L’Objectif de cette thèse est de développeré une théorie de l’identification spécifique pour les systèmes Hamiltonien à ports. Les raisons principales pour motiver cette théorie résident dans les propriétés remarquables de ces systèmes, notamment leur structure de Dirac et sa stabilité par interconnexion conservative de puissance (e.g. parallèle, séries ou feedback). Dans la première partie, les systèmes Hamiltoniens sont analysés en ce qui concerne leur identifiabilité structurelle, par par analyse de leur observabilité/commandabilité, par tests directs, par l’analyse en série de puissance de leur fonction de transfert ou par une nouvelle approche énergétique d’analyse d’une identifiabilité spécifique associée à un port. Dans la partie suivante, des modèles de perturbation par port d’interaction sont introduits et permettent l’analyse de l’identifiabilité « pratique » des systèmes hamiltoniens à ports. Le quatrième chapitre présente des schémas de discrétisation en temps qui préserve les bilans de puissance et d’énergie et leur application sur des exemples de système hamiltoniens à ports linéaires et non linéaires. L’erreur de discrétisation est analysée en introduisant la notion de représentation hamiltonienne de l’erreur de discrétisation. Dans la dernière partie de cette thèse, une approche d’identification dans l’espace d’état est développée pour les systèmes obtenus par discrétisation symplectique des systèmes hamiltoniens à ports. Les cas déterministe est analysé et une approche énergétique basée sur les résultats d’identifiabilité structurelle développé dans la première partie est proposée. Enfin, dans la dernière partie, les contributions du travail sont rappelées et quelques perspectives pour des travaux futurs sont présentées. / The objective of this thesis is to develop a specific identification theory for Port Controlled Hamiltonian (PCH) systems. The main reasons to develop this theory comes from their remarkable properties like power conservation and stability under power preserving interconnection (e.g. parallel, series or feedback interconnections). In a first part PCH systems are analysed for structural identifiability using some classical or new techniques: observability/controllability identifiability, direct test, power series expansion or a new power energy approach, defining also a new concept of port identifiability. Further it is proposed a perturbation model by means of the interaction port together with a practical identifiability analysis realized using the controllability and observability concepts. The fourth part presents a new framework for time-discretization of PCH systems in the nonlinear or linear case, by combined discretization of the flows and efforts preserving in the same time their characteristic properties. Also in this part it is proposed a discretization error Hamiltonian to distinguish the continuous-time PCH system from the discrete-time one. The fifth part of the thesis makes an analysis of PCH systems identifiability using the subspace identification approach in the deterministic case, proposing also a new power energy approach in direct connection with the structural identifiability results. In the end are presented the main conclusions, personal contributions and perspectives for future work.

Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...

Markov chain Monte Carlo (MCMC) methods are a widely applicable class of algorithms for estimating integrals in statistical inference problems. A common approach in MCMC methods is to introduce additional auxiliary variables into the Markov chain state and perform transitions in the joint space of target and auxiliary variables. In this thesis we consider novel methods for using auxiliary variables within MCMC methods to allow approximate inference in otherwise intractable models and to improve sampling performance in models exhibiting challenging properties such as multimodality. We first consider the pseudo-marginal framework. This extends the Metropolis–Hastings algorithm to cases where we only have access to an unbiased estimator of the density of target distribution. The resulting chains can sometimes show ‘sticking’ behaviour where long series of proposed updates are rejected. Further the algorithms can be difficult to tune and it is not immediately clear how to generalise the approach to alternative transition operators. We show that if the auxiliary variables used in the density estimator are included in the chain state it is possible to use new transition operators such as those based on slice-sampling algorithms within a pseudo-marginal setting. This auxiliary pseudo-marginal approach leads to easier to tune methods and is often able to improve sampling efficiency over existing approaches. As a second contribution we consider inference in probabilistic models defined via a generative process with the probability density of the outputs of this process only implicitly defined. The approximate Bayesian computation (ABC) framework allows inference in such models when conditioning on the values of observed model variables by making the approximation that generated observed variables are ‘close’ rather than exactly equal to observed data. Although making the inference problem more tractable, the approximation error introduced in ABC methods can be difficult to quantify and standard algorithms tend to perform poorly when