Дисертації з теми "Principe de Hamilton"
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1
Marone-Hitz, Pernelle. "Modélisation de structures spatiales déployées par des mètres ruban : vers un outil métier basé sur des modèles de poutre à section flexible et la méthode asymptotique numérique." Thesis, Ecole centrale de Marseille, 2014. http://www.theses.fr/2014ECDM0011/document.
Анотація:
Les dimensions des satellites spatiaux tendent à croître fortement alors que le volume disponible dans la coiffe des lanceurs est limité. L'utilisation de structures déployables permet de résoudre cette contradiction. Afin de développer l'offre disponible, le département Recherche de Thales Alenia Space étudie les mètres rubans comme solution innovante de déploiement. La première structure envisagée est un télescope déployé par le déroulement de six mètres rubans assurant également le positionnement du miroir secondaire. D'autres structures déployables utilisant les propriétés des mètres rubans sont également en cours d'étude : mât, panneaux solaires, etc.Il convient alors de se doter d'outils de modélisation spécifiques pour modéliser les scénarios de déploiement et multiplier les configurations envisagées. Deux précédentes thèses ont conduit à l'élaboration de modèles énergétiques de poutre à section flexible, rendant compte du comportement plan des rubans ([Guinot2011]) puis de leur comportement tridimensionnel ([Picault2014]). Cette thèse présente différentes contributions autour de ces modèles de poutre à section flexible. Les hypothèses du modèle ont été améliorées. Le re-positionnement de la ligne de référence sur le barycentre des sections conduit à des résultats plus proches des scénarios physiques (apparition et disparition des plis sur le ruban). A ce jour, les hypothèses et les équations du modèle sont définitivement formalisées. Nous avons établi les équations locales 1D (équilibre, comportement) dans le cas des comportements tridimensionnels avec le souci de la plus grande généralité. Établir ensuite les équations dans des cas dérivés simplifiés (restriction aux comportements 2D, section faiblement courbée) nous a permis d'obtenir un certain nombre de solutions analytiques et les équations à implémenter dans l'outil métier.Nous avons développé sur le logiciel de continuation ManLab les premiers éléments d'un outil métier performant dédié à la modélisation des mètres rubans. Nous avons ainsi pu réaliser deux contributions principales :- Un outil généraliste, performant en temps de calcul, permettant d'étudier les systèmes différentiels 1D (BVP, Boundary Value Problems). Les équations locales des modèles de poutre à section flexible ont été implémentées dans cet outil, avec une discrétisation par interpolation polynomiale et collocation orthogonale.- Un élément fini spécifique pour les poutres à section flexible et son implémentation dans ManLab.Ces éléments ont permis de réaliser différentes simulations numériques conduisant à une meilleure compréhension du comportement des mètres rubans grâce aux diagrammes de bifurcation associés à plusieurs essais significatifsDimensions of spatial satellites tend to grow bigger and bigger, whereas the volume in launchers remains very limited. Deployable structures must be used to meet this contradiction. To expand the offer of possible solutions, the Research Department of Thales Alenia Space is currently studying tape springs as an innovative deployment solution. The first structure to be considered is a telescope that is deployed by the uncoiling of six tape springs that also ensure the positioning of the secondary mirror. Other deployable structures that use the properties of tape springs are under investigation : mast, solar panels,...Specific modeling tools then appear compulsory to model deployment scenarios and multiply the tested configurations. Two previous PhD thesis lead to the development of energetic rod models with flexible cross-sections that account for planar ([Guinot2011])and three dimensional behavior of tape springs ([Picault2014]). This PhD thesis presents several contributions on these rod models with flexible cross-sections. The hypotheses of the model were improved. Re-positioning the reference rod line so that it passes through the sections' centroids leads to results that are closer to experimental scenarios (creation and disappearance of folds in the spring). The hypotheses and equations of the model are now definitively formalized.We have derived the 1D local equations in the three-dimensional behavior case in the most generalist way. Then, the derivation of the equations in simplified cases (restriction to 2D behavior, shallow cross-section) enabled us to obtain several analytic solutions and the equations to implement in the specific modeling tool.We have developed on the continuation software ManLab the first elements towards a home made, efficient modeling tool dedicated to the modeling of tape springs. Two main contributions can be listed :- A generalist tool, efficient in calculus times, to study 1D differential problems (BVP, Boundary Value Problems). The local equations of the rod models with flexible cross sections were implemented in this tool, with a discretization based on polynomial interpolation and orthogonal collocation.- A specific finite element for rods with flexible cross sections and its implementation in ManLab.These elements enabled us to perform several numerical simulations and have a better understanding of the behavior of tape springs thanks to full bifurcation diagrams obtained for significant tests
2
Nguyen, Thi Tuyen. "Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S089/document.
Анотація:
La motivation principale de cette thèse est l'étude du comportement en temps grand des solutions non-bornées d'équations de Hamilton-Jacobi visqueuses dans RN en présence d'un terme d'Ornstein-Uhlenbeck. Nous considérons la même question dans le cas d'une équation de Hamilton-Jacobi du premier ordre. Dans le premier cas, qui constitue le cœur de la thèse, nous généralisons les résultats de Fujita, Ishii et Loreti (2006) dans plusieurs directions. La première est de considérer des opérateurs de diffusion plus généraux en remplaçant le Laplacien par une matrice de diffusion quelconque. Nous considérons ensuite des opérateurs non-locaux intégro-différentiels de type Laplacien fractionnaire. Le second type d'extension concerne le Hamiltonien qui peut dépendre de x et est seulement supposé sous-linéaire par rapport au gradientThe main aim of this thesis is to study large time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN in presence of an Ornstein-Uhlenbeck drift. We also consider the same issue for a first order Hamilton-Jacobi equation. In the first case, which is the core of the thesis, we generalize the results obtained by Fujita, Ishii and Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a non-local integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear
3
Claisse, Julien. "Dynamique des populations : contrôle stochastique et modélisation hybride du cancer." Phd thesis, Université Nice Sophia Antipolis, 2014. http://tel.archives-ouvertes.fr/tel-01066020.
Анотація:
L'objectif de cette thèse est de développer la théorie du contrôle stochastique et ses applications en dynamique des populations. D'un point de vue théorique, nous présentons l'étude de problèmes de contrôle stochastique à horizon fini sur des processus de diffusion, de branchement non linéaire et de branchement-diffusion. Dans chacun des cas, nous raisonnons par la méthode de la programmation dynamique en veillant à démontrer soigneusement un argument de conditionnement analogue à la propriété de Markov forte pour les processus contrôlés. Le principe de la programmation dynamique nous permet alors de prouver que la fonction valeur est solution (régulière ou de viscosité) de l'équation de Hamilton-Jacobi-Bellman correspondante. Dans le cas régulier, nous identifions également un contrôle optimal markovien par un théorème de vérification. Du point de vue des applications, nous nous intéressons à la modélisation mathématique du cancer et de ses stratégies thérapeutiques. Plus précisément, nous construisons un modèle hybride de croissance de tumeur qui rend compte du rôle fondamental de l'acidité dans l'évolution de la maladie. Les cibles de la thérapie apparaissent explicitement comme paramètres du modèle afin de pouvoir l'utiliser comme support d'évaluation de stratégies thérapeutiques.
4
Delacroix, Bastien. "Développement d'un modèle intégral avec transport d'une fonction couleur pour la simulation d'écoulements de films minces partiellement mouillants." Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0005.
Анотація:
Pourquoi une goutte d’eau a tendance à prendre la forme d’une sphère ? Pourquoi reste-t-elle accrochée sur sa feuille lors de la rosée du matin ? Pourquoi, au contraire, ruisselle-t-elle jusque sur le sol ? Toutes ces questions en apparence simplistes font appel à des phénomènes microscopiques très complexes dont la nature physique est encore aujourd’hui sujet à débat. Leur compréhension est cependant un enjeu majeur dans de nombreux cas d'application industrielle. C’est notamment le cas en aéronautique où après le passage d’un aéronef au travers d’un nuage ou après une opération de dégivrage, un film mince se forme sur l’aile. L’évolution de la surface mouillée par ce film, comme lors de sa transition en ruisselets sous l’effet du cisaillement de l’air, ainsi que son éventuel regel un peu plus loin en dehors des zones de protection, n’est pas prise en compte dans les outils de simulations des dégivreurs thermiques ; ou alors de manière rudimentaire via des corrélations empiriques. Cependant, cette accrétion de givre se doit d’être contrôlée pour des raisons de sécurité et de performances aérodynamiques. C’est pourquoi, il est nécessaire d’améliorer les outils existant en développant de nouveaux modèles capables de prendre en compte l'influence des forces capillaires à l’échelle macroscopique, notamment au niveau de la ligne triple, pour pouvoir prédire la dynamique d’un film cisaillé.L’objectif général de cette étude est donc le développement d’un modèle adapté à la simulation à grande échelle d’écoulement de film mince partiellement mouillant.Dans cette optique, une approche basée sur un système d'équations de type Saint-Venant a été adoptée. Cependant, ce système sous sa forme classique ne permet pas la simulation de films minces avec effet de mouillage partiel. Une solution pour prendre en compte ces effets est d'ajouter une force macroscopique concentrée à la ligne de contact. Cette force singulière permet ainsi de vérifier localement la loi macroscopique de Young-Dupré. La difficulté de cette approche est alors de localiser la force uniquement à la ligne triple. Contrairement aux modèles rencontrés dans la littérature qui se basent tous sur l’utilisation d’un paramètre ajustable, permettant de faire la distinction entre zone sèche et zone mouillée, nous proposons ici une approche avec transport d’une fonction couleur. Cette fonction, définie comme égale à un dans les zones mouillées et nulle dans les zones sèches, présente l'intérêt d'avoir un gradient identiquement nul, sauf à la ligne triple, permettant de localiser la force de ligne de contact.L'introduction de cette fonction couleur oblige à reformuler en partie le système d'équations de Saint-Venant afin de tenir compte de cette nouvelle fonction dans l'expression des différents termes de forces agissant sur le film. Pour justifier le choix de cette nouvelle formulation, une méthode basée sur une formulation eulérienne du principe de Hamilton a été utilisée. Cette méthode permet d’obtenir une équation de quantité de mouvement compatible avec la conservation de l'énergie du système étudié avec comme unique point de départ une expression de la densité d'énergie du système en fonction des variables utilisées.Ce nouveau système d’équations, en plus d’être complètement affranchi d’un paramètre de calibration, présente l’avantage d’être complètement hyperbolique dans le cas où les effets de courbure ne sont pas pris en compte. Cela a permis le développement d’un solveur de Riemann de type HLLC pour résoudre numériquement ce système d’équations. Afin de tester la robustesse des modèles physiques et numériques, un ensemble de cas de vérification et de validation a été mis en place.Enfin, les termes de courbure ont été pris en compte dans le schéma numérique final permettant d’étendre considérablement le champ d’application de ce nouveau modèle avec fonction couleur. Ainsi des problèmes où les effets capillaires sont prédominants ont pu être simulésWhy does a drop of water tend to form a sphere? Why does it cling to its leaf in the morning dew? On the contrary, why does it flow down towards the ground? All these seemingly simplistic questions involve highly complex microscopic phenomena whose physical nature is still the subject of debate. However, understanding them is a major challenge in many industrial applications. This is particularly true in aeronautics, where a thin film forms on the wings after the aircraft has passed through a cloud or after a defreezing operation. The evolution of the wetted surface by this film, like its transition into rivulets under the effect of air shear, as well as its eventual refreezing a little further outside the protection zones, is not taken into account in thermal defrost simulation tools; or only in a rudimentary way via empirical correlations. However, this ice accretion must be controlled for safety reasons and aerodynamic performance. This is why it is necessary to improve existing tools by developing new models capable of considering the influence of capillary forces on a macroscopic scale, specifically at the contact line level, in order to be able to predict the dynamics of a sheared film.The overall objective of this study is therefore to develop a suitable model for large-scale simulation of partially wetting thin film flow.To answer this objective, an approach based on a Shallow-water equations was adopted. However, this system in its classical form does not allow the simulation of thin films with partial wetting effects. One solution to consider these effects is to add a macroscopic force concentrated to the contact line. This singular force enables the macroscopic Young-Dupré law to be verified locally. The issue with this approach is to localize the force at the contact line only. Unlike other models in the literature, which are all based on the use of an adjustable parameter allowing the distinction between dry and wet zones, we offer here an approach involving the transport of a color function. This function, defined as equal to one in wet zones and zero in dry zones, has the advantage of having an identically zero gradient, except at the contact line, enabling the contact line force to be localized.The introduction of this color function needs a partial reformulation of the Shallow-water equations, in order to integrate this new function in the expression of the various force terms acting on the film. In order to justify the choice of this new formulation, a method based on an eulerian formulation of Hamilton's principle was used. This method helps to obtain a momentum equation compatible with the conservation of energy of the system under study, with the only starting point being an expression of the system's energy density as a function of the variables used.This new system of equations, in addition to being completely calibration parameter free, has the advantage of being entirely hyperbolic in the case where curvature effects are not taken into account. This has helped us to develop an HLLC-type Riemann solver to solve this equation system numerically. In order to test out the robustness of the physical and numerical models, a set of verification and validation cases was set up.Finally, curvature terms were considered in the final numerical scheme, considerably extending the scope of application of this new color function model. In this way, problems where capillary effects are predominant could be simulated
5
Kogevnikov, Ivan. "Modélisation des systèmes de dimension infinie - Application à la dynamique des pneumatiques." Phd thesis, Ecole des Ponts ParisTech, 2006. http://pastel.archives-ouvertes.fr/pastel-00001850.
