turn provokes dielectric stress on the motor bearings, its lubricant and hence the possibility of generating bearing currents in the machine that can be fatal for the machine. To reduce the common mode voltage a space vector modulation strategy is developed based on intelligent placement of zero vectors. (...)

Cette thèse porte sur l’étude d’une méthode de type Galerkin discontinu en domaine temporel (GDDT), afin de résoudre numériquement les équations de Maxwell instationnaires sur des maillages hybrides tétraédriques/hexaédriques en 3D (triangulaires/quadrangulaires en 2D) et non-conformes, que l’on note méthode GDDT-PpQk. Comme dans différents travaux déjà réalisés sur plusieurs méthodes hybrides (par exemple des combinaisons entre des méthodes Volumes Finis et Différences Finies, Éléments Finis et Différences Finies, etc.), notre objectif principal est de mailler des objets ayant une géométrie complexe à l’aide de tétraèdres, pour obtenir une précision optimale, et de mailler le reste du domaine (le vide environnant) à l’aide d’hexaèdres impliquant un gain en terme de mémoire et de temps de calcul. Dans la méthode GDDT considérée, nous utilisons des schémas de discrétisation spatiale basés sur une interpolation polynomiale nodale, d’ordre arbitraire, pour approximer le champ électromagnétique. Nous utilisons un flux centré pour approcher les intégrales de surface et un schéma d’intégration en temps de type saute-mouton d’ordre deux ou d’ordre quatre. Après avoir introduit le contexte historique et physique des équations de Maxwell, nous présentons les étapes détaillées de la méthode GDDT-PpQk. Nous réalisons ensuite une analyse de stabilité L2 théorique, en montrant que cette méthode conserve une énergie discrète et en exhibant une condition suffisante de stabilité de type CFL sur le pas de temps, ainsi que l’analyse de convergence en h (théorique également), conduisant à un estimateur d’erreur a-priori. Ensuite, nous menons une étude numérique complète en 2D (ondes TMz), pour différents cas tests, des maillages hybrides et non-conformes, et pour des milieux de propagation homogènes ou hétérogènes. Nous faisons enfin de même pour la mise en oeuvre en 3D, avec des simulations réalistes, comme par exemple la propagation d’une onde électromagnétique dans un modèle hétérogène de tête humaine. Nous montrons alors la cohérence entre les résultats mathématiques et numériques de cette méthode GDDT-PpQk, ainsi que ses apports en termes de précision et de temps de calcul. / This thesis is concerned with the study of a Discontinuous Galerkin Time-Domain method (DGTD), for the numerical resolution of the unsteady Maxwell equations on hybrid tetrahedral/hexahedral in 3D (triangular/quadrangular in 2D) and non-conforming meshes, denoted by DGTD-PpQk method. Like in several studies on various hybrid time domain methods (such as a combination of Finite Volume with Finite Difference methods, or Finite Element with Finite Difference, etc.), our general objective is to mesh objects with complex geometry by tetrahedra for high precision and mesh the surrounding space by square elements for simplicity and speed. In the discretization scheme of the DGTD method considered here, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered approximation for the surface integrals. Time integration of the associated semi-discrete equations is achieved by a second or fourth order Leap-Frog scheme. After introducing the historical and physical context of Maxwell equations, we present the details of the DGTD-PpQk method. We prove the L2 stability of this method by establishing the conservation of a discrete analog of the electromagnetic energy and a sufficient CFL-like stability condition is exhibited. The theoritical convergence of the scheme is also studied, this leads to a-priori error estimate that takes into account the hybrid nature of the mesh. Afterward, we perform a complete numerical study in 2D (TMz waves), for several test problems, on hybrid and non-conforming meshes, and for homogeneous or heterogeneous media. We do the same for the 3D implementation, with more realistic simulations, for example the propagation in a heterogeneous human head model. We show the consistency between the mathematical and numerical results of this DGTD-PpQk method, and its contribution in terms of accuracy and CPU time.

