A falta de um membro, devido a doenças, más-formações ou traumas, impacta enormemente na vida de um indivíduo. Para que o mesmo possa realizar Atividades de Vida Diária (AVD), sem drásticas limitações, faz-se necessário o desenvolvimento de próteses e cientes. Para auxiliar no projeto de tais produtos, este trabalho visa criar e solucionar um modelo de sistema dinâmico capaz de simular o comportamento de joelhos prostéticos. A m de alcançar tal objetivo, foi estudada a biomecânica da marcha humana, além dos tipos de amputações existentes e seus impactos na mesma. Buscou-se também estudar os principais componentes de próteses existentes atualmente no mercado, além de suas geometrias básicas. Após de nir-se um modelo simpli cado que representasse os componentes protéticos e as partes remanescentes do corpo, foram buscadas métodos de solução disponíveis para tal sistema. Baseado nos estudos encontrados em uma revisão bibliográ ca, foi de nida uma metodologia de solução numérica de sistemas multi-corpos. Durante o trabalho, surgiu a necessidade de representar forças de contato entre corpos rígidos, e foram incluídas soluções de atuais teorias do assunto. Essas metodologias foram então empregadas para a construção de um algoritmo capaz de solucionar o sistema proposto. Depois de resolvido o sistema, os valores encontrados para as variáveis cinéticas foram comparados com valores obtidos por uma simulação numérica utilizando dois programas computacionais comercias, cujas fundamentações teóricas utilizam diferentes métodos de solução. A comparação das diferenças entre os resultados apontou similaridade entre o algoritmo e os programas utilizados, mas com a necessidade de validação do método através de ensaio mecânico. Ao nal foram sugeridas ideias para trabalhos futuros. / The lack of a member due to diseases, malformations or trauma, greatly impacts the life of an individual. In order to perform Activities of Daily Living (ADL) without drastic limitations, it is necessary to develop e cient prosthetic devices. To assist the design of such products, this work aims to create and solve a dynamic system model to simulate the behavior of prosthetic knees. In order to achieve this goal, the biomechanics of human gait was studied, as well as the existing types of amputation and their impact on human gait. The main components of existing prosthetic devices, currently on the market, were identi ed, as well as its basic geometries. After de ning a simpli ed model able to incorporate the prosthetic components and the individual remaining body parts, an available methodology for the solution of such a system was prospected. Based on the studies found in the currently literature of multibodysystems, a numerical solution methodology for has been set. During the work, the need to represent contact between parts occurred, leading to the implementation of currently theories of contact forces for rigid bodies. These methodologies were then used to construct an algorithm for solving the proposed system. After the system has been solve, the values found for the kinetic variables were compared with those obtained by numerical simulations using two commercial softwares, whose theoretical foundation used di erent solution methodology. Comparing the di erences in results of these simulations, it was revealed a similar behavior between the algorithm and the commercial programs, but with the need of an experimental test, for truly validation of the method. At the end of this work, ideas for future improvement were suggested.