Анотація:
La thèse est consacrée au problème de modélisation d'un type de roue avec pneus comme système mécanique à degré de liberté infini et à son étude par les méthodes de la dynamique analytique. On étudiera en particulier les régimes stationnaires de roulement de la roue sur un plan avec et sans glissement. Le système mécanique comprend une partie déformable et une partie rigide. La partie rigide est la jante (disque) représentée par un corps solide ayant six degrés de liberté. La partie déformable est le pneu, qu'on peut fractionner en trois parties le bandage, par lequel la roue est en contact avec le plan, et deux surfaces latérales joignant le bandage à la jante. Dans l'état non déformé le bandage est une partie de cylindre circulaire, les surfaces latérales sont des parties de surfaces de tores. La structure des pneus modernes est telle que par chaque point du bandage passent trois familles de fils inextensibles et par chaque point des surfaces latérales du pneu passe une famille. Le pneu est rempli par un gaz sous pression, et le gaz est supposé parfait et son évolution isotherme. La force extérieure F et le moment extérieur M sont appliqués à la jante de la roue. La roue roule sur un plan avec lequel elle est en contact par une certaine partie du bandage a priori inconnue. Le roulement peut avoir lieu avec ou sans glissement dans la zone de contact. Dans ce travail on modélise ce système mécanique et on étudie ses mouvements par les méthodes de la mécanique analytique.
6
Guinot, François. "Déploiement régulé de structures spatiales : vers un modèle unidimensionnel de mètre ruban composite." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10019.
Анотація:
Dans un contexte où l'utilisation de structures déployables s'est généralisée, le département Recherche de la société Thales Alenia Space étudie un nouveau concept de télescope spatial dont le miroir secondaire est déployé grâce au déroulement de six mètres rubans. Des études antérieures ont permis la mise au point d'un prototype constitué de rubans métalliques dont le déploiement s'est avéré trop violent. Dans ce travail de thèse nous proposons d'une part un nouveau type de ruban à la vitesse de déroulement maîtrisable et d'autre part un modèle original décrivant le comportement dynamique de tels rubans, permettant de mieux appréhender les phénomènes complexes pouvant intervenir lors de scénarios de pliage, de déploiement ou de déroulement. La solution envisagée pour contrôler la vitesse de déroulement repose sur l'exploitation des propriétés mécaniques d'une couche de matériau viscoélastique collée à la surface du ruban. Ces propriétés variant avec la température permettent de garantir un maintien de la position enroulée à froid et assurent un déroulement régulé grâce à un réchauffage localisé. Ces phénomènes ont été mis en évidence expérimentalement et numériquement. La lourdeur des méthodes classiques de modélisation et le manque de richesse des méthodes simplifiées nous ont conduit à développer un modèle de poutre à section fortement déformable permettant de décrire le comportement dynamique des rubans en grands déplacements. Partant d'un modèle de coque, l'originalité de la méthode repose essentiellement sur l'introduction d'une cinématique de type elastica pour décrire les grandes variations de forme de la section. Un modèle énergétique 1D est obtenu en intégrant dans la section et le problème est résolu à l'aide du logiciel de modélisation par éléments finis COMSOL. On propose finalement un modèle continu 1D à 4 paramètres cinématiques qui permet de rendre compte d'une large gamme de phénomènes intervenant dans des scénarios complexes de pliage, de déroulement et de déploiement dynamiqueThe research department of Thales Alenia Space is studying new concepts of space telescopes whose secondary mirror is deployed thanks to the unreeling of six tape-springs. A breadboard using metallic tape-springs has been built during preliminary studies and has exhibited a deployment that is too energetic and induce too important shocks.In this thesis a new kind of tape-spring with a controlled uncoiling speed is introduced. Secondly a rod model with highly deformable thin-walled cross-sections describing the dynamic behaviour of tape-springs is derived.In order to over come the deployment speed of a tape spring, a viscoelastic layer is stuck on its sides. Thanks to its properties varying with the temperature, the viscoelastic layer is used to maintain the tape-spring in a coiled configuration at low temperature whereas a local heating leads to a controlled uncoiling. These phenomenons have been underlined experimentally and numerically.Because of the high complexity of classical shell models and the lack of details of simplified models, smart modelling methods need to be developed to describe the highly non linear behaviour of a tape-spring. A planar rod model with highly deformable thin-walled cross-sections that accounts for large displacements and large rotations in dynamics is proposed. Starting from a classical shellmodel, the main additional assumption consists in introducing an elastica kinematics to describe thelarge changes of the cross-section shape with very few parameters. The expressions of the strain andkinetic energies are derived by performing an analytical integration over the section. The Hamilton principle is directly introduced in a suitable finite element software to solve the problem. Several examples (folding, coiling and deployment of a tape spring) are studied through the FEM software COMSOL to demonstrate the ability of the 4-parameter model to account for several phenomena: creation of a single fold and associated snap-through behaviour, splitting of a fold into two, motion of a fold along the tape during a dynamic deployment, scenarios of coiling and uncoiling of a bistable tape-spring
7
Valcárcel, Flores Carlos Enrique [UNESP]. "Estudo clássico completo do formalismo de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102544.
Анотація:
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Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a fim de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From fixed point variations and using the Carathéodory’s method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills field as well as its correspondent self-dual and to the Linearized Gravity field
8
Valcárcel, Flores Carlos Enrique. "Estudo clássico completo do formalismo de Hamilton-Jacobi /." São Paulo, 2012. http://hdl.handle.net/11449/102544.
Анотація:
Orientador: Bruto Max Pimentel EscobarBanca: Abraham Zimerman
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Resumo: Nesta tese, apresentamos a formulação clássica completa da teoria de Hamilton-Jacobi para sistemas vinculados. Usando o método de Lagrangianas Equivalentes de Carathéodory obtemos um conjunto de Equações Diferenciais Parciais de Hamilton-Jacobi, também chamado de Hamiltonianos. A Condição de Integrabilidade nos permite dividir os Hamiltonianos entre involutivos e não-involutivos. Construímos os Parênteses Generalizados a fim de eliminar os Hamiltonianos não-involutivos, enquanto que relacionamos os Hamiltonianos involutivos com o Gerador das transformações canônicas. Por outro lado, a Equação de Lie é resultado da realização das variações totais no funciona lde ação, e que é relacionada às simetrias da teoria. Usamos a Equação de Lie e a estrutura das Equaçõoes Características, que indicam a evolução dinâmica do sistemas, para associar o Gerador de transformações canônicas às simetrias de calibre. Aplicamos o formalismo de Hamilton-Jacobi ao modelo da Mecânica Quântica Topologica, ao modelo BF bi-dimensional equivalente à Teoria de Jackiw-Teitelboim, ao campo de Yang-Mills Topologicamente Massivo e seu equivalente Auto-dual, assim como para o campo da Gravitação linearizada
Abstract: It is presented the complete classical formulation of the Hamilton-Jacobi theory for constrained systems. From fixed point variations and using the Carathéodory's method of Equivalent Lagrangian we obtain a set of Hamilton-Jacobi Partial Differential Equations, also called Hamiltonians. The Integrability Condition allow us to divide the Hamiltonians between involutive and non-involutive ones. We build the Generalized Brackets in order to eliminate the non-involutive Hamiltonians, whereas we relate the involutive Hamiltonians to the Generator of Canonical Transformations. On the other hand, we build the Lie Equation, result of perform total variations to the action functional and which is related to the symmetries of the theory. We use the Lie equation along with the structure of the Characteristic Equations, related to the dynamical evolution of the systems, to associate the Generator of Canonical Transformation to Gaugesymmetries. We apply this formalism to the Topologically Quantum Mechanics, the two dimensional BF model equivalent to the Jackiw-Teitelboim theory, the Topologically Massive Yang-Mills field as well as its correspondent self-dual and to the Linearized Gravity field
Doutor
9
Maia, Natália Tenório [UNESP]. "Estudo sobre a teoria de vínculos de Hamilton-Jacobi." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/132007.
Анотація:
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A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo
The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism
CNPq: 133488/2011-0
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Maia, N. T. (Natália Tenório). "Estudo sobre a teoria de vínculos de Hamilton-Jacobi /." São Paulo, 2013. http://hdl.handle.net/11449/132007.
Анотація:
Orientador: Bruto Max Pimentel EscobarCo-orientador:
Banca:Andrey Yuryevich Mikhaylov
Banca: Edmundo Capelas de Oliveira
Resumo: A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo
Abstract: The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism
Mestre
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Rondepierre, Aude. "Algorithmes hybrides pour le contrôle optimal des systèmes non linéaires." Phd thesis, Grenoble INPG, 2006. http://tel.archives-ouvertes.fr/tel-00112203.
Анотація:
Cette thèse est consacrée à la résolution des problèmes de contrôle non linéaires par des méthodes de calcul hybride. L'idée défendue est que la modélisation par les systèmes hybrides permet la résolution approchée des problèmes non linéaires sans connaissance a priori du comportement du système étudié. Dans un premier temps, nous nous intéressons à la modélisation des systèmes de contrôle non linéaires par une nouvelle classe de systèmes hybrides affines par morceaux. Un soin particulier est apporté à l'étude de l'erreur et de la convergence de l'approximation hybride. La deuxième partie est consacrée au problème de la contrôlabilité à l'origine des systèmes non linéaires. Nous nous intéressons tout d'abord à la quantification de l'erreur commise entre le domaine contrôlable non linéaire et son approximation hybride. Nous proposons ensuite une approche constructive pour le calcul du domaine contrôlable, permettant alors de réduire l'exploration des états discrets de l'automate hybride. La dernière partie est dédiée à la recherche de solutions optimales des problèmes de contrôle non linéaires et hybrides. Nous justifions tout d'abord la pertinence de la modélisation hybride à travers deux approches : le principe du maximum de Pontryagin et les solutions de viscosité des équations d'Hamilton-Jacobi-Bellman. Nous énonçons en particulier un principe du maximum hybride qui nous permet alors de déterminer la structure du contrôle optimal hybride. Ces trois parties répondent à un objectif principal : développer par le calcul hybride combinant analyse numérique et calcul formel, des outils mathématiques et algorithmiques efficaces pour l'étude de dynamiques contrôlées non linéaires.
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Barbagallo, Mathias. "Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures." Doctoral thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118427.