conditioning on high dimensional observations. This often requires further approximation by reducing the observations to lower dimensional summary statistics. We show how including all of the random variables used in generating model outputs as auxiliary variables in a Markov chain state can allow the use of more efficient and robust MCMC methods such as slice sampling and Hamiltonian Monte Carlo (HMC) within an ABC framework. In some cases this can allow inference when conditioning on the full set of observed values when standard ABC methods require reduction to lower dimensional summaries for tractability. Further we introduce a novel constrained HMC method for performing inference in a restricted class of differentiable generative models which allows conditioning the generated observed variables to be arbitrarily close to observed data while maintaining computational tractability. As a final topicwe consider the use of an auxiliary temperature variable in MCMC methods to improve exploration of multimodal target densities and allow estimation of normalising constants. Existing approaches such as simulated tempering and annealed importance sampling use temperature variables which take on only a discrete set of values. The performance of these methods can be sensitive to the number and spacing of the temperature values used, and the discrete nature of the temperature variable prevents the use of gradient-based methods such as HMC to update the temperature alongside the target variables. We introduce new MCMC methods which instead use a continuous temperature variable. This both removes the need to tune the choice of discrete temperature values and allows the temperature variable to be updated jointly with the target variables within a HMC method.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 1996-08Bitstream added on 2014-06-13T19:32:40Z : No. of bitstreams: 1 teixeira_rg_me_ift.pdf: 565736 bytes, checksum: 47638723d76926fa1da8cc7e9ede904d (MD5) / Neste trabalho apresentamos o formalismo Hamiltoniano de Dirac para sistemas singulares, analisando inclusive a construção do gerador de transformações de gauge. A seguir discutimos brevemente a generalização, já conhecida, desse formalismo para o caso de Lagrangeanos singulares de segunda ordem fazendo também uma análise da estrutura de vínculos presente em tais teorias. Desenvolvemos então o formalismo de Hamilton-Jacobi para sistemas singulares fazendo sua generalização para Lagrangeanos de segunda ordem. Por último, ambos formalismos são aplicados à Eletrodinâmica de Podols y e os resultados obtidos são comparados. / In this work we study Dirac's Hamiltonian formulation for singular systems including the construction of the gauge transformations generator. Next we briefy discuss the generalization, already developed, of this formalism for singular second order La grangians. Besides that we also make an anlysis of the constrains structure present in such theories. Then we develop the Hamilton-Jacobi formalism for singular systems making its generalization for the case of second order Lagrangians. Finally, both formalisms are applied to Podols y's eletrodynamics and the obtained results are comparad.

Submitted by Célia Mayumi Kuwana (celiamkuwana@hotmail.com) on 2018-05-16T16:10:10Z No. of bitstreams: 1 kuwana_cm_me_rcla.pdf: 1196862 bytes, checksum: 37b452d62ccbc0a6e02de1a013df0849 (MD5) / Rejected by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br), reason: Prezada Célia, O documento enviado para a coleção Instituto de Biociências Rio Claro foi recusado pelo(s) seguinte(s) motivo(s): - Falta a capa, elemento obrigatório, que deve ser inserida antes da folha de rosto no arquivo pdf. - Falta a informação de Aprovada na folha de aprovação, sendo que a folha, deve ser solicitada à Seção de Pós-Graduação e inserida após a ficha catalográfica. O documento enviado não foi excluído. Para revisá-lo e realizar uma nova tentativa de envio, acesse: https://repositorio.unesp.br/mydspace Em caso de dúvidas entre em contato pelo email repositoriounesp@reitoria.unesp.br. Agradecemos a compreensão e aguardamos o envio do novo arquivo. Atenciosamente, Biblioteca Campus Rio Claro Repositório Institucional UNESP https://repositorio.unesp.br on 2018-05-16T17:44:23Z (GMT) / Submitted by Célia Mayumi Kuwana (celiamkuwana@hotmail.com) on 2018-05-17T18:36:34Z No. of bitstreams: 2 kuwana_cm_me_rcla.pdf: 1196862 bytes, checksum: 37b452d62ccbc0a6e02de1a013df0849 (MD5) kuwana_cm_me_rcla.pdf: 1484457 bytes, checksum: 49f6c72467f2a1cd318e79d6f53b0ec8 (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-05-18T16:28:17Z (GMT) No. of bitstreams: 1 kuwana_cm_me_rcla.pdf: 1334658 bytes, checksum: f623f773fd644ffaefb15c97d13db854 (MD5) / Made available in DSpace on 2018-05-18T16:28:17Z (GMT). No. of bitstreams: 1 kuwana_cm_me_rcla.pdf: 1334658 bytes, checksum: f623f773fd644ffaefb15c97d13db854 (MD5) Previous issue date: 2018-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho apresentaremos e discutiremos algumas propriedades dinâmicas para uma família de mapeamentos discretos que preservam a área no espaço de fases nas variáveis momentum, I, e coordenada generalizada, θ. O mapeamento é descrito por dois parâmetros de controle, sendo eles ε, ajustando a intensidade da não linearidade, e γ, um parâmetro que fornece a forma da divergência da variável “θ”no limite em que I → 0. O parâmetro