A falta de um membro, devido a doenças, más-formações ou traumas, impacta enormemente na vida de um indivíduo. Para que o mesmo possa realizar Atividades de Vida Diária (AVD), sem drásticas limitações, faz-se necessário o desenvolvimento de próteses e cientes. Para auxiliar no projeto de tais produtos, este trabalho visa criar e solucionar um modelo de sistema dinâmico capaz de simular o comportamento de joelhos prostéticos. A m de alcançar tal objetivo, foi estudada a biomecânica da marcha humana, além dos tipos de amputações existentes e seus impactos na mesma. Buscou-se também estudar os principais componentes de próteses existentes atualmente no mercado, além de suas geometrias básicas. Após de nir-se um modelo simpli cado que representasse os componentes protéticos e as partes remanescentes do corpo, foram buscadas métodos de solução disponíveis para tal sistema. Baseado nos estudos encontrados em uma revisão bibliográ ca, foi de nida uma metodologia de solução numérica de sistemas multi-corpos. Durante o trabalho, surgiu a necessidade de representar forças de contato entre corpos rígidos, e foram incluídas soluções de atuais teorias do assunto. Essas metodologias foram então empregadas para a construção de um algoritmo capaz de solucionar o sistema proposto. Depois de resolvido o sistema, os valores encontrados para as variáveis cinéticas foram comparados com valores obtidos por uma simulação numérica utilizando dois programas computacionais comercias, cujas fundamentações teóricas utilizam diferentes métodos de solução. A comparação das diferenças entre os resultados apontou similaridade entre o algoritmo e os programas utilizados, mas com a necessidade de validação do método através de ensaio mecânico. Ao nal foram sugeridas ideias para trabalhos futuros. / The lack of a member due to diseases, malformations or trauma, greatly impacts the life of an individual. In order to perform Activities of Daily Living (ADL) without drastic limitations, it is necessary to develop e cient prosthetic devices. To assist the design of such products, this work aims to create and solve a dynamic system model to simulate the behavior of prosthetic knees. In order to achieve this goal, the biomechanics of human gait was studied, as well as the existing types of amputation and their impact on human gait. The main components of existing prosthetic devices, currently on the market, were identi ed, as well as its basic geometries. After de ning a simpli ed model able to incorporate the prosthetic components and the individual remaining body parts, an available methodology for the solution of such a system was prospected. Based on the studies found in the currently literature of multibodysystems, a numerical solution methodology for has been set. During the work, the need to represent contact between parts occurred, leading to the implementation of currently theories of contact forces for rigid bodies. These methodologies were then used to construct an algorithm for solving the proposed system. After the system has been solve, the values found for the kinetic variables were compared with those obtained by numerical simulations using two commercial softwares, whose theoretical foundation used di erent solution methodology. Comparing the di erences in results of these simulations, it was revealed a similar behavior between the algorithm and the commercial programs, but with the need of an experimental test, for truly validation of the method. At the end of this work, ideas for future improvement were suggested.

Proteins are involved in numerous functions in the human body, including chemical transport, molecular recognition, and catalysis. To perform their function most proteins must adopt a specific structure (often referred to as the folded structure). A microscopic description of folding is an important prerequisite for elucidating the underlying basis of protein misfolding and rational drug design. However, protein folding occurs on heterogeneous length and time scales, presenting a grand challenge to both experiments and simulations. In computer simulations, challenges are generally mitigated by adopting coarse-grained descriptions of the physical environment, employing enhanced sampling strategies, and improving computing code and hardware. While significant advances have been made in these areas, for numerous systems a large spatiotemporal gap between experiment and simulations still exists, due to the limited time and length scales achieved by simulation, and the inability of many experimental techniques to probe fast motions and short distances. In this thesis, kinetic transition networks (KTNs) are constructed for various protein folding systems, via approaches based on the potential energy landscape (PEL) framework. By applying geometry optimisation techniques, the PEL is discretised into stationary points (i.e.~low-energy minima and the transition states that connect them). Essentially, minima characterise the low-lying regions of the PEL (thermodynamics) and transition states encode the motion between these regions (dynamics). Principles from statistical mechanics and unimolecular rate theory may then be employed to derive free energy surfaces and folding rates, respectively, from the KTN. Furthermore, the PEL framework can take advantage of parallel and distributed computing, since stationary points from separate simulations can be easily integrated into one KTN. Moreover, the use of geometry optimisation facilitates greater conformational sampling than conventional techniques based on molecular dynamics. Accordingly, this framework presents an appealing means of probing complex processes, such as protein folding. In this dissertation, we demonstrate the application of state-of-the-art theory, combining PEL analysis and KTNs to three diverse protein systems. First, to improve the efficiency of protein folding simulations, the intrinsic rigidity of proteins is exploited by implementing a local rigid body (LRB) approach. The LRB approach effectively integrates out irrelevant