Анотація:
Multilayered structures have many application in industry and society: they have peculiar properties and serve a variety of purposes, like structural support, thermal insulation, vibrational and acoustic isolation. This thesis concerns the prediction of sound transmission in multilayered structures. Two problems are herein investigated: the transmission of energy through structures and the transmission of energy along structures. The focus of the analysis is on the mid to high frequency range. To predict sound transmission in these structures, statistical energy analysis (SEA) is used.SEA models are devised for the prediction of the sound reduction index for two kinds of multilayered structures, double-walls used in buildings and trim-panels in vehicles; the double-walls comprise an air cavity in between flat plasterboard or glass plates, whereas the trim-panels a porous layer in between curved aluminium and rubber layers. The SEA models are based upon the wave-types carrying energy. The novelty in these SEAs is an element describing the waves in the air cavity, or in the porous layer, fully coupled to the mass-impeded external layers. Compared to measurements, the proposed SEA performs well: for double-walls, it performs better than previous models; for trim-panels, it is an original result. The parameters of the new SEA element, such as modal density, are derived from the coupling equations describing the fully coupled waves. For double-walls, these equations are derived via Newton's laws. For trim-panels, a variational approach based upon a modified Hamilton's principle valid for non-conservative systems is preferred, because it is a powerful machinery for deriving equations of motion and coupling conditions of a medium as complex as the porous layer. The modified Hamilton's principle for non-conservative systems is based upon a self-adjoint functional analogous to the Lagrangian, inspired by Morse and Feshbach's construction. A self-adjoint variational principle for Biot's equations in the displacement formulation is devised. An equivalent mixed formulation is obtained changing the coordinates of the displacement formulation via Lagrange multipliers. From this mixed formulation, the Lagrangian for a porous material with a limp frame is derived, which yields the continuity of the total displacement of the porous layer. Lagrange multipliers help to obtain the correct coupling functionals between a porous material and a solid. The Lagrange multipliers introducing the continuity of the frame and the solid displacements equal the traction of the in-vacuo frame, thus disappearing if the latter is limp. Measurements to gather material parameters for a Biot model of the porous layer have been conducted.The effects of spatial energy decay in the transmission along structures predicted by SEA is studied: a major effect is the increased relevance of indirect coupling loss factors between SEA elements. This may jeopardize the usefulness of SEA at higher frequencies.QC 20130218
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Barreto, Gilmar Wilian. "Projeto de uma perfuratriz multifuncional para execução de estacas e desenvolvimento de um ensaio de campo que utiliza o sistema de monitoração eletrônica da perfuratriz." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-18032015-152955/.
Анотація:
Esta tese apresenta, o projeto de uma perfuratriz que permite a execução de cinco tipos de fundação profunda, e o desenvolvimento de um ensaio de campo que possibilita avaliar as resistências por atrito lateral desenvolvidas entre o instrumento envolvido pelo solo escavado e o terreno natural. A perfuratriz foi projetada para executar estacas dos tipos hélice contínua monitorada, escavadas com trado mecânico, hélice segmentada monitorada, raiz e hollow-auger. As estacas dos tipos hélice contínua monitorada e as escavadas com trado mecânico são muito utilizadas no Brasil; as estacas raiz e hollow-auger são utilizadas em situações especiais e a estaca hélice segmentada monitorada é mais recente, mas sua aplicação tem tido um crescimento importante nos últimos dez anos. Para a perfuratriz multifuncional são apresentados cálculos e desenhos básicos dos principais conjuntos. Para a nova investigação de campo, denominada FDT - Full Displacement Test, é apresentado um desenvolvimento teórico com base no princípio universal da conservação de energia que, em termos práticos, resulta na obtenção da parcela de atrito lateral, denominado atrito lateral unitário equivalente (fse). Os resultados obtidos a partir dos dados aquisitados pelo sistema de monitoramento eletrônico da perfuratriz apresentaram-se concordantes entre si, indicando a possibilidade de praticamente se conseguir a repetibilidade do ensaio. Entre os diversos ensaios realizados, foi dada ênfase aos ensaios realizados no campo experimental de Fundações e Geotecnia da Faculdade de Engenharia Agrícola FEAGRI, da Universidade de Campinas - UNICAMP e foram feitas correlações com as resistências obtidas nas provas de carga estáticas realizadas no local por Albuquerque (2001), a partir dos ajustes feitos para o nível instrumentado na profundidade de 11,70 m para o qual foi determinado um fator (G2), para cada tipo de estaca ensaiada (escavada, hélice contínua e ômega). A partir dos ajustes feitos para o nível 11,70 m foram feitas previsões de capacidade de carga por atrito lateral para os outros níveis instrumentados (5,00 m; 11,10 m e 12,00 m), sendo que os resultados apresentaram-se concordantes.This thesis presents the design of a drilling rig that allows the execution of five types of deep foundation, and the development of a field test that allows measuring the skin friction resistance developed between the instrument involved by the excavated ground and the natural soil. The drilling rig was designed to make continuous flight auger, bored pile, continuous flight auger with segmented auger, root pile and hollow-auger pile. The continuous flight auger and bored piles are widely used in Brazil; the root pile and hollow-auger pile are used for in special conditions, and the continuous flight auger with segmented auger, is although more recent, but its application has had increased application grown in over the last ten years. For the multifunctional drilling rig, calculations and basic designs of the main sets are presented. For the new field test denominated FDT - Full Displacement Test, a theoretical development based on the universal principle of energy conservation was made carried out resulting and the result, in practical terms, was to obtain in the attainment of the skin friction defined in this thesis as equivalent unit skin friction (fse). The results obtained from the data acquired by the electronic monitoring system of drilling rigs were consistent among themselves, indicating the possibility of practically achieve the repeatability of the test. Among the various tests performed, emphasis was given to tests in the experimental field of foundations and geotechnics, of the College of Agricultural Engineering FEAGRI, Campinas University UNICAMP, and were correlated to the skin friction resistance obtained from the static load tests performed on site by Albuquerque (2001), based on the adjustments done to the instrumented level depth of 11.70 m, for which a factor (G2) was given in each type tested (bored, C.F.A and omega). From the adjustments made to the 11,70 m level, load-bearing capacity of skin friction predictions were made for other instrumented levels (5.00 m; 11.10 m and 12.00 m) presenting consistent results.
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Rousseau, Grégory. "Véhicule hybride et commande optimale." Phd thesis, École Nationale Supérieure des Mines de Paris, 2008. http://pastel.archives-ouvertes.fr/pastel-00005237.
Анотація:
Dans le contexte automobile actuel, étroitement lié à la volonté de réduire les émissions de CO2 dans l'atmosphère, les véhicules hybrides demeurent un passage obligé à court et moyen terme. Un véhicule hybride possède deux sources d'énergie pour assurer sa propulsion : en général un moteur thermique constitue la principale source d'énergie, tandis qu'un moteur électrique représente la source secondaire. La capacité d'un véhicule hybride à consommer moins de carburant, et à rejeter moins de CO2, provient de la présence du moteur électrique. Celui-ci peut être utilisé soit conjointement avec le moteur thermique, soit seul, aucun carburant n'étant alors consommé. La présence de ces deux sources d'énergie impose au système global d'être régi par une stratégie de contrôle déterminant la répartition du couple entre les deux moteurs en fonction de l'état de charge de la batterie. Cette répartition peut être déterminée pour être optimale vis-à-vis de critères tels que la consommation de carburant, les émissions de polluants, etc. L'objectif de la thèse est de développer des méthodes d'optimisation de la répartition de couple entre les deux moteurs d'un véhicule hybride, dans l'objectif de minimiser les émissions de CO2. Une première étape a consisté à développer des modèles représentatifs d'une architecture type adaptés aux types d'optimisation réalisée. Les algorithmes d'optimisation diffèrent selon qu'ils soient capables de traiter des problèmes hors-ligne, ou temps-réel. Parmi les algorithmes d'optimisation hors-ligne étudiés, la programmation dynamique a été utilisée pour déterminer le dimensionnement optimal des éléments principaux d'une architecture hybride, et en déterminer le gain théorique par rapport à une motorisation traditionnelle. Par ailleurs, un algorithme de tir original nommé SCOP a été développé, celui-ci permettant de traiter des problèmes de commande optimale avec contraintes sur l'état, tout en multipliant les performances par 50 par rapport à la méthode de programmation dynamique. Une stratégie de contrôle temps-réel, basée sur l'Equivalent Consumption Minimization Strategy (ECMS) utilisant le principe de Pontryagin, a été développée et implémentée sur un prototype de véhicule hybride, une Smart équipée d'un alterno-démarreur. Les résultats obtenus démontrent de l'action de la stratégie pour la réduction de la consommation de carburant et des émissions de CO2.
15
Ašković, Veljko. "Aerial vehicle guidance problem through the Pontryagin Maximum Principle and Hamilton Jacobi Bellman approach." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS553.
Анотація:
La thèse comporte deux volets principaux: Le premier volet, d'ordre théorique, porte sur le développement asymptotique de la fonction valeur associée à un problème de contrôle optimal lorsque l'horizon tend vers l'infini. Un développement asymptotique à deux termes a été démontré d'abord dans le cas linéaire quadratique puis ensuite a été étendu au cas non linéaire dans la classe de systèmes dissipatifs. La seconde partie de la thèse porte sur la résolution numérique d'un problème de guidage de véhicules aériens. Après avoir modélisé le problème, nous mettons en œuvre trois méthodes afin de résoudre des variantes du problème: une méthode directe, une méthode indirecte basée sur la continuation et le tir et enfin l'approche Hamilton Jacobi Bellman. Cette dernière nous permet également d'évaluer numériquement des domaines atteignables par notre systèmeThis thesis is mainly composed of two parts. In the first part, we investigate the large time behavior of the value function associated to an optimal control problem in the finite dimensional case. We first establish the large time asymptotic expansion in the linear quadratic (LQ) theory. We then generalize this expansion to nonlinear dynamical systems more precisely within the class of dissipative systems. In the second part, we solve numerically the guidance problem of an aerial vehicle. We first model mathematically the equations of motion. Then, we implement three methods in order to solve the problem: a direct method, an indirect method based on the continuation process and the shooting method. Finally, we implement a numerical method derived from the Hamilton Jacobi Bellman theory in order to compute optimal trajectories and at the same time the reachable sets
16
Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/657266.
Анотація:
Se presenta un modelo de elementos finitos que describe el comportamiento de vibración de libre de vigas compuestas laminadas. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los laminados compuestos son ortotrópicos con fibras orientadas en diferentes direcciones. Se implementa un programa para materiales compuestos laminado en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio de convergencia y paramétrico con un mismo número de lámina y diferentes direcciones. Se verifica que la formulación que es bastante precisa con resultados satisfactorios en la investigación.In this work, is presented a finite element model that describes the free vibration behavior of laminated composite beams. The model is developed by the Hamilton principle and the Timoshenko theory that includes shear deformations. Composite laminates are assumed to be orthotropic with fibers oriented in different directions, such as Angle Ply and Cross Ply cases. This investigation works out on a MAPLE program for laminated composites materials that will be completed all in MATLAB program. In order to validate the model, the results are compared with different literatures, also verify the formulation that is quite accurate and obtain quite satisfactory results in the investigation. High order interpolations are assumed to approximate fundamental variables. A convergence study and parametric study will be carried out with the same number of laminas in different directions.
Tesis
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Oussaily, Aya. "Étude théorique et numérique des systèmes modélisant la dynamique des densités des dislocations." Thesis, Compiègne, 2021. https://bibliotheque.utc.fr/Default/doc/SYRACUSE/2021COMP2634.
Анотація:
Dans cette thèse, nous nous intéressons à l’analyse théorique et numérique de la dynamique des densités des dislocations. Les dislocations sont des défauts linéaires qui se déplacent dans les cristaux lorsque ceux-ci sont soumis à des contraintes extérieures. D’une manière générale, la dynamique des densités des dislocations est décrite par un système d’équations de transport, où les champs de vitesse dépendent de manière non-locale des densités des dislocations. Au départ, notre travail se focalise sur l’étude d’un système unidimensionnel (2 × 2) de type Hamilton-Jacobi dérivé d’un système bidimensionnel proposé par Groma et Balogh en 1999. Pour ce modèle, nous montrons un résultat d’existence globale et d’unicité. En addition, nous nous intéressons à l’étude numérique de ce problème, complété par des conditions initiales croissantes, en proposant un schéma aux différences finies implicite dont on prouve la convergence. Ensuite, en s’inspirant du travail effectué pour la résolution de la dynamique des densités des dislocations, nous mettons en œuvre une théorie plus générale permettant d’obtenir un résultat similaire d’existence et d’unicité d’une solution dans le cas des systèmes de type eikonal unidimensionnels. En considérant des conditions initiales croissantes, nous faisons une étude numérique pour ce système. Sous certaines conditions de monotonies sur la vitesse, nous proposons un schéma aux différences finies implicite permettant de calculer la solution discrète et simuler ainsi la dynamique des dislocations à travers ce modèleIn this thesis, we are interested in the theoretical and numerical studies of dislocations densities. Dislocations are linear defects that move in crystals when those are subjected to exterior stress. More generally, the dynamics of dislocations densities are described by a system of transport equations where the velocity field depends non locally on the dislocations densities. First, we are interested in the study of a one dimensional submodel of a (2 × 2) Hamilton-Jacobi system introduced by Groma and Balogh in 1999, proposed in the two dimensional case. For this system, we prove global existence and uniqueness results. Adding to that, considering nondecreasing initial data, we study this problem numerically by proposing a finite difference implicit scheme for which we show the convergence. Then, inspired by the first work, we show a more general theory which allows us to get similar results of existence and uniqueness of solution in the case of one dimensional eikonal systems. By considering nondecreasing initial data, we study this problem numerically. Under certain conditions on the velocity, we propose a finite difference implicit scheme allowing us to calculate the discrete solution and simulate then the dislocations dynamics via this model
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Neves, Luis Fernando de Seixas. "Metodologia para a determinação da eficiência do ensaio SPT através de prova de carga estática sobre o amostrador padrão." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-02032016-142441/.