ε controla a transição de integrabilidade, quando ε = 0, para não integrabilidade, no limite em que ε ≠ 0. O objetivo principal deste trabalho é descrever o comportamento das curvas do momentum médio, I_RMS(ε,n), em função de n, a partir de uma função de probabilidade, P(I(n)), de observar um determinado momentum I em um instante n. Para tanto, resolveremos a Equação da Difusão analiticamente, considerando os casos: (i) o momentum inicial nulo, I_0 = 0, e (ii) o momentum inicial não nulo, I_0 ≠ 0. Nossos resultados descrevem bem os resultados fenomenológicos conhecidos na literatura (Physics Letters A, 379: 1808 (2015)). / In this work we will present and discuss some dynamical properties of a family of mappings that preserves area in the phase space for two variables momentum, I, and generalized coordinate, θ. The mapping is controled by two parameters: ε, tunning the intensity of nonlinearity, and γ, that describes the form of divergence of θ when I → 0. The parameter ε defines a transition from integrability, when ε = 0, to nonintegrability, when ε ≠ 0. The main goal of this work is to describe the curves of average momentum, I_RMS(ε,n), in terms of n, from a probability function, P(I(n)), to observe a determined momentum I at an instant n. Therefore, we will solve the Diffusion equation analitically considering the cases: (i) the initial momentum is null, I_0 = 0, and (ii) the initial momentum is nonzero, I_0 ≠ 0. Our results describe well the known phenomenological results in literature (Physics Letters A, 379: 1808 (2015)). / CAPES-DS: 3300413-7.

Les propriétés des matériaux ferroélectriques proviennent principalement de l’influencedes conditions aux limites et des déformations sur la polarisation. Cette influence est encoreplus grande à de petites échelles ou des structures particulières de la polarisation apparaissent,comme les vortex dans les cubes quantiques ou des structures en rayures dans lescouches minces. Pour le calcul, à très basses échelles, de telles structures de polarisation, lesHamiltonien effectifs, basés sur les calculs ab-initio sont les plus utilisés. Parallèlement Lesmodèles continus sont préconisés à plus grandes échelles. Néanmoins, il n’existe pas de lienentre ces deux modèles. Le but de cette thèse est alors de construire une approche permettantde relier ces deux modèles et par cela même ces différentes échelles.Notre modèle se base sur un Hamiltonien effectif écrit pour le titanate de baryum enfonction de la polarisation et des déformations. Cet Hamiltonien est reformulé de façon àdécrire un milieu continu. Les difficultés de cette reformulation proviennent des interactionsnon locales. Le résultat est alors un système d’équations aux dérivées partielles, décrivantl’équilibre et les conditions aux limites. La température est ensuite introduite de façon effectivedans les coefficients de ces équations. Notre modèle ressemble fortement aux modèlesde Landau.Une telle approche est appliquée dans les cubes quantiques et les couches minces óu l’organisationdes domaines dépend de la taille. Les résultats montrent l’implication de la méthodedes éléments finis sur la précision. La formation de vortex dans les cubes quantiquesest bien reproduite. L’agencement en domaines de polarisation alternée dans les couchesminces est elle aussi bien reproduite pour les couches minces. De plus en augmentant l’épaisseurde ces couches minces, la périodicité de cet agencement alterné est modifié, comportementdécrit par la loi de Kittel qui est ici calculée et comparée aux résultats expérimentaux. / Physicals properties of ferroelectric materials mainly arise from the fact that the polarizationis strongly influenced by strain and electrical boundary conditions, which may changeits orientation and magnitude. At small scales, this influence is even stronger and unusualdomain structures are produced like vortices in quantum dots or stripes in thin films. For thecalculation of domain structures, at small scales, first-principle-based effective Hamiltonianare widely used whereas at higher scales, continuum models are predominants. Nevertheless,in between there is no computational method connecting both scales. Therefore„ thegoal of this dissertation is to develop and build new approaches in order to bridge these twoseparated scales.Our model stems for classical effective Hamiltonian, written for barium titanate as afunction of the polarization and strain. This Hamiltonian is then formulated in order tocorrespond to a continuous description. Difficulties arise from non local interactions. In theend, the Hamiltonian is transformed into a set of partial differential equations describing theequilibrium and the boundary conditions. The temperature is then introduced in such a waythat makes evolve the coefficients of those sets of equations. We therefore reconstructed aLandu-like model.Such approach can be applied in quantum dots and thin films where the domain organizationdepend on the size. The results show how to apply finite element in order to obtainpatterns of polarizations with the wanted precision. The vortices shapes of domain patternin quantum dots is well reproduced. The stripes-like polarization pattern is also well reproducedin thin films. Besides expanding thickness of those films change the periodicity ofthose stripes, behaviour described by the Kittel law. This law is calculated and compared tomeasurements.