degrees of freedom from the geometry optimisation procedure and further accelerates conformational sampling. The effects of this approach on the underlying PEL are analysed in a systematic fashion for a model protein (tryptophan zipper\,1). We demonstrate that conservative local rigidification can reproduce the thermodynamic and dynamic properties for the model protein. Next, the PEL framework is employed to model large-scale conformational changes in proteins, which have conventionally been difficult to probe in silico. Methods based on geometry optimisation have proved useful in overcoming the broken ergodicity issue, which is associated with proteins that switch morphology. The latest PEL-based approaches are utilised to investigate the most extreme case of fold-switching found in the literature:~the α-helical hairpin to β-barrel transition of the C-terminal domain of RfaH, a bacterial transcription factor. PEL techniques are employed to construct the free energy landscape (FEL) for the refolding process and to discover mechanistic details of the transition at an atomistic level. The final part of the thesis focuses on modelling intrinsically disordered proteins (IDPs). Due to their inherent structural plasticity, IDPs are generally difficult to characterise, both experimentally and via simulations. An approach for studying IDPs within the PEL framework is implemented and tested with various contemporary potential energy functions. The cytoplasmic tail of the human cluster of differentiation 4 (CD4), implicated in HIV-1 infection, is characterised. Metastable states identified on the FEL help to unify, and are consistent with, several earlier predictions.

No description available.

Nous présentons une théorie d'existence complète pour le système physique composé de fluides visqueux et des corps rigides plongés dedans. Nous considérons un domaine borné et les conditions aux limites de Dirichlet homogènes pour la vélocité. Le fluide et les corps sont conducteurs thermiques et ils échangent la chaleur. L'existence de la solution variationnelle globale dans le temps est démontrée par la méthode de pénalisation par la viscosité due à Conca, San Martin et Tucsnak. Dans les approximations ainsi que dans la dernière limite nous employons la théorie d'existence pour un fluide visqueux compressible développé par Feireisl. Le deuxième sujet est une amélioration dans la théorie d'existence pour un écoulement barotropique stationnaire. Nous utilisons les estimations potentielles pour la pression proposées par Plotnikov, Sokolowski, Frehse, Goj et Steinhauer. En utilisant ces estimations avec la théorie potentielle non-linéaire nous en concluons les estimations à priori et nous prouvons l'existence des solutions faibles

Dans cette thèse, nous présentons un modèle granulaire décrivant la dynamique d'un assemblage de floes rigides de tailles et de formes diverses, soumis aux forces de traînée dues aux courants atmosphérique et océanique. Ce modèle est basé sur les équations des moments linéaire et angulaire pour décrire la dynamique régulière des floes et sur la résolution de problèmes linéaires de complémentarité pour traiter les collisions entre les floes. Entre les collisions, le mouvement d'un floe isolé satisfait la conservation des équations des moments linéaire et angulaire écrites à partir des formulations classiques des traînées dues au vent et à l'océan. Nous décrivons les collisions entre les floes comme des événements instantanés et les traitons avant qu'elles n'entraînent une interpénétration. Cela implique la notion d'impulsion de contact et la mise sous la forme de problèmes linéaires de complémentarité basés sur la condition de Signorini pour la non interpénétration et la loi de Coulomb. La nature du contact est représentée à travers un coefficient de friction et un coefficient de restitution décrivant la perte d'énergie cinétique durant la collision. Dans cette présente version du modèle, le coefficient de restitution est fixé. Le modèle a été validé en utilisant des données obtenues du mouvement de disques de bois évoluant en bassin de test aussi bien qu'en comparant le comportement des floes simulés avec un comportement attendu dans des scénarios classiques de dérive de glace et de collisions entre des solides rigides. Les résultats de simulations comprenant différents assemblages contenant des floes de tailles et de formes variées, soumis à différents scénarios de forçage, sont aussi discutés. Ils montrent tout le potentiel de notre approche sans qu'une analyse détaillée et complète n'ait encore été proposée. / In this thesis, we present a model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag. The granular model presented is based on simplified momentum equations for ice floe motion between collisions and on the resolution of linear complementarity problems to deal with ice floe collisions. Between collisions, the motion of an individual ice floe satisfies the linear and angular momentum conservation equations, with classical formula applied to account for atmospheric and oceanic skin drag. To deal with collisions, before they lead to interpenetration, we included a linear complementarity problem based on the Signorini condition and Coulombs law. The nature of the contact is described through a constant coefficient of friction, as well as a coefficient of restitution describing the loss of kinetic energy during the collision. In the present version of our model, this coefficient is fixed. The model was validated using data obtained from the motion of interacting artificial wood floes in a test basin. The results of simulations comprising few hundreds of ice floes of various shapes and sizes, exposed to different forcing scenarios, and under different configurations, are also discussed. They show that the progressive clustering of ice floes as the result of kinetic energy dissipation during collisions is well captured, and suggest a collisional regimes of floe dispersion at small scales, different from a large-scale regime essentially driven by wind forcing.