Анотація:
O ensaio de simples reconhecimento de solos (SPT) é a ferramenta de investigação de solos mais utilizada no mundo. Devido ao grande número de parâmetros que influenciam os seus resultados, a medida de sua eficiência passa a ser indispensável à transposição de experiências entre as práticas desenvolvidas em diferentes locais. Infelizmente, a medida da eficiência através da instrumentação do impacto do martelo é economicamente inviável para a maioria das empresas de sondagem no Brasil. Este trabalho apresenta uma metodologia para a determinação da eficiência do SPT baseada no princípio de Hamilton e na realização de prova de carga estática sobre o amostrador, que pode ser uma alternativa para sanar esta situação.The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.
19
Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2001. http://hdl.handle.net/10757/654828.
Анотація:
Esta investigación se enfoca en el análisis de vibración libre de vigas Timoshenko utilizando el método de elementos finitos. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los materiales para emplear son isotrópicos. Se implementa un programa para estos materiales en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio paramétrico con una misma longitud y diferentes esbelteces. Se verifica que la formulación sea bastante precisa con resultados muy satisfactorios.This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
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Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Vibración libre de vigas de material isotrópico utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/654828.
Анотація:
Esta investigación se enfoca en el análisis de vibración libre de vigas Timoshenko utilizando el método de elementos finitos. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los materiales para emplear son isotrópicos. Se implementa un programa para estos materiales en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio paramétrico con una misma longitud y diferentes esbelteces. Se verifica que la formulación sea bastante precisa con resultados muy satisfactorios.This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
21
Morais, Thaise da Silva Oliveira. "Interpretação racional de resultados de ensaios SPT com base em conceitos de energia." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-29022016-111249/.
Анотація:
A sondagem de simples reconhecimento do solo com medida do índice de resistência à penetração dinâmica do amostrador (NSPT), universalmente conhecida como ensaio SPT, é um dos ensaios de campo mais difundidos no Brasil. A popularidade deste ensaio deve-se a sua praticidade, baixo custo, à experiência já adquirida e a fácil utilização dos seus resultados. Entretanto, este ensaio tem sido amplamente criticado devido às variações de equipamentos e procedimentos, que causa dispersões significativas nos resultados. Usualmente, o índice NSPT é utilizado na estimativa da capacidade de carga e recalque de fundações, a partir de correlações empíricas ou semi-empíricas, o que também recebe críticas, visto que essas correlações são baseadas em observações práticas e sem fundamento científico. O índice NSPT é função da quantidade de energia entregue ao amostrador, durante o golpe no ensaio SPT. Assim, o conhecimento da eficiência permite normalizar os valores de NSPT para um valor de referência padrão. O valor padrão adotado internacionalmente, correspondente a uma eficiência de 60%. Desta forma, a análise racional dos resultados de ensaios SPT, concentra-se na estimativa das quantidades de energia envolvidas no ensaio. Neste contexto, o presente trabalho trata da interpretação racional de ensaios SPT realizados com o monitoramento das quantidades de energia envolvidas no ensaio. As energias foram obtidas indiretamente, através de sinais de força e aceleração durante a propagação da onda de tensão pela composição de haste. Para tanto, foram utilizados segmentos de hastes instrumentadas com células de carga e acelerômetros; e um sistema de aquisição de dados indicado para o monitoramento de eventos dinâmicos. Os ensaios SPT foram realizados com instrumentação dinâmica em duas seções ao longo da composição de hastes (topo e base, simultaneamente). Assim, a partir desse arranjo, foram determinadas as quantidades de energia responsáveis pela cravação do amostrador e as perdas ocorridas. A partir dos sinais de força no topo do amostrador, foram determinadas as resistências dinâmicas mobilizadas no sistema solo-amostrador devido à cravação. Estes resultados experimentais foram comparados com resultados teóricos de resistência dinâmica e estática, obtidos com base no Princípio de Hamilton. De posse dos resultados de eficiência, comprimento das amostras recuperadas e do atrito adesão entre a parede externa do amostrador e o solo, foi feito o equilíbrio das reações mobilizadas no amostrador, segundo a proposta de Aoki (2013), sendo obtidas as resistências de ponta e atrito (interno e externo) no sistema solo-amostrador.The Standard Penetration Test (SPT) with measurement of the index of resistance to dynamic penetration of the sampler (NSPT) is one of the most widespread in situ tests in Brazil. The popularity of this test is due to its practicality, low cost, acquired experience by practitioners and simple applicability of its results. However, this test has been widely criticized because of variation in equipment and procedures, which causes significant dispersion in the results. The NSPT index is usually used to estimate the bearing capacity and settlement of foundations, using empirical or semi-empirical correlations. This fact also receives criticism, as these correlations are based on practical observations without any scientific basis. The NSPT index depends on the amount of energy delivered to the sampler, during the blow in the SPT test. Thus, knowing the equipment efficiency allows normalizing the NSPT values to a standard reference value. The international reference value corresponds to an efficiency of 60%. In this way, the rational analysis of the results of SPT tests essentially depends on the estimation of the quantities of energy involved in the test. This research presents the rational interpretation of the SPT test results based on monitoring the amounts of energy involved in the test. The energies were indirectly obtained through force and acceleration signals during the stress wave propagation along the string of rods. For this, rod subassemblies instrumented with load cells and accelerometers were used. A suitable data acquisition system for monitoring dynamic events was also used. The SPT tests were performed with instrumented subassemblies placed at two positions along the string of rods (top and bottom simultaneously). Thus, from this arrangement, the amounts of energy accountable for the sampler penetration and the energy losses occurred were determined. Likewise, the dynamic resistances mobilized in the soil-sampler system during the penetration were determined from the force and acceleration signals at the top of the sampler. These experimental results were compared with those theoretical results, based on the Principle of Hamilton. With the efficiency results, the length of recovered samples and the external skin friction in the soil-sampler system, the balance of the reactions mobilized in the sampler was verified, as proposed by Aoki (2013). Thus, the tip and skin friction (internal and external) resistances in the soil-sampler system were obtained.
22
Gourma, Mustapha. "Towards better understanding of the Smoothed Particle Hydrodynamic Method." Thesis, Cranfield University, 2003. http://hdl.handle.net/1826/133.
Анотація:
Numerous approaches have been proposed for solving partial differential equations; all these
methods have their own advantages and disadvantages depending on the problems being treated. In
recent years there has been much development of particle methods for mechanical problems.
Among these are the Smoothed Particle Hydrodynamics (SPH), Reproducing Kernel Particle
Method (RKPM), Element Free Galerkin (EFG) and Moving Least Squares (MLS) methods. This
development is motivated by the extension of their applications to mechanical and engineering
problems.
Since numerical experiments are one of the basic tools used in computational mechanics, in
physics, in biology etc, a robust spatial discretization would be a significant contribution towards
solutions of a number of problems. Even a well-defined stable and convergent formulation of a
continuous model does not guarantee a perfect numerical solution to the problem under
investigation.
Particle methods especially SPH and RKPM have advantages over meshed methods for problems,
in which large distortions and high discontinuities occur, such as high velocity impact,
fragmentation, hydrodynamic ram. These methods are also convenient for open problems. Recently,
SPH and its family have grown into a successful simulation tools and the extension of these
methods to initial boundary value problems requires further research in numerical fields.
In this thesis, several problem areas of the SPH formulation were examined. Firstly, a new approach based on ‘Hamilton’s variational principle’ is used to derive the equations of motion in the SPH form. Secondly, the application of a complex Von Neumann analysis to SPH method reveals the
existence of a number of physical mechanisms accountable for the stability of the method. Finally, the notion of the amplification matrix is used to detect how numerical errors propagate permits the identification of the mechanisms responsible for the delimitation of the domain of numerical stability.
By doing so, we were able to erect a link between the physics and the numerics that govern the SPH formulation.
23
Buechler, Miles A. "Variational Modeling of Ionic Polymer-Based Structures." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/34309.
Анотація:
Ionomeric polymers are a promising class of intelligent material which exhibit electromechanical coupling similar to that of piezoelectric bimorphs. Ionomeric polymers are much more compliant than piezoelectric ceramics or polymers and have been shown to produce actuation strain on the order of 2\% at operating voltages between 1 V and 3 V \citep{Akle2}. Their high compliance is advantageous in low force sensing configurations because ionic polymers have a very little impact on the dynamics of the measured system. Here we present a variational approach to the dynamic modeling of structures which incorporate ionic polymer materials. The modeling approach requires a priori knowledge of three empirically determined material properties: elastic modulus, dielectric permittivity, and effective strain coefficient. Previous work by Newbury and Leo has demonstrated that these three parameters are strongly frequency dependent in the range between less than 1 Hz to frequencies greater than 1 kHz. Combining the frequency-dependent material paramaters with the variational method produces a second-order matrix representation of the structure. The frequency dependence of the material parameters is incorporated using a complex-property approach similar to the techniques for modeling viscoelastic materials. Three structural models are developed to demonstrate this method. First a cantilever beam model is developed and the material properties of a typical polymer are experimentally determined. These properties are then used to simulate both actuation and sensing response of the transducer. The simulations compare very well to the experimental results. This validates the variational method for modeling ionic polymer structures. Next, a plate model is developed in cylindrical coordinates and simulations are performed using a variety of boundary conditions. Finally a plate model is developed in cartesian coordinates. Methods for applying non-homogenious boundary conditions are then developed and applied to the cartesian coordinate model. Simulations are then compared with experimental data. Again the simulations closely match the experiments validating the modeling method for plate models in 2 dimensions.Master of Science
24
Machů, Zdeněk. "Výpočtové modelování piezoelektrických vrstevnatých kompozitů a analýza jejich elektro-mechanické odezvy při harmonickém kmitání." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-400492.
Анотація:
V současnosti je velmi aktuálním tématem generování elektrické energie z alternativních zdrojů, zejména z vibrací. Zařízení, která přeměňují mechanickou energii na elektrickou, využívají často ke své činnosti piezoelektrický jev. Pro optimální nastavení takového elektromechanického měniče pro danou aplikaci je třeba mít k dispozici výpočtový model, který bude schopný postihnout všechny klíčové aspekty jeho provozu. Tato práce se tedy zabývá vytvořením takovéhoto nástroje, který je schopen komplexně popsat elektromechanickou odezvu studovaného piezoelektrického měniče energie v podobě vetknutého, vícevrstvého keramického nosníku s piezoelektrickými vrstvami. Uvažovaná vícevrstvá konstrukce je během své činnosti vystavena kinematickému buzení a je rovněž zatížena tepelnou zbytkovou napjatostí vznikající při její výrobě. Vytvořený výpočtový model využívá klasickou laminátovou teorii k určení statické elektromechanické odezvy dané konstrukce. Elektromechanická odezva při kmitání uvažované konstrukce v ustáleném stavu je získána s využitím Hamiltonova variačního principu a teorie kmitání prutů. Vytvořený výpočtový model je dále schopen odhadnout zdánlivou lomovou houževnatost dané vícevrstvé konstrukce pomocí metody váhových funkcí. Výstupy vytvořeného výpočtového modelu jsou ověřeny s využitím numerických simulací na bázi MKP a dostupných experimentálních výsledků. V diplomové práci je následně vytvořený výpočtový model aplikován při hledání optimálního rozložení jednotlivých vrstev konkrétního vícevrstvého nosníku s cílem maximalizovat jeho elektrický výkon a odolnost vůči šíření povrchových trhlin, resp. vzniku křehkého lomu. Tohoto cíle je dosaženo pomocí vhodného rozložení tepelných zbytkových napětí v jednotlivých vrstvách uvažované konstrukce (řízeného použitými materiály a tloušťkami jednotlivých vrstev).
25
Noreña, Pablo Cesar Trejo. "Estimativa da eficiência do ensaio SPT através da execução da prova de carga estática sobre o amostrador." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-08112012-113424/.