Aufgrund ihrer niedrigen Stoffwechselrate zeigen Puppen des Atlasspinners Attacus atlas diskontinuierlichen Gasaustausch (DGC) mit drei deutlich getrennten Phasen. Andererseits sind einzelne Stigmen entweder vollständig offen oder vollständig geschlossen. In dieser Arbeit wurden Attacus Puppen mit künstlichen Gasmischungen perfundiert, um das Steady-State Verhalten der Stigmen zu ermitteln. Es konnte gezeigt werden, daß die Flutterphase des DGC kein Gleichgewichtsverhalten darstellt. Weiterhin deuteten die Ergebnisse der Perfusion auf eine mögliche Interaktion zweier unabhängiger Regelkreise hin. Zwei mathematische Modelle untersuchten daraufhin mögliche theoretische Mechanismen, welche die beobachteten Muster erzeugen könnten. Die Modelle erlaubten die Erzeugung der Gasaustauschmuster ohne komplexe neurale Integration und deuten auf eine rein passive Erzeugung des DGC. Die Diskussion erläutert mögliche biologische Mechanismen, welchen den abstrakten Beschreibungen der Modelle zu Grunde liegen könnten. Sowohl die Perfusion als auch die Modelle sind dabei mit der ''Emergent Property Hypothesis'' der DGC Entstehung vereinbar. Zusätzlich wird dargelegt, wie alternative Hypothesen widerspruchslos in das sich abzeichnende Bild eingefügt werden können. / While having low metabolic activity, pupae of the giant silk moth Attacus atlas show triphasic discontinuous gas exchange cycles (DGC). However, a single spiracle is either fully open or fully closed. In this study moth pupae have been perfused to assess the steady state behavior of the spiracles in response to the endotracheal gas composition. It could be shown that the flutter phase of DGC is not a steady state behavior. Moreover, the results from the perfusion hint to a possible interaction between two independent spiracle control mechanisms. Two mathematical models then explore possible mechanisms of generating the observed respiratory patterns during DGC. The models indicate that DGC might be generated without complex neural integration and might thus be a purely ''passive'' pattern. The discussion focuses on biological processes and mechanisms that may back the abstract descriptions in the models. Both, the perfusion and the two mathematical models, are consistent with the emergent property hypothesis of DGC origin. However, it is discussed that other existing hypotheses are not mutually exclusive and that they can be subsumed using the non-adaptive emergent property hypothesis as a framework.

In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.

Made available in DSpace on 2016-04-04T18:21:59Z (GMT). No. of bitstreams: 1 Leticia Jorge Wassal.pdf: 22765531 bytes, checksum: 12a7548f718bdf6fb83860a224401a1a (MD5) Previous issue date: 2011-02-16 / The research sought to understand the emergence of the new central service center in Paul?nia and the changes in the urban fabric of the city, relating thecase to the phenomenon of urban sprawl, often seen in Brazilian metropolitan regions, including the Metropolitan Region of Campinas. Herefore, was studied aspects of urban, architectural, usage and ownership of this new central space. Based on historical surveys, census and management data, enabling reflection on the influence of this new center, split and discontinuous to the main center in the urban dynamic of the city and evaluate the effects resulting from this process. Supported by the previous case study on the Bar?o Geraldo district, carried out in scientific initiation research funded by FAPESP (Foundation for Research Support of S?o Paulo), we could to delineate the common factors in the genesis of these spaces, because they are inserted in the same socio-economic context, and at the same time, the generation of distinct conformations, because they evolved different factors present or previous vocations. As a result of the analysis of flows and demands between the municipality of Paulinia and the Bar?o Geraldo district and the specific political and administrative management of these adjoining areas, we intended to contribute to the understanding of the consequences of this process in the region, among other things, the formation and reproduction of a fragmented landscape with no identity. / A pesquisa buscou compreender o surgimento do novo p?lo centralizador de servi?os do munic?pio de Paul?nia e as mudan?as ocorridas no tecido urbano da cidade, relacionando o processo ao fen?meno da urbaniza??o dispersa, freq?entemente observado nas regi?es metropolitanas brasileiras, inclusive na Regi?o Metropolitana de Campinas. Para tal, foram realizados estudos dos aspectos urban?sticos, arquitet?nicos, de uso e apropria??o desta nova centralidade, a partir de levantamentos de dados hist?ricos, censit?rios e de gest?o, que possibilitaram refletir sobre a influ?ncia desta nova ?rea, desdobrada e descont?nua ao centro principal, na din?mica urbana do munic?pio, avaliando os efeitos advindos deste processo. Com o aux?lio de estudo de caso anterior sobre o distrito de Bar?o Geraldo, realizado em pesquisa de inicia??o cient?fica financiado pela FAPESP (Funda??o de Amparo ? Pesquisa do Estado de S?o Paulo), foi poss?vel delinear a presen?a de fatores comuns na g?nese destes espa?os, j? que inseridos no mesmo contexto s?cio-econ?mico, e, ao mesmo tempo, a gera??o de conforma??es distintas, dado que se desenvolveram a partir de diferentes fatores ou voca??es anteriores presentes. Como resultado da an?lise dos fluxos e demandas entre o munic?pio de Paul?nia e o distrito de Bar?o Geraldo e das especificidades de gest?o pol?tico-administrativas destas ?reas lim?trofes, pretendeu-se contribuir para a compreens?o das conseq??ncias deste processo na regi?o, entre outros aspectos, na forma??o e reprodu??o de uma paisagem fragmentada e sem identidade