Le sujet de cette thèse est l'étude de la rotation à long terme des corps célestes.La première partie est consacrée à l’étude de la rotation à long terme de Cérès et Vesta, les deux corps les plus massifs de la ceinture principale d’astéroïdes. Ils sont l’objet d’étude de la sonde spatiale Dawn, qui a permis de déterminer précisément les caractéristiques physiques et de rotation nécessaires au calcul de leurs rotations. La distribution de glace sous et à la surface de Cérès dépend du mouvement de son axe de rotation par le biais de l’obliquité, inclinaison de l’équateur sur l’orbite. Les rotations de Cérès et Vesta étant rapides, l’évolution à long terme des axes de rotation de Cérès et Vesta a été obtenue à l'aide d'une intégration symplectique des équations de la rotation, où une moyenne a été réalisée sur la rotation propre rapide. La stabilité des axes de rotation de Cérès et Vesta a été étudiée en fonction des paramètres de la rotation avec un modèle séculaire semi-analytique, qui a permis de montrer que les axes de rotation ne présentaient pas de caractère chaotique.La seconde partie concerne le développement d'intégrateurs symplectiques dédiés au corps solide. L'intégration de la rotation propre d'un corps solide nécessite d’intégrer les équations issues du hamiltonien du corps solide libre. Ce hamiltonien est certes intégrable et présente une solution explicite nécessitant l’usage des fonctions elliptiques de Jacobi, cependant le coût numérique de ces fonctions est élevé. Lorsque le hamiltonien du corps solide libre est couplé avec une énergie potentielle, l’orientation du corps doit être calculée à chaque pas d’intégration, ce qui augmente le temps de calcul. Des intégrateurs symplectiques ont ainsi été précédemment proposés pour le corps solide libre. Dans ce travail, des intégrateurs spécifiques au corps solide ont été développés en utilisant les propriétés de l’algèbre de Lie du moment cinétique. / This thesis concerns the long-term rotation of celestial bodies.The first part is a study of the long-term rotation of Ceres and Vesta, the two heaviest bodies of the main asteroid belt. The spacescraft Dawn studied these two objects and determined the physical and rotational characteristics, which are necessary for the computation of their rotations. The ice distribution under and on the surface of Ceres depends on the evolution of the obliquity, which is the inclination of the equatorial plane on the orbital plane. As the rotations of Ceres and Vesta are fast, the long-term evolution of the spin axes of Ceres and Vesta was obtained by realizing a symplectic integration of the equations of the rotation averaged on the fast proper rotation. The stability of the spin axes of Ceres and Vesta was studied with respect to the parameters of the rotation with a secular and semi-analytical model, which allowed to show that the spin axes are not chaotic.The second part concerns the development of symplectic integrators dedicated to the rigid body. The integration of the proper rotation of a rigid body needs to integrate the equations given by the Hamiltonian of the free rigid body. This Hamiltonian is integrable and presents an explicit solution using the Jacobi elliptic functions. However, the numerical cost of these functions is high. When the Hamiltonian of the free rigid body is coupled to a potential energy, the orientation of the body is needed at each step, which increases the computation time. Symplectic integrators were then previously proposed for the free rigid body. In this work, symplectic integrators dedicated to the rigid body were developed using the properties of the Lie algebra of the angular momentum.