Анотація:
O ensaio de simples reconhecimento com o SPT é um dos mais utilizados para investigação do subsolo nos EUA e no Brasil. Os dados obtidos com este ensaio dinâmico, tais como o índice de resistência à penetração NSPT, classificação do solo e nível freático são usados por diferentes métodos para estimativa de capacidade de carga de fundações rasas e profundas. Para um mesmo solo, o índice NSPT pode ser diferente se diferentes equipamentos forem usados devido ao fato de que diferentes equipamentos de SPT mostram diferentes níveis de eficiência. Em vista disso, uma alternativa para estimar a eficiência do ensaio SPT é utilizando-se o ensaio de prova de carga estática sobre o amostrador. Este ensaio foi implementado para poder avaliar a eficiência do ensaio SPT. Para este fim, foram executados 13 ensaios dinâmicos e 13 ensaios estáticos no campus experimental do Laboratório de Engenharia Civil da UNESP (Bauru). Para estimar a eficiência do ensaio SPT através do ensaio dinâmico, um sistema de aquisição analógico-digital foi utilizado para obter registros de aceleração e força na seção localizada junto ao amostrador SPT. O ensaio dinâmico foi modificado para utilizar várias energias potenciais nominais do martelo e sistemas de elevação. A determinação da eficiência do ensaio através da execução da prova de carga estática foi obtida com base no princípio de Hamilton. Adicionalmente, realizando-se a comparação entre o comportamento de carregamento dinâmico e estático, pode-se obter a resistência estática do sistema amostrador-solo. Esta resistência é calculada utilizando a base de dados obtidas no campo e a aplicação de vários métodos de estimativa como: Aoki et al.(2007), De Souza (2009) e Odebrecht (2003). Os resultados da estimativa da eficiência através do ensaio de prova de carga estática sobre o amostrador mostraram-se consistentes em relação aos valores obtidos com o ensaio dinâmico. Concluiu-se que a execução do ensaio de prova de carga estática sobre, o amostrador é uma alternativa simples e econômica para obter a eficiência do SPT.The Standard Penetration Test, SPT, is one of the most used one for subsoil information in the USA and Brazil. The data obtained in this dynamic test, such as the penetration resistance index, NSPT, the soil classification and phreatic level are used by different methods to estimate the shallow and deep foundations load capacity. For the same soil, the index NSPT can be different if different equipments are used, because different SPT equipments show different efficiency levels. Having this in mind, an alternative to estimate the essay efficiency of the SPT test is using the static load test (SLT) to the sampler. This test was implemented in order to evaluate the efficiency of SPT. To do so, 13 dynamic tests and 13 static tests were performed in the experimental campus of the State University of São Paulo at Bauru (Unesp- Bauru-Brazil). To estimate the efficiency of the SPT test through the dynamic test, a data acquisition system was used to register accelerations and forces at the located section close to the sampler SPT. The dynamic test was modified so that it would be possible to use many nominal potential energy of the hammer and elevation systems. The estimation of the efficiency made through the SLT tests was based on Hamilton\'s principle. Furthermore, by comparing the dynamic and static behavior, we can get the soil-sampler interface static resistance. This resistance is calculated by using the field data through various estimation methods such as Aoki\'s (2007), De Souza\'s (2009) and Odebrecht\'s (2003). The estimates of the efficiency obtained through SLT test were found to be consistent with those obtained through the SPT modified tests. We conclude that SLT is a simple and non-expensive alternative to obtain the efficiency of SPT equipment.
26
Getgood, Thomas. "On the necessity of the maximum principle for systems in the proof of Hamilton's matrix Harnack inequality." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66799.
Анотація:
The heat equation, while well understood in R^n , presents many novel difficulties in curved spaces. Among the techniques developed to deal with these new intricacies are differential Harnack inequalities. Beginning with the work of Li and Yau in [9] this paper will discuss the motivations and methods leading up to differential Harnack estimates culminating in Hamilton's full matrix Harnack inequality [7]. A new tool called the constant rank theorem will thereupon be developed and deployed to reprove Hamilton's result by a different route. This new proof deviates from the original substantially, but achieves the same result under the same assumptions without recourse to Hamilton's matrix maximum principle. The possible implications of this new proof are discussed in closing.L'équation de la chaleur, bien comprise dans les espaces plats, présete un certain degré de difficulté sur les variétés Riemannienne. Parmi les outils importants pour comprendre ses solutions, on trouve l'inégalité matricielle d'Hamilton [7]. Ensuite, nous présenterons un nouvel outil qui est le théorèm de rang invariable et nous l'utiliserons afin de créer une nouvelle prueve de l'inégalité matricielle d'Hamilton. Cette nouvelle prueve nous fournie le meme hypotèses mais sans avoir recours au principe du maximum pour les systèmes d'équations d'Hamilton [6]. Finalement, nous discuterons les implications potentielles de cette nouvelle technique de preuve.
27
Wahbi, Wassim. "Contrôle stochastique sur les réseaux." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED072.
Анотація:
Cette thèse se décompose en trois grandes parties, qui traitent des EDP quasi linéaires paraboliques sur une jonction, des diffusions stochastiques sur une jonction, et du contrôle optimal également sur une jonction, avec contrôle au point de jonction. Nous commençons au premier Chapitre par introduire une nouvelle classe d'EDP non dégénérée et quasi linéaire, satisfaisant une condition de Neumann (ou de Kirchoff) non linéaire et non dynamique au point de jonction. Nous prouvons l'existence d'une solution classique, ainsi que son unicité. L'une des motivations portant sur l'étude de ce type d'EDP, est de faire le lien avec la théorie du contrôle optimale sur les jonctions, et de caractériser la fonction valeur de ce type de problème à l'aide des équations d'Hamilton Jacobi Bellman. Ainsi, au Chapitre suivant, nous formulons une preuve donnant l'existence d'une diffusion sur une jonction. Ce processus admet un temps local, dont l'existence et la variation quadratique dépendent essentiellement de l'hypothèse d'ellipticité des termes du second ordre au point de jonction. Nous formulerons une formule d'Itô pour ce processus. Ainsi, grâce aux résultats de ces deux Chapitres, nous formulerons dont le dernier Chapitre un problème de contrôle stochastique sur les jonctions, avec contrôle au point de jonction. L'espace des contrôles est celui des mesures de Probabilités résolvant un problème martingale. Nous prouvons la compacité de l'espace des contrôles admissibles, ainsi que le principe de la programmation dynamiqueThis thesis consists of three parts which deal with quasi linear parabolic PDE on a junction, stochastic diffusion on a junction and stochastic control on a junction with control at the junction point. We begin in the first Chapter by introducing and studying a new class of non degenerate quasi linear parabolic PDE on a junction, satisfying a Neumann (or Kirchoff) non linear and non dynamical condition at the junction point. We prove the existence and the uniqueness of a classical solution. The main motivation of studying this new mathematical object is the analysis of stochastic control problems with control at the junction point, and the characterization of the value function of the problem in terms of Hamilton Jacobi Bellman equations. For this end, in the second Chapter we give a proof of the existence of a diffusion on a junction. The process is characterized by its local time at the junction point, whose quadratic approximation is centrally related to the ellipticty assumption of the second order terms around the junction point.We then provide an It's formula for this process. Thanks to the previous results, in the last Chapter we study a problem of stochastic control on a junction, with control at the junction point. The set of controls is the set of the probability measures (admissible rules) satisfying a martingale problem. We prove the compactness of the admissible rules and the dynamic programming principle
28
Tabet, Tchamba Thierry Wilfried. "Comportement asymptotique des solutions du problème de Cauchy-Dirichlet généralisé pour des équations de Hamilton-Jacobi visqueuses." Thesis, Tours, 2010. http://www.theses.fr/2010TOUR4007/document.
Анотація:
Cette thèse, constituée de trois grandes parties, a pour objet l’étude générale ducomportement, en temps grands, de l’unique solution du problème de Cauchy-Dirichlet pour deséquations de Hamilton-Jacobi visqueuses de type sur et sous quadratiques. Après un bref rappeldes notions de base de la théorie sur les solutions de viscosité qui constitue le cadre de ce travail, lapremière partie établit des résultats sur l’existence globale en temps et l’unicité de la solution deviscosité dudit problème de Cauchy-Dirichlet. La deuxième partie s’intéresse au comportement decette solution pour des Hamiltoniens sur quadratiques. Sous des hypothèses très générales, nousprouvons que le comportement de la solution dépend du signe de l’unique constante ergodiquec du problème ergodique associé à des conditions aux limites de type contrainte d’état. Lorsquec∗ < 0; nous obtenons (i) une convergence vers l’unique solution du problème stationaire associétandis que lorsque c∗ ≥ 0; nous obtenons (ii) un comportement de type Hamilton-Jacobi (ou detype ergodique) se produit. Dans la troisième partie, consacrée à l’étude pour des Hamiltonienssous-quadratiques, nous montrons qu’il se produit un comportement de type (i) lorsque l’uniqueconstante ergodique c∗; du problème ergodique associé à des conditions aux limites de typeexplosives, est strictement négative et lorsque c∗ > 0 et 3/2< m ≤ 2; un comportement de type(ii) se produit, où m représente l’exposant du terme en gradient. Mais lorsque c∗ = 0 ou c∗ > 0et 1 < m ≤ 3/2; nous prouvons que pour certains domaines, la fonction u(x; t) + c∗t n’est pasminorée où u est la solution des équations de Hamilton-Jacobi visqueuses étudiées, produisantainsi un résultat de non-convergenceThe main goal of this thesis is the general study of the large time behavior of theunique solution of the Cauchy-Dirichlet problem for viscous Hamilton-Jacobi equations of subandsuperquadratic types. This work splits into three parts. After a brief review of basic conceptsof the theory on the viscosity solutions which is the framework of this work, the first part mainlyprovides results on the global in time existence and the uniqueness of the viscosity solution of theabove mentioned Cauchy-Dirichlet problem. The second part studies the large time behavior ofthat solution for superquadratic Hamiltonians. Under rather general assumtions, we prove thatthe behavior of the solution depends on the the sign of the unique ergodic constant c∗ of theergodic problem associated with boundary condition of state constraint-type. When c∗ < 0; weobtain (i) a convergence to the unique solution of the associated stationary problem whereaswhen c∗ ≥ 0; we obtain (ii) a behavior of Hamilton-Jacobi–type (or ergodic-type) happen.In thethird part, devoted to the study for subquadratic Hamiltonians, we prove that a behavior of(i)-type happens when the unique ergodic constant c∗; of the ergodic problem associated withblow-up boundary condition, is non-positve and when c∗ > 0 and 3/2 < m ≤ 2; we obtain abehavior of (ii)-type. But when c∗ = 0 ou c∗ > 0 et 1 < m ≤ 3/2; we prove that for some domains,the function u(x; t)+c∗t is unbounded from below where u is the solution of the studied viscousHamilton-Jacobi, thus providing us with a result of non-convergence
29
Lukiantchuki, Juliana Azoia. "Interpretação de resultados do ensaio SPT com base em instrumentação dinâmica." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18132/tde-24052013-103725/.