Le défis principal de l'industrie de la micro électronique est de créer d'augmenter la capacité de stockage mais aussi la vitesse des ordinateurs. Pour atteindre cette objectif, les composants électroniques doivent être miniaturisés à l'échelle du nanomètre. À cette échelle, les propriétés de la matière sont encore mal connues.Les matériaux les plus prometteurs dans cette recherche sont les multiferroïques où l'ordre magnétique et l'ordre ferroélectrique sont couplés. Ils pourraient amener des composants électroniques plus rapide et moins consommateur d'énergie dans des composants tels que les Random Access Memory. Ce travail traite de l'étude d'un multiferroïque typique BiFeO3 (BFO) en se concentrant sur les couplages entre les ordres magnétiques, ferroélectriques et le contrainte dans des systèmes de taille nanométrique / A major challenge in microelectronics is the increase of data storage as well as processors performancies. Unfortunatelly, this challenge involves a drastic reduction of size of the fundamental device of a computer down to the nano scale. At this scale, properties of matter are still not fully understood. One of the key materials to reach this challenge are multiferroics where the magnetism and the ferroelectricity can interact leading to low consuming and fast Random Access Memories. This work deals with the study of famous multiferroics BiFeO3 (BFO) focussing on the coupling between magnetic ordering, ferroelectric ordering and strain as the dimensionality of the system is reduced to several nanometers

Neste trabalho foi realizado um estudo do transporte de partículas em um plasma, confinado em um campo magnético uniforme, devido às ondas eletrostáticas de deriva. O modelo adotado consiste em descrever o movimento do centro de guia de uma partícula no campo magnético perpendicular a um campo elétrico radial perturbado pelas ondas de deriva. Usamos uma descrição Hamiltoniana para o movimento dos centros de guia. A velocidade de deriva produzida pelo campo elétrico radial é representada pela parte integrável da Hamiltoniana e a esta foram adicionadas perturbações periódicas representando as flutuações do campo elétrico associadas às ondas de deriva. Assim, obtemos órbitas caóticas que determinam o transporte radial das partículas. Apresentamos, para várias condições de equilíbrio, a variação do transporte radial de partículas com a amplitude da perturbação. Utilizamos dados experimentais, sobre a turbulência eletrostática no tokamak TBR-1, para verificar a validade do modelo e a importância das ondas de deriva no transporte radial das partículas. Comparamos os valores do coeficiente de difusão experimental com os do modelo e obtivemos os resultados com a mesma ordem de grandeza. / In this work we have studied the transport of particles in a magnetically confined plasma, due to electrostatic drift waves. The adopted model describes the trajectory of the guiding center of a particle in a uniform magnetic field perpendicular to a radial electric field perturbed by drift waves. We have used the Hamiltonian description for the guiding center trajectory. The drift produced by the radial electric field is represented by the integrable part of the Hamiltonian, while the other part contains periodic perturbations representing the fluctuations of the electric field associated to the drift waves. In this way we obtain chaotic orbits that determine the particles radial transport. For several balance conditions, we present the variation of the radial transport of particles with the amplitude of the perturbation. V/e have used the experimental data of the electrostatic turbulence measured in TBR-1 tokamak to verify, the validity of the model and the importance of the drift waves in the particles radial transport. We have also compared the values of the experimental diffusion coefficient with those provided by using the model, obtaining results with the same order of magnitude.