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-06-21T21:21:46Z No. of bitstreams: 2 Dissertação - Liliane de Azevedo Oliveira - 2017.pdf: 1274368 bytes, checksum: 9b7a4aa781e0951c3f12045277a55582 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2017-06-29T18:27:23Z (GMT) No. of bitstreams: 2 Dissertação - Liliane de Azevedo Oliveira - 2017.pdf: 1274368 bytes, checksum: 9b7a4aa781e0951c3f12045277a55582 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-06-29T18:27:23Z (GMT). No. of bitstreams: 2 Dissertação - Liliane de Azevedo Oliveira - 2017.pdf: 1274368 bytes, checksum: 9b7a4aa781e0951c3f12045277a55582 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-02-22 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In this work we applied an algorithm based on the resolution of integer linear models for the problem of packing boxes into a single container considering the cargo stability constraint. The problem consists of arranging items (boxes) of different sizes inside a large object (container) to maximize the occupied container volume while respecting the imposed constraints. Four methods are investigated and compared due to vertical cargo stability, in which three of these methods are proposed in this work and based on the equilibrium of rigid bodies, and the other one is based on the factor of support of boxes bottom faces. In the case of the factor of support, a set of constraints can be inserted totally in the integer formulation, while in the other methods cutting planes are inserted during optimization of the formulation by a branch-and-cut algorithm. Computational tests on instances from the literature show that the usage of a factor of support underestimates the value of the optimal solution. The computational tests showed that the use of the factor of support may underestimate the solution, but its use with integer linear programming models has the advantage that feasible solutions are stable, while the other developed methods only verify stability and thus they depend of the integer linear program to return feasible solutions more quickly. By the way, the methods for the cargo stability developed here also overcame the factor of support for tests involving different types of mesh to pack into the container. / Aplica-se um algoritmo baseado na resolução de modelos de programação linear inteira para o problema de carregamento de caixas dentro de um único contêiner considerando a restrição de estabilidade de carga. O problema em estudo consiste em arranjar itens (caixas) de diferentes tamanhos dentro de um objeto maior (contêiner), de maneira maximizar a ocupação do volume do contêiner enquanto respeita as restrições dadas. Quatro métodos são investigados e comparados quanto a estabilidade vertical do empacotamento, sendo que três deles são desenvolvidos neste trabalho e baseados em conceitos do equilíbrio de corpos rígidos, enquanto um deles é baseado no fator de suporte da base das caixas. No caso do fator de suporte, um conjunto de restrições pode ser inserido totalmente dentro da formulação inteira, enquanto nos demais métodos planos de corte são inseridos durante a resolução da formulação por um algoritmo branch-and-cut. Os testes computacionais mostraram que o uso do fator de suporte pode subestimar a solução, porém seu uso com modelos de programação linear inteira tem a vantagem das soluções viáveis poderem ser estáveis, enquanto os demais métodos desenvolvidos apenas verificam a estabilidade e, assim, dependem do programa linear inteiro retornar soluções viáveis mais rapidamente. Os métodos para a estabilidade de carga desenvolvidos neste trabalho mostraram-se superiores ao fator de suporte para testes envolvendo diferentes tipos de malhas para o empacotamento no contêiner.