Анотація:
O ensaio de simples reconhecimento do solo (SPT) e usualmente utilizado para estimar a resistência do solo, atraves do índice NSPT, que representa a resistencia a penetração dinâmica do amostrador no solo. Esse índice é usado diretamente em correlações empíricas ou semi-empíricas na determinação da capacidade de suporte e recalque das fundações. Entretanto, esse ensaio tem sido alvo de críticas devido a utilização dessas correlações empíricas, geralmente baseadas em observações práticas e sem nenhum fundamento científico. Críticas também estão relacionadas com a dispersão dos resultados, devido a utilização de diferentes tipos de equipamentos e procedimentos executivos. O índice NSPT depende da parcela de energia que e efetivamente transmitida ao amostrador durante a queda do martelo. Assim, análises racionais dos resultados de ensaios SPT dependem essencialmente da estimativa da quantidade dessa energia. Por esse motivo, tem sido desenvolvidas diversas pesquisas relacionados com a energia envolvida no ensaio SPT. Este trabalho apresenta interpretações dos resultados do ensaio SPT a partir das quantidades de energia envolvidas durante a queda do martelo. Essas quantidades de energia são determinadas indiretamente, através dos sinais de força normal e aceleração durante a propagação da onda de tensão ao longo da composição de hastes. Para isso, foi desenvolvido um equipamento que inclui uma instrumentação capaz de registrar esses sinais de força normal e aceleração. Uma série de ensaios SPT foi realizada com instrumentação instalada tanto no topo como na base da composição de hastes. Esse arranjo permitiu estimar as quantidades de energia disponíveis no topo e na base da composição de hastes. Assim, foi possível determinar a eficiência dos equipamentos SPT com base na quantidade de energia que efetivamente atinge o amostrador. A partir dos sinais registrados, também foi possível determinar a resistência dinâmica mobilizada no sistema solo-amostrador. Os resultados experimentais foram comparados com resultados obtidos através de métodos teóricos, baseados no Princípio de Hamilton, para a determinação da resistência estática e dinâmica do solo. Essas análises mostraram que equações teóricas podem ser adequadas para a determinação da resistência do solo, desde que seja considerada a quantidade de energia que efetivamente atinge o amostrador. Desta forma, essas equações teóricas podem ser facilmente incorporadas na prática de projeto de fundações, contribuindo para o desenvolvimento de métodos baseados na quantidade de energia necessária para a penetração do amostrador no solo.The standard penetration test (SPT) is usually used to estimate the soil strength through the NSPT index which represents the dynamic reaction force of the sampler penetration into the soil. This index is directly used in empirical or semi-empirical correlations for the determination of the bearing capacity and foundation settlements. However, this test has been criticized due to the use of these empirical correlations, often based on practical observation without any scientific basis. Criticism is also related to result dispersion due to the use of different types of equipment and execution procedures. The NSPT index depends on the amount of energy that is effectively transmitted to the sampler during the hammer fall. Thus, rational analyses of the SPT test results essentially depend on the estimation of this amount of energy. For this reason, several studies related to the energy involved in SPT test have been developed. This research presents interpretations of the SPT test results from the amounts of energy involved during the hammer fall. These amounts of energy are indirectly assessed by means of normal force and acceleration signals during the stress wave propagation along the string of rods. For this reason, a device that includes instrumentation capable of registering these signals of normal force and acceleration was developed. A series of tests was performed with the instrumentation installed at the top and the bottom of the string of rods. This arrangement allowed estimating the amount of energy available at the top and bottom of the string of rods. Thus, it was possible to estimate the efficiency of the SPT equipment basing on the amount of energy that actually reaches the sampler. From the recorded signals, it was also possible to assess the dynamic reaction force mobilized in the soil-sample system. The results were compared with other results obtained by theoretical methods, based on the Hamilton´s Principle, for evaluating the static and dynamic reaction force of the soil. These analyzes have shown that theoretical equations may be suitable for the determination of the soil strength, provided that the amount of energy that actually reaches the sampler be considered. Thus, these theoretical equations can be easily incorporated into the practice of foundation designs contributing to the development of methods based on the amount of energy required for the penetration of the sampler into the soil.
30
Adams, Ross Montague. "A study of a class of invariant optimal control problems on the Euclidean group SE(2)." Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1006060.
Анотація:
The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
31
Flygare, Mattias. "Holonomic versus nonholonomic constraints." Thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-13378.
Анотація:
Courses in analytical mechanics for undergraduate students are often limited to treatment of holonomic constraints, which are constraints on coordinates. The concept of nonholonomic constraints, constraints on velocities, is usually only mentioned briefly and it is easy to get a wrongful idea of what they are and how to treat them. This text explains and compares the methods of deriving the Euler-Lagrange equations and the consequences when imposing different kinds of constraints. One way to properly treat both holonomic and nonholonomic constraints is given, pinpointing the difficulties and common errors. Along the way, the treatment in local coordinates is also put in more modern terms, in the language of differential geometry, which is the language most commonly used in modern texts on the subject.
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GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.
Анотація:
This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is divided in three parts.
The first part is devoted to analyze strong maximum principles for fully nonlinear second order degenerate PDEs structured on Hörmander vector fields, having as a particular example fully nonlinear subelliptic PDEs on Carnot groups. These results are achieved by introducing a notion of subunit vector field for these nonlinear degenerate operators in the spirit of the seminal works on linear equations. As a byproduct, we then prove some new strong comparison principles for equations that can be written in Hamilton-Jacobi-Bellman form and Liouville theorems for some second order fully nonlinear degenerate PDEs.
The second part of the thesis deals with time-dependent fractional Mean Field Game systems. These equations arise when the dynamics of the average player is described by a stable Lévy process to which corresponds a fractional Laplacian as diffusion operator. More precisely, we establish existence and uniqueness of solutions to such systems of PDEs with regularizing coupling among the equations for every order of the fractional Laplacian $sin(0,1)$. The existence of solutions is addressed via the vanishing viscosity method and we prove that in the subcritical regime the equations are satisfied in classical sense, while if $sleq1/2$ we find weak energy solutions. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We finally show uniqueness of solutions both under the Lasry-Lions monotonicity condition and for short time horizons.
The last part focuses on the regularizing effect of evolutive Hamilton-Jacobi equations with Hamiltonian having superlinear growth in the gradient and unbounded right-hand side. In particular, the analysis is performed both for viscous Hamilton-Jacobi equations and its fractional counterpart in the subcritical regime via a duality method. The results are accomplished exploiting the regularity of solutions to Fokker-Planck-type PDEs with rough velocity fields in parabolic Sobolev and Bessel potential spaces respectively.
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Veronese, Andrea. "Portfolio optimization in presence of a self-exciting jump process: from theory to practice." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/339574.
Анотація:
We aim at generalizing the celebrated portfolio optimization problem "à la Merton", where the asset evolution is steered by a self-exciting jump-diffusion process. We first define the rigorous mathematical framework needed to introduce the stochastic optimal control problem we are interesting in. Then, we provide a proof for a specific version of the Dynamic Programming Principle (DPP) with respect to the
general class of self-exciting processes under study. After, we state the Hamilton-Jacobi-Bellman (HJB) equation, whose solution gives the value function for the corresponding optimal control problem.
The resulting HJB equation takes the form of a Partial-Integro Differential Equation (PIDE), for which we prove both existence and uniqueness for the solution in the viscosity sense. We further derive a suitable numerical scheme to solve the HJB equation corresponding to the portfolio optimizationproblem. To this end, we also provide a detailed study of solution dependence on the parameters of the problem. The analysis is performed by calibrating the model on ENI asset levels during the COVID-19 worldwide breakout. In particular, the calibration routine is based on a sophisticated Sequential Monte Carlo algorithm.
34
Widehammar, Svante. "A Method for Dispersive Split Hopkinson Pressure Bar Analysis Applied to High Strain Rate Testing of Spruce Wood." Doctoral thesis, Uppsala University, Department of Materials Science, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2872.
Анотація:
En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet
Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB).
Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också.
Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden.
The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique.
Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed.
Tests on spruce wood specimens were carried out at a high strain rate (about 103 s-1) using the adapted SHPB technique, and for comparison at low (8×10-3 s-1) and medium (17 s-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.
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Schwalbe, Karsten. "Stochastic Fluctuations in Endoreversible Systems." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-219268.
Анотація:
In dieser Arbeit wird erstmalig der Einfluss stochastischer Schwankungen auf endoreversible Modelle untersucht. Hierfür wird die Novikov-Maschine mit drei verschieden Wärmetransportgesetzen (Newton, Fourier, asymmetrisch) betrachtet. Während die maximale verrichtete Arbeit und der dazugehörige Wirkungsgrad recht einfach im Falle konstanter Wärmebadtemperaturen hergeleitet werden können, ändern sich dies, falls die Temperaturen stochastisch fluktuieren können. Im letzteren Fall muss die stochastische optimale Kontrolltheorie genutzt werden, um das Maximum der zu erwartenden Arbeit und die dazugehörige Kontrollstrategie zu ermitteln. Im Allgemeinen kann die Lösung derartiger Probleme auf eine nichtlineare, partielle Differentialgleichung, welche an eine Optimierung gekoppelt ist, zurückgeführt werden. Diese Gleichung wird stochastische Hamilton-Jacobi-Bellman-Gleichung genannt. Allerdings können, wie in dieser Arbeit dargestellt, die Berechnungen vereinfacht werden, wenn man annimmt, dass die Fluktuationen unabhängig von der betrachteten Kontrollvariablen sind. In diesem Fall zeigen analytische Betrachtungen, dass die Gleichungen für die verrichtete Arbeit and den Wirkungsgrad ihre ursprüngliche Form behalten, aber manche Terme müssen durch entsprechende Zeitmittel bzw. Erwartungswerte ersetzt werden, jeweils abhängig von der betrachteten Art der Kontrolle. Basierend auf einer Analyse der Leistungsparameter im Falle einer Gleichverteilung der heißen Temperatur der Novikov-Maschine können Schlussfolgerungen auf deren Monotonieverhalten gezogen werden. Der Vergleich verschiedener, zeitunabhängiger, symmetrischer Verteilungen führt zu einer bis dato unbekannten Erweiterung des Curzon-Ahlborn-Wirkungsgrades im Falle kleiner Schwankungen. Weiterhin wird eine Analyse einer Novikov-Maschine mit asymmetrischen Wärmetransport, bei der das Verhalten der heißen Temperatur durch einen Ornstein-Uhlenbeck-Prozess beschrieben wird, durchgeführt. Abschließend wird eine Novikov-Maschine mit Fourierscher Wärmeleitung, bei der die Dynamik der heißen Temperatur von der Kontrollvariable abhängt, betrachtet. Durch das Lösen der Hamilton-Jacobi-Bellman-Gleichung können neuartige Schlussfolgerungen gezogen werden, wie derartige Systeme optimal zu steuern sindIn this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn
36
Tocci, Monaco Giovanni. "Analisi di nano piastre composite con effetti piezo-elettro-magneto-igrotermici e teoria non locale: teoria e applicazioni." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
Анотація:
Utilizzando la teoria delle piastre sottili di Kirchhoff in combinazione con la teoria elastica non locale del gradiente di deformazione del secondo ordine si analizza il comportamento statico, dinamico e d'instabilità di nanopiastre composite con proprietà piezo-elettro-magneto-igrotemiche. Le equazioni indefinite di equilibrio vengono ricavate attraverso il principio di Hamilton e la soluzione analitica è ottenuta utilizzando il campo di spostamenti alla Navier. Nell'elaborato vengono presentati prima i confronti con i risultati reperiti in letteratura scientifica e in seguito vengono esposti i nuovi risultati ottenuti durante il lavoro.
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MAININI, ALESSANDRA. "Saggi in economia dell'informazione." Doctoral thesis, Università Cattolica del Sacro Cuore, 2009. http://hdl.handle.net/10280/504.
Анотація:
Questa tesi è una raccolta di tre articoli riguardanti l’economia dell’informazione. Il primo articolo riguarda i possibili effetti negativi delle elezioni sul benessere degli elettori. Infatti, il controllo ottimo nei confronti di un politico dipende in modo non banale dalla relazione tra effetto disciplinante, effetto di selezione e effetto di riduzione della rendita. Il risultato è che un eccessivo controllo nei confronti di un politico può ridurre il benessere sociale. Il secondo articolo analizza un modello di competizione elettorale nel quale l’abilità del politico è sconosciuta anche al politico stesso oltre che agli elettori. L’analisi è in tempo continuo e sviluppata mediante tecniche di programmazione dinamica e di filtraggio. Le credenze sull’abilità vengono aggiornate secondo la regola di Bayes tramite l’osservazione del processo diffusivo che descrive il valore del settore pubblico. Il politico trae utilità da una rendita che è però inferiore in presenza di una scadenza elettorale. Il terzo articolo descrive una relazione principale-agente in tempo continuo dove l’output è rappresentato da un processo diffusivo il cui drift è determinato dallo sforzo dell’agente, che il principale non osserva, e dall’abilità dell’agente, che non è osservata nemmeno dall’agente stesso. Vengono analizzati sia gli incentivi espliciti dati dal contratto che gli incentivi impliciti legati ai career-concerns. L’analisi è sviluppata in tempo continuo; vengono applicate tecniche di programmazione dinamica e di filtraggio.This thesis is a collection of three essays about information economics. The first essay studies the possible negative effects of elections on voters’ welfare. In fact, the optimal control of politicians depends on the interplay of disciplining, selection and rent-shrinking effects in a non-trivial way. We show that too much control on the politician may reduce social welfare. The second essay studies an agency model of electoral competition where the incumbent’s ability is unknown to the voters as well as to the politician herself. The analysis is developed in a continuous-time stochastic framework using dynamic programming techniques. Competence is unobservable to everyone and learned over time in a Bayesian fashion through the observation of the value of the public sector. Politicians can divert resources being in office thus reducing the economy wealth but this rent is lower (all other things the same) with an electoral constraint. The third essay describes a continuous-time principal-agent model in which the output is a diffusion process whose drift is determined by the agent’s unobserved effort and by manager’s competence (it is assumed symmetric information about it). We study separately both explicit incentives arising from the contract and implicit incentives arising from career concerns.. All the analysis is developed in a continuous-time stochastic framework; we apply dynamic programming and filtering techniques.