Através de um mapa de ondas de deriva, estudamos o transporte de partículas no Texas Helimak, considerando diversos perfis do campo elétrico radial. O Texas Helimak é um equipamento de confinamento magnético caracterizado por linhas de campo helicoidais e que fornece uma aproximação experimental de um plasma unidimensional. Ele possibilita a imposição de um potencial elétrico externo ao plasma, chamado bias, que altera o perfil radial do campo elétrico de equilíbrio e, consequentemente, possui influência sobre as características de transporte no plasma. Para estudar o efeito do bias sobre o transporte, utilizamos um modelo que considera flutuações eletrostáticas, associadas à deriva E x B, como mecanismo de turbulência. Com isso, introduzimos um mapa de ondas de deriva, cujos parâmetros estão relacionados a dados experimentais para diversos valores de bias. Assim, ao variar o bias, pudemos observar a formação e a destruição da curva sem shear, bem como seu efeito sobre o transporte das trajetórias no espaço de fase. / Using a drift wave map, we studied the particle transport in Texas Helimak considering various electric field radial profiles. Texas Helimak is a device for magnetic confinement characterized by helical field lines, and constitutes an experimental approximation to a one-dimensional plasma. It allows for the imposing of an external electric potential, known as bias, which changes the equilibrium electric field radial profile and hence the transport properties of the plasma. In order to study the effects of the bias potential on the particle transport, we used a model with electrostatic fluctuations associated to E x B drift as the turbulence mechanism. Thus, we introduced a drift wave map whose parameters are related to experimental data for various values of bias. Therefore, by varying the bias, we observed the formation and destruction of the shearless curve, as well as its effects on trajectories transport in the map\'s phase space.

A presente tese analisa diferentes aspectos de sistemas de espalhamento clássico com caos. Espalhamento caótico é uma forma de caos transiente que ocorre em diversos sistemas físicos. Nestes sistemas o espaço de fase é aberto, mas o caos ocorre apenas em uma região restrita do espaço, chamada de região de espalhamento. Os efeitos desta dinâmica apresentam-se em qualquer relação de espalhamento pela presença de conjuntos fractais, que geram hiper-sensibilidade a condições iniciais. Em nosso primeiro trabalho, mostramos que as bifurcações que levam ao caos manifestam-se na Seção de Choque Diferencial (SCD) pela criação de infinitas singularidades arco-íris. Estas singularidades aparecem na forma de cascatas, registrando na SCD todas as transições sofridas pela sela caótica. O segundo trabalho mostra que a introdução de dissipação em sistemas de espalhamento pode limitar a autosimilaridade de conjuntos originalmente fractais. Uma partícula espalhada por potenciais repulsivos encontra regiões não acessíveis, que dependem do valor de sua energia. Estas regiões determinam a estrutura da sela caótica. Com a perda de energia, o cenário de órbitas presas é alterado e, dependendo do valor da dissipação, podem existir nas funções de espalhamento estruturas fractais truncadas. O terceiro estudo aborda a presença de advecção caótica em fluxos sanguíneos. Doenças circulatórias estão geralmente associadas a uma mudança de geometria de artérias ou veias. Essas deformações podem gerar espalhamento caótico das partículas sanguíneas carregadas pelo fluxo. Em nosso trabalho mostramos, a partir de simulações numéricas, que caos pode existir em fluxos sanguíneos e, assim, formar um ciclo no desenvolvimento de anomalias circulatórias. / In this thesis we study different scattering systems with chaos. Chaotic scattering, present in a large variety of physical systems, is a type of transient chaos. While the phase-space of such systems is unbounded, irregular motion occurs only in a bounded area, called the scattering region. Still, any (nontrivial) scattering function relating initial conditions to asymptotic variables contains fractal structures, resulting in a very sharp sensitivity to initial conditions. Our first work shows that bifurcations leading to chaos manifest themselves through an infinitely fine-scale structure of rainbow singularities in the cross section. These singularities appear as cascades, mirroring the bifurcation cascade undergone by the chaotic saddle. The second work shows that the presence of dissipation in scattering systems can limit the auto-similarity of originally fractal structures. Depending on the value of their energy, particles scattered by repulsive potentials find forbidden regions in the space-phase. These regions determinate the structure of the chaotic saddle. With friction, the scenario of trapped orbits changes and, depending on the ammount dissipation, scattering functions follow a truncated fractal structure. Our third study concerns the presence of chaotic advection in blood flows. Typically, circulatory diseases are due to sudden changes on the geometry of vessel walls. These deformations can generate chaotic scattering of blood particles carried by the flow. We show, with numerical simulations, that chaos can occur in blood flows and thus form a hazardous cycle in the further developing of circulatory anomalies.