Cette thèse aborde une étude biomécanique de l’Articulation Temporo Mandibulaire (ATM), dont l’un des objectifs est la définition d’une approche complète, faisant appel à des outils modernes, permettant la conception d’une prothèse d’ATM personnalisée. Tout d’abord, nous avons conçu et réalisé un tribomètre reproduisant les conditions physiologiques de fonctionnement de l’ATM, afin d’étudier les interactions entre un matériau prothétique et de l’os porcin et de quantifier leurs usures respectives. La conception prothétique personnalisée passe par la réalisation d’un « état des lieux ». Nous avons donc défini un protocole de caractérisation non invasif de l’ATM. Il correspond à l’acquisition de sa géométrie actuelle et des mouvements élémentaires de la mandibule. Dans un deuxième temps, des simulations numériques en dynamique des corps rigides et/ou en éléments finis ont été réalisées pour accéder à des grandeurs mécaniques, telles que contraintes et déformations, nécessaires à la conception d’une prothèse. La totalité du protocole a été menée sur deux sujets d’étude : un sujet présentant une résorption condylienne et un sujet asymptomatique. Des modèles numériques personnalisés ont été construits pour chaque cas. Ces modèles nous ont permis d’étudier le fonctionnement articulaire de chaque individu. Nous avons effectué des comparaisons entre ces deux sujets et nous avons pu constater des différences notables concernant le fonctionnement articulaire. Il s’est avéré que les changements morphologiques occasionnés par la résorption osseuse ont des conséquences sur l’activité musculaire, ainsi que sur les efforts articulaires. Ce travail a permis d’enrichir les connaissances fondamentales par rapport au fonctionnement de l’ATM. Il a également permis de valider des outils d’évaluation de l’état fonctionnel de l’articulation. L’approche développée durant cette thèse est mise en pratique au sein de la société OBL, spécialisée dans la conception et la réalisation de prothèses maxillo-faciales sur mesure. Elle peut également être utilisée comme outil d’évaluation de solutions prothétiques existantes et à venir / This thesis deals with a biomechanical study of the Temporo-Mandibular Joint (TMJ); one of the objectives of this work is the definition of a complete approach, using modern tools, allowing the design of a personalized TMJ prosthesis. First of all, a tribometer reproducing the TMJ physiological conditions was designed and built, in order to study the interactions between porcine bone and a prosthetic material and to quantify their respective wears. Through this device, the relationships between the contact parameters and bone wear were determined. Personalized prosthetic design needs first to carry out “a state-of-the-art”. We defined a non invasive protocol for TMJ characterization. It corresponds to the acquisition of its current geometry and of the mandible elementary motions. In a second step, numerical simulations of rigid bodies and/or finite elements were achieved to obtain the mechanical quantities, such as stresses and strains, necessary for the prosthesis design. The entire protocol was conducted on two subjects: an asymptomatic one and a second one with condylar resorption. Personalized numerical models were built for each case. These models allowed us study the joint functioning of each subject. We made comparisons between these subjects and significant differences were found. It was proved that the changes produced by bone resorption have an impact on muscle activity, as well as contact forces in joints. This work allowed enhancing the fundamental knowledge regarding TMJ operating conditions. It also enabled to validate evaluation tools of the functional state of the joint. The approach developed during this thesis is applied by OBL society, specialized in the design of customed maxillofacial prostheses. The approach proposed in this work can also be used as an evaluation tool of existing prosthetic solutions, as well as future solutions

This MSc Thesis focuses on the collision detection between scene objects and consequent resolution of such collisions on the basis of physical model. The implementation of all the applications and algorithms is achieved in Win32 environment in Visual Studio using the programming language C++; it also employs the graphical library Open Inventor based on OpenGL. The work also includes additional application for the calculation of physical values. The demo applications involve algorithms for detection and resolution of explosive collision by the use of a simple and physical reflection on the basis of physical formulas and relationships. The main demo application called "tunnel transit" incorporates a simple game engine. The thesis also includes a discussion over the aroused problems with collision solving and some suggestions how to overcome them.