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MAININI, ALESSANDRA. "Saggi in economia dell'informazione." Doctoral thesis, Università Cattolica del Sacro Cuore, 2009. http://hdl.handle.net/10280/504.
Анотація:
Questa tesi è una raccolta di tre articoli riguardanti l’economia dell’informazione. Il primo articolo riguarda i possibili effetti negativi delle elezioni sul benessere degli elettori. Infatti, il controllo ottimo nei confronti di un politico dipende in modo non banale dalla relazione tra effetto disciplinante, effetto di selezione e effetto di riduzione della rendita. Il risultato è che un eccessivo controllo nei confronti di un politico può ridurre il benessere sociale. Il secondo articolo analizza un modello di competizione elettorale nel quale l’abilità del politico è sconosciuta anche al politico stesso oltre che agli elettori. L’analisi è in tempo continuo e sviluppata mediante tecniche di programmazione dinamica e di filtraggio. Le credenze sull’abilità vengono aggiornate secondo la regola di Bayes tramite l’osservazione del processo diffusivo che descrive il valore del settore pubblico. Il politico trae utilità da una rendita che è però inferiore in presenza di una scadenza elettorale. Il terzo articolo descrive una relazione principale-agente in tempo continuo dove l’output è rappresentato da un processo diffusivo il cui drift è determinato dallo sforzo dell’agente, che il principale non osserva, e dall’abilità dell’agente, che non è osservata nemmeno dall’agente stesso. Vengono analizzati sia gli incentivi espliciti dati dal contratto che gli incentivi impliciti legati ai career-concerns. L’analisi è sviluppata in tempo continuo; vengono applicate tecniche di programmazione dinamica e di filtraggio.This thesis is a collection of three essays about information economics. The first essay studies the possible negative effects of elections on voters’ welfare. In fact, the optimal control of politicians depends on the interplay of disciplining, selection and rent-shrinking effects in a non-trivial way. We show that too much control on the politician may reduce social welfare. The second essay studies an agency model of electoral competition where the incumbent’s ability is unknown to the voters as well as to the politician herself. The analysis is developed in a continuous-time stochastic framework using dynamic programming techniques. Competence is unobservable to everyone and learned over time in a Bayesian fashion through the observation of the value of the public sector. Politicians can divert resources being in office thus reducing the economy wealth but this rent is lower (all other things the same) with an electoral constraint. The third essay describes a continuous-time principal-agent model in which the output is a diffusion process whose drift is determined by the agent’s unobserved effort and by manager’s competence (it is assumed symmetric information about it). We study separately both explicit incentives arising from the contract and implicit incentives arising from career concerns.. All the analysis is developed in a continuous-time stochastic framework; we apply dynamic programming and filtering techniques.
39
Lo, Hung-Chieh. "Vibration Characteristics of Thin-Walled Noncircular Composite Cylinders." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/77207.
Анотація:
The lowest natural frequencies of thin-walled noncircular fiber-reinforced composite cylinders, specifically cylinders with elliptical cross sections, are investigated. Of interest is the variation of the lowest natural frequency, the so-called fundamental frequency, as a function of wall laminate properties, cross-sectional eccentricity and other cylinder geometric parameters. Both simple and clamped support boundary conditions are investigated. Laminate properties that are uniform with circumferential location and laminate properties that vary with circumferential location, by way of varying laminate fiber angle with circumferential location, are considered. As the radius of curvature of a noncircular cylinder varies with circumferential location, it is logical to consider the influence of circumferentially varying fiber orientation on the fundamental frequency. The analysis for predicting the fundamental frequency is based on Donnell shell theory, linear elastic properties, and the use of Hamilton's Principle in conjunction with the Rayleigh-Ritz technique. By use of a so-called shape factor, the magnitude of cylinder normal displacements are modulated to be larger in the regions of the cross section with the largest radius of curvatures and smaller in the regions with the smallest radius of curvature. The final equations for predicting the fundamental frequency are quite complex, but a series of approximations results in a hierarchy of simpler equations, the simplest being referred to as Lo's approximation. The prediction of the fundamental frequencies is spot checked by comparing the results as predicted by the various levels of approximation with predictions of a shell-based finite element model. Considering uniform laminate properties, comparisons between the developed analysis and the finite element model are good for all levels of simpler equations, and excellent in some cases. The developed analysis is subsequently used for parameter studies. It is found that compared to a circular cylinder of the same circumference and with uniform laminate properties, the fundamental frequency of an elliptical cylinder is always less. Surprisingly, based on the results obtained, it appears that for a given cylinder geometry the fundamental frequency is not particularly sensitive to wall lamination sequence, though the wave number in the circumferential direction of the mode shape associated with the fundamental frequency is sensitive to lamination sequence. Considering cylinders with circumferentially varying fiber orientation, comparisons between the developed analysis and the finite element model for most of the cases studied are good. However, the developed equations are limited since it is difficult to find a set of known functions to describe the deformation of an arbitrary lamination sequence when applying the Rayleigh-Ritz technique. In general, in can be concluded that the effect of varying fiber orientation on the fundamental frequency is much less than the influence of cylinder aspect ratio. It can also be concluded that the developed analysis would be an excellent tool for design purposes, as the calculation of the fundamental frequency is done quickly, and design trade-offs studies would be easy.Ph. D.
40
Lorenz, Michael. "Berechnungsmodelle zur Beschreibung der Interaktion von bewegtem Sägedraht und Ingot." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-130678.
Анотація:
Die vorliegende Arbeit widmet sich der Aufgabe makroskopische Berechnungsmodelle zur Beschreibung des Drahtsägens zu erarbeiten. Ziel ist es, die wesentlichen Effekte abzubilden und den Einfluss von Prozessparametern auf die Dynamik des Systems zu bestimmen. Ein zentraler Punkt ist die Modellierung des bewegten Sägedrahtes. Durch die dem Kontinuum an den Auflagern aufgeprägte Führungsbewegung sind einerseits die Randbedingungen und andererseits ortsfest auf den Draht wirkende Lasten nichtmateriell. Die korrekte kinematische Beschreibung dieses Sachverhaltes ist essentielle Grundlage für die spätere Anwendung des Prinzips von HAMILTON. Durch die Führungsbewegung, die Formulierung der Kontaktkräfte als Folgelasten und durch explizit zeitabhängige Systemparameter ergibt sich ein kompliziertes Systemverhalten. Die dargestellten Berechnungsergebnisse umfassen Studien zu stationären Lagen, die Berechnung von Eigenfrequenzen, Stabilitätsnachweise des dynamischen Grundzustandes, die Bestimmung von Zeitlösungen und die Simulation des Materialabtrages beim EinschnittThe aim of the present thesis is to generate macroscopic models to describe the wire sawing process. The principal purpose is to illustrate basic effects and to investigate the influence of important process parameters relating to the dynamics of the system. A fundamental point is the modeling of the moving wire. Because of the axially movement of the continuum the boundary conditions and spatial acting loads are non-material. The precise kinematical description of this issue is the pre-condition for the correct evaluation of HAMILTON’s principle to characterize the dynamics of the system. The resultant complex system behavior is a consequence of the movement of the wire, of the formulation of the contact forces as follower loads and of explicitly time-dependent model parameters. The results of research contain studies of steady state equilibrium solutions and the proof of their LJAPUNOW stability, the calculation of eigenfrequencies, steady state time solutions under harmonically oscillating contact forces and the simulation of the material removal during the cutting process
41
Hermosilla, Cristopher. "Problèmes de commande optimale sur des domaines structurés et lois de commandes en boucles fermées stratifiées." Palaiseau, École nationale supérieure de techniques avancées, 2015. http://www.theses.fr/2015ESTA0011.
Анотація:
Cette thèse porte sur la théorie de la commande optimale. Les problèmes de contrôle optimal sous contraintes d'état bien structurées et les lois de feedback stratifiées sont considérés. Les techniques utilisées dans ce manuscrit concernent principalement la théorie de la commande, l'analyse non lisse, l'analyse variationnelle, la géométrie modérée, l'analyse convexe et les inclusions différentielles. La première partie de la thèse est consacrée à donner des résultats et définitions généraux mais nécessaires pour mieux comprendre les parties suivantes de la thèse. En particulier, un critère d'invariance forte est présenté. De plus, un bref aperçu sur les variétés lisses et les ensembles stratifiés est exposé. La notion d'ensemble relativement wedged est introduite et de plus, quelques de ses propriétés sont aussi analysées. La deuxième partie est concernée à caractériser la Fonction Valeur d'un problème de contrôle optimal sous contraintes d'état. Trois situations ont été considérées. Le premier cas traite les contraintes d'état qui sont également des ensembles stratifiés, c'est-à-dire ceux qui peuvent être décomposé en une collection de variétés de différents dimensions. La deuxième situation se concentre sur les systèmes linéaires sous contraintes d'état convexes. Le dernier cas considère aussi les contraintes d'état qui sont ensembles convexes mais avec une technique de pénalisation. Dans cette dernière situation, les dynamiques sont non linéaires et absorbants sur la frontière de l'ensemble de contraintes. La troisième partie se focalise sur les lois de feedback discontinues dont les ensembles de points singuliers ont une structure stratifiée par rapport à l'espace d'état. Ces contrôles produisent des équations différentielles ordinaires stratifiées, ce qui motive une étude sur l'existence des solutions et sur la robustesse par rapport aux perturbations externes de ses équations. La construction de lois de feedback continues mais sous-optimaux à partir de l'information fourni par les contrôles optimaux est aussi traitée dans cette partie. La quatrième partie est dédiée à l'étude des problèmes de contrôle optimale sur des réseaux. La principale contribution de cette étude est qu'il n'y a pas de hypothèse de contrôlabilité autour des jonctions. Les résultats sont étendus aux réseaux généralisés dont les jonctions ne sont plus de points isolés mais de variétésThe aim of this dissertation is to study some issues in Control Theory of ordinary differential equations. Optimal control problems with tame state-constraints and feedback controls with stratified discontinuities are of special interest. The techniques employed along the manuscript have been chiefly taken from control theory, nonsmooth analysis, variational analysis, tame geometry, convex analysis and differential inclusions theory. The first part of the thesis is devoted to provide general results and definitions required for a good understanding of the entire manuscript. In particular, a strong invariance criterion adapted to manifolds is presented. Moreover, a short insight into manifolds and stratifications is done. The notions of relatively wedged sets is introduced and in addition, some of its properties are stated. The second part is concerned with the characterization of the Value Function of an optimal control problem with state-constraints. Three cases have been taken into account. The first one treats stratifiable state-constraints, that is, sets that can be decomposed into manifolds of different dimensions. The second case is focused on linear systems with convex state-constraints, and the last one considers convex state-constraints as well, but from a penalization point of view. In the latter situation, the dynamics are nonlinear and verify an absorbing property at the boundary. The third part is about discontinuous feedbacks laws whose singularities form a stratified set on the state-space. This type of controls yields to consider stratified discontinuous ordinary differential equations, which motivates an analysis of existence of solutions and robustness with respect to external perturbation for these equations. The construction of a suboptimal continuous feedback from an optimal one is also addressed in this part. The fourth part is dedicated to investigate optimal control problems on networks. The main feature of this contribution is that no controllability assumption around the junctions is imposed. The results can also be extended to generalized notions of networks, where the junction is not a single point but a manifold
42
Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.
Анотація:
Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since then, there has been a strong development in the intrinsic treatment of a variety of topics in theoretical physics, applied mathematics and control theory using methods of differential geometry.
Most of the work done in geometrical physics since its first days has been devoted to study first-order theories, that is, those theories whose physical information depends on (at most) first-order derivatives of the generalized coordinates of position (velocities). However, there are theories in physics in which the physical information depends explicitly on accelerations or higher-order derivatives of the generalized coordinates of position, and thus more sophisticated geometrical tools are needed to model them acurately.
In this Ph.D. Thesis we pretend to give a geometrical description of some of these higher-order theories. In particular, we focus on dynamical systems and field theories whose dynamical information can be given in terms of a Lagrangian function, or a Hamiltonian that admits Lagrangian counterpart. More precisely, we will use the Lagrangian-Hamiltonian unified approach in order to develop a geometric framework for autonomous and non-autonomous higher-order dynamical system, and for second-order field theories. This geometric framework will be used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
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Ourodová, Ludmila. "Johann Georg de Hamilton. Život a dílo." Doctoral thesis, 2015. http://www.nusl.cz/ntk/nusl-334590.
Анотація:
The content of this dissertation is the life and œuvre of Johann Georg de Hamilton, a relatively obscure painter of hunts, portraits of horses, hunting still-lifes and hunting scenes. Johann Georg de Hamilton (1672-1737), a painter belonging to a famous Scottish family, was influenced in his creative work considerably by the 17th -century Flemish painters of still-lifes and hunting scenes. He was active predominantly in Vienna and in South Bohemia, in service of Adam František, Prince of Schwarzenberg, as well as Karl VI of House Habsburg. He created hunting-themed paintings and portraits of horses to members of both the secular and the ecclesiastic aristocracy of the lands of the Austrian Empire, such as the Houses of Liechtenstein, Serényi, Althan and others. This dissertation is the very first attempt at a monographic analysis of the life and œuvre of this painter. In addition to new bibliographic data, it offers an in-depth insight into the relationship between the person who commissioned his work, Adam František, Prince of Schwarzenberg, and the painter Johann Georg de Hamilton on the basis of extant correspondence, and also attempts to present the painter's œuvre in a cultural-historical and artistic context. The dissertation mentions the first exhibition of a collection of Hamilton's work,...
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POZZA, MARCO. "Stochastic representation formulas for viscosity solutions to nonlinear partial differential equations." Doctoral thesis, 2020. http://hdl.handle.net/11573/1386359.
Анотація:
We provide a representation formula for viscosity solutions to nonlinear second order PDE problems given as a sup-envelope function. This is done through a dynamic programming principle derived from Denis, Hu and Peng (2010). The formula can be seen as a nonlinear extension of the Feynman--Kac formula and is based on the backward stochastic differential equations theory.
45
Schwalbe, Karsten. "Stochastic Fluctuations in Endoreversible Systems." Doctoral thesis, 2016. https://monarch.qucosa.de/id/qucosa%3A20641.
Анотація:
In dieser Arbeit wird erstmalig der Einfluss stochastischer Schwankungen auf endoreversible Modelle untersucht. Hierfür wird die Novikov-Maschine mit drei verschieden Wärmetransportgesetzen (Newton, Fourier, asymmetrisch) betrachtet. Während die maximale verrichtete Arbeit und der dazugehörige Wirkungsgrad recht einfach im Falle konstanter Wärmebadtemperaturen hergeleitet werden können, ändern sich dies, falls die Temperaturen stochastisch fluktuieren können. Im letzteren Fall muss die stochastische optimale Kontrolltheorie genutzt werden, um das Maximum der zu erwartenden Arbeit und die dazugehörige Kontrollstrategie zu ermitteln. Im Allgemeinen kann die Lösung derartiger Probleme auf eine nichtlineare, partielle Differentialgleichung, welche an eine Optimierung gekoppelt ist, zurückgeführt werden. Diese Gleichung wird stochastische Hamilton-Jacobi-Bellman-Gleichung genannt. Allerdings können, wie in dieser Arbeit dargestellt, die Berechnungen vereinfacht werden, wenn man annimmt, dass die Fluktuationen unabhängig von der betrachteten Kontrollvariablen sind. In diesem Fall zeigen analytische Betrachtungen, dass die Gleichungen für die verrichtete Arbeit and den Wirkungsgrad ihre ursprüngliche Form behalten, aber manche Terme müssen durch entsprechende Zeitmittel bzw. Erwartungswerte ersetzt werden, jeweils abhängig von der betrachteten Art der Kontrolle. Basierend auf einer Analyse der Leistungsparameter im Falle einer Gleichverteilung der heißen Temperatur der Novikov-Maschine können Schlussfolgerungen auf deren Monotonieverhalten gezogen werden. Der Vergleich verschiedener, zeitunabhängiger, symmetrischer Verteilungen führt zu einer bis dato unbekannten Erweiterung des Curzon-Ahlborn-Wirkungsgrades im Falle kleiner Schwankungen. Weiterhin wird eine Analyse einer Novikov-Maschine mit asymmetrischen Wärmetransport, bei der das Verhalten der heißen Temperatur durch einen Ornstein-Uhlenbeck-Prozess beschrieben wird, durchgeführt. Abschließend wird eine Novikov-Maschine mit Fourierscher Wärmeleitung, bei der die Dynamik der heißen Temperatur von der Kontrollvariable abhängt, betrachtet. Durch das Lösen der Hamilton-Jacobi-Bellman-Gleichung können neuartige Schlussfolgerungen gezogen werden, wie derartige Systeme optimal zu steuern sind.In this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn.
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Lorenz, Michael. "Berechnungsmodelle zur Beschreibung der Interaktion von bewegtem Sägedraht und Ingot." Doctoral thesis, 2013. https://tubaf.qucosa.de/id/qucosa%3A22896.
Анотація:
Die vorliegende Arbeit widmet sich der Aufgabe makroskopische Berechnungsmodelle zur Beschreibung des Drahtsägens zu erarbeiten. Ziel ist es, die wesentlichen Effekte abzubilden und den Einfluss von Prozessparametern auf die Dynamik des Systems zu bestimmen. Ein zentraler Punkt ist die Modellierung des bewegten Sägedrahtes. Durch die dem Kontinuum an den Auflagern aufgeprägte Führungsbewegung sind einerseits die Randbedingungen und andererseits ortsfest auf den Draht wirkende Lasten nichtmateriell. Die korrekte kinematische Beschreibung dieses Sachverhaltes ist essentielle Grundlage für die spätere Anwendung des Prinzips von HAMILTON. Durch die Führungsbewegung, die Formulierung der Kontaktkräfte als Folgelasten und durch explizit zeitabhängige Systemparameter ergibt sich ein kompliziertes Systemverhalten. Die dargestellten Berechnungsergebnisse umfassen Studien zu stationären Lagen, die Berechnung von Eigenfrequenzen, Stabilitätsnachweise des dynamischen Grundzustandes, die Bestimmung von Zeitlösungen und die Simulation des Materialabtrages beim Einschnitt.:1 Einleitung
1.1 Technische Problemstellung und Motivation der Arbeit
1.2 Literaturübersicht
1.3 Thema und Gliederung der Arbeit
2 Theoretische Grundlagen
2.1 Notation und mathematische Grundlagen
2.2 Kinematische Grundlagen der Kontinuumsmechanik
2.2.1 Konfiguration und Betrachtungsweisen
2.2.2 Verformungskinematik
2.2.3 Zeitableitungen
2.3 Variationsrechnung
2.3.1 Grundlagen
2.3.2 Verallgemeinerte Variationen
2.4 Kinetik / Prinzip von HAMILTON
2.5 Diskretisierung von Feldproblemen
2.6 Stabilität stationärer Lösungen
2.6.1 Grundlagen der kinetischen Stabilitätstheorie
2.6.2 Erste Methode von LJAPUNOW
2.6.3 Stabilitätsbetrachtung für bewegte Kontinua
2.7 Zeitlösung
2.7.1 Homogene Lösung der Störungsdifferentialgleichungen
2.7.2 Partikuläre Lösung der Störungsdifferentialgleichungen
3 Mechanisches Modell und Modellvarianten
3.1 Kinematik des Drahtes in LAGRANGE-Koordinaten
3.2 Kinematik des Drahtes in EULER-Koordinaten
3.3 Modell I
3.3.1 Variationsformulierung und Feldgleichungen
3.3.2 Ortsdiskretisierung der Variationsformulierung
3.3.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung
3.4 Modell II
3.4.1 Variationsformulierung und Feldgleichungen
3.4.2 Ortsdiskretisierung der Variationsformulierung
3.4.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung
3.5 Numerische Umsetzung
3.6 Berechnungsergebnisse
3.6.1 Stationäre Lagen
3.6.2 Eigenfrequenzen
3.6.3 Stabilitätsuntersuchungen
3.6.4 Zeitlösungen
4 Ankopplung des Ingot und Modellierung des Materialabtrages
4.1 FE- Modell des Gesamtblocks
4.1.1 Bestimmung der mechanischen Eigenschaften des Ingot
4.1.2 Berechnungsergebnisse
4.2 Strukturmechanisches Modell des Gesamtblocks und Ankopplung an den Sägedraht
4.3 Variationsformulierungen der gekoppelten Gesamtsysteme unter Berücksichtigung des Materialabtrages
4.3.1 Gesamtmodell I
4.3.2 Gesamtmodell II
4.4 Simulation des Schnittvorganges
5 Zusammenfassung / Ausblick
6 Verzeichnisse
6.1 Literaturverzeichnis
6.1.1 Allgemeine Literatur
6.1.2 Literatur zum Thema Drahtsägen
6.1.3 Literatur zum Thema bewegte Kontinua
AnhangThe aim of the present thesis is to generate macroscopic models to describe the wire sawing process. The principal purpose is to illustrate basic effects and to investigate the influence of important process parameters relating to the dynamics of the system. A fundamental point is the modeling of the moving wire. Because of the axially movement of the continuum the boundary conditions and spatial acting loads are non-material. The precise kinematical description of this issue is the pre-condition for the correct evaluation of HAMILTON’s principle to characterize the dynamics of the system. The resultant complex system behavior is a consequence of the movement of the wire, of the formulation of the contact forces as follower loads and of explicitly time-dependent model parameters. The results of research contain studies of steady state equilibrium solutions and the proof of their LJAPUNOW stability, the calculation of eigenfrequencies, steady state time solutions under harmonically oscillating contact forces and the simulation of the material removal during the cutting process.:1 Einleitung 1.1 Technische Problemstellung und Motivation der Arbeit 1.2 Literaturübersicht 1.3 Thema und Gliederung der Arbeit 2 Theoretische Grundlagen 2.1 Notation und mathematische Grundlagen 2.2 Kinematische Grundlagen der Kontinuumsmechanik 2.2.1 Konfiguration und Betrachtungsweisen 2.2.2 Verformungskinematik 2.2.3 Zeitableitungen 2.3 Variationsrechnung 2.3.1 Grundlagen 2.3.2 Verallgemeinerte Variationen 2.4 Kinetik / Prinzip von HAMILTON 2.5 Diskretisierung von Feldproblemen 2.6 Stabilität stationärer Lösungen 2.6.1 Grundlagen der kinetischen Stabilitätstheorie 2.6.2 Erste Methode von LJAPUNOW 2.6.3 Stabilitätsbetrachtung für bewegte Kontinua 2.7 Zeitlösung 2.7.1 Homogene Lösung der Störungsdifferentialgleichungen 2.7.2 Partikuläre Lösung der Störungsdifferentialgleichungen 3 Mechanisches Modell und Modellvarianten 3.1 Kinematik des Drahtes in LAGRANGE-Koordinaten 3.2 Kinematik des Drahtes in EULER-Koordinaten 3.3 Modell I 3.3.1 Variationsformulierung und Feldgleichungen 3.3.2 Ortsdiskretisierung der Variationsformulierung 3.3.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung 3.4 Modell II 3.4.1 Variationsformulierung und Feldgleichungen 3.4.2 Ortsdiskretisierung der Variationsformulierung 3.4.3 Stationäre Lage, Stabilitätsuntersuchung und Zeitlösung 3.5 Numerische Umsetzung 3.6 Berechnungsergebnisse 3.6.1 Stationäre Lagen 3.6.2 Eigenfrequenzen 3.6.3 Stabilitätsuntersuchungen 3.6.4 Zeitlösungen 4 Ankopplung des Ingot und Modellierung des Materialabtrages 4.1 FE- Modell des Gesamtblocks 4.1.1 Bestimmung der mechanischen Eigenschaften des Ingot 4.1.2 Berechnungsergebnisse 4.2 Strukturmechanisches Modell des Gesamtblocks und Ankopplung an den Sägedraht 4.3 Variationsformulierungen der gekoppelten Gesamtsysteme unter Berücksichtigung des Materialabtrages 4.3.1 Gesamtmodell I 4.3.2 Gesamtmodell II 4.4 Simulation des Schnittvorganges 5 Zusammenfassung / Ausblick 6 Verzeichnisse 6.1 Literaturverzeichnis 6.1.1 Allgemeine Literatur 6.1.2 Literatur zum Thema Drahtsägen 6.1.3 Literatur zum Thema bewegte Kontinua Anhang