Este trabalho trata o problema genérico da obtenção analítica exata das variedades algébricas que definem domínios de estabilidade e multiestabilidade para sistemas dinâmicos dissipativos com equações de movimento definidas por funções racionais. Apresentamos um método genérico, válido para qualquer sistema dinâmico, que permite reduzir a análise de sistemas multidimensionais arbitrários à análise de um sistema unidimensional equivalente. Este método é aplicado ao mapa de Hénon, o exemplo paradigmático de sistema multidimensional, para estudar a estrutura aritmética imposta pela dinâmica das órbitas de períodos 4, 5, e 6, bem como seus domínios de estabilidade no espaço de parâmetros. Graças à obtençao de resultados analíticos exatos, podemos explorar pela primeira vez as peculariedades de cada um dos períodos mencionados. Algumas das novidades mais marcantes encontradas são as seguintes: Para período 4, encontramos um domínio de multiestabilidade caracterizado pela coexistência de duas órbitas definidas em corpos algébricos distintos. Observamos a existência de discontinuidades na dinâmica simbólica quando os parâmetros são mudados adiabáticamente ao longo de circulações fechadas no espaço de parâmetros e explicamos sua origem algébrica. Publicamos tais resultados em dois artigos: Physica A, 295, 285-290(2001) e Physical Review E, 65, 036231 (2002). Para período 5, obtivemos a variedade algébrica que define o "camarão" (shrimp) característico, obtemos uma expressão analítica para todas as órbitas de período 5, classificamos todas as singulariedades presentes no espaço de parâmetros e analisamos todas as mudanças que ocorrem ao circular-se em torno de tais singulariedades. Para período 6, da expressão analítica que fornece todas as órbitas, encontramos um resultado muito surpreendente, o mais notável desta dissertação: a possibilidade de coexistência de órbitas reais e complexas estáveis, para valores reais dos parâmetros físicos. Resultados preliminares parecem indicar serem tais órbitas complexas uma espécie de órbitas fantasmas, com semelhanças as órbitas encontradas por Gutzwiller para sistemas Hamiltonianos (não- dissipativos).

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-20T17:21:43Z No. of bitstreams: 2 Dissertação - Túlio Max de Oliveira Guimarães - 2014.pdf: 2190502 bytes, checksum: 95a9c8660ff6a8f4fee3c71a61784e47 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-21T10:06:29Z (GMT) No. of bitstreams: 2 Dissertação - Túlio Max de Oliveira Guimarães - 2014.pdf: 2190502 bytes, checksum: 95a9c8660ff6a8f4fee3c71a61784e47 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-21T10:06:29Z (GMT). No. of bitstreams: 2 Dissertação - Túlio Max de Oliveira Guimarães - 2014.pdf: 2190502 bytes, checksum: 95a9c8660ff6a8f4fee3c71a61784e47 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-04-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Understand how species are spatially distributed has been exhaustively discussed in ecology over the last decades. Recently, frameworks based on Ecological Niche Models (ENM) have emerged to avoid problems related to the lack of species geographical information, once it identify which environmental suitable conditions of geographic space enable the persistence of species. Recently this approach has become a significant component in Systematic Conservation Planning, helping managers to select better areas to create reserves. Several factors limit the fundamental niche of species and poor geographical information about species distribution may lead to be an underestimation of suitable conditions that one specie occur,, revealing an non-equilibrium with climate. Thus, using good fossil records to construct ecological niche models can be a better way to evaluate and improve ENM predictions and it allows us to estimate other suitable conditions not seen before. Thereby, our aim was to investigate if ENMs built for Mauritia flexuosa, and Tapirus terrestris improve with the addition of fossil information. So, different ENMs were built using, first, current records and, second, using different proportions of fossil data. The results showed that species closer to equilibrium with climate (M. flexuosa) had an improvement in model’s performance with the addition of fossil records, while species with higher non-equilibrium (T. terrestris) decreased the model’s performance. / Entender como as espécies estão espacialmente distribuídas pelo planeta tem sido um assunto exaustivamente discutido em ecologia ao longo das últimas décadas. Recentemente, abordagens baseadas nos Modelos de Nicho Ecológico têm surgido com o intuito de eliminar problemas relacionados à lacuna de informação geográfica sobre as espécies, uma vez que identifica locais no espaço geográfico que apresenta as condições ambientais favoráveis à persistência das mesmas. Vários fatores limitam o nicho fundamental das espécies e informações geográficas enviesadas acerca de sua distribuição podem levar a uma subestimativa das condições adequadas à ocorrência, revelando um desequilíbrio com o clima. Deste modo, a utilização de registros fósseis na construção dos Modelos de Nicho Ecológico pode ser uma maneira de melhorar as predições dos modelos, já que adiciona novas informações ambientais que não haviam sido encontradas atualmente. Deste modo, nosso objetivo foi investigar se os Modelos de Nicho Ecológico construídos para Mauritia flexuosa e Tapirus terrestris apresentaram melhora no poder preditivo pela adição de informação fóssil. Para isso, foram construídos diferentes modelos utilizando dados atuais apenas e modelos utilizando tanto informação atual quanto informação fóssil, em diferentes porcentagens. Através de uma Análise de Variância Fatorial, medimos se a adição de informação fóssil apresentava melhora significativa no poder preditivo dos modelos. Nossos resultados mostram que quando há pouca variação na informação ambiental adicionada (M. flexuosa), os modelos apresentam uma melhora significativa no poder preditivo, ao passo que para aqueles dados com maior variação (T. terrestris) o efeito é inverso. Isso se deve pela variação dos erros de omissão e comissão gerados durante o processo de modelagem.

[pt] A teoria da gravidade quântica em laços (loop quantum gravity ou LQG) é atualmente uma das mais promissoras abordagens para descrever a relatividade geral em termos quânticos. Um dos problemas-chave é detectar na teoria quântica estados semiclássicos, que apresentem propriedades macroscópicas iguais às de configurações específicas da teoria clássica. Nesta dissertação, começamos apresentando o formalismo da LQG e sua interpretação física. Do ponto de vista matemático, a LQG pode ser pensada como uma quantização canônica de uma teoria de gauge de SU(2) em uma 3-variedade. No entanto, diferentemente da abordagem usual, que gera uma representação apenas por operadores auto-adjuntos, a abordagem polimérica da LQG gera uma representação mista que usa operadores auto-adjuntos e unitários. Tomamos então um modelo polimérico, análogo à LQG, do sistema físico mais simples: o movimento unidimensional de uma partícula pontual. Neste contexto, desenvolvemos um arcabouço que resolve o problema dos estados semiclássicos, que são estudados em detalhe. Finalmente, consideramos a quantização polimérica do campo eletromagnético livre, resultando numa teoria abeliana muito similar à LQG. Neste contexto, o mesmo arcabouço desenvolvido para o caso anterior pode ser aplicado. / [en] Loop quantum gravity (LQG) is currently one of the most promising approaches to describing general relativity in quantum terms. One of its key issues is to detect in the quantum theory semiclassical states whose macroscopic properties are the same as those of specific configurations of the classical theory. In this dissertation, we begin by presenting the LQG formalism and its physical interpretation. From a mathematical point of view, LQG can be thought of as a canonical quantization of a SU(2) gauge theory in a 3-manifold. However, whereas the usual approach generates a representation exclusively by self-adjoint operators, LQG's polymer approach generates a mixed representation using both self- adjoint and unitary operators. We then take a polymer model, analogous to LQG, of the simplest physical system: the one-dimensional movement of a point particle. In this context, we develop a framework that solves the problem of semiclassical states, which are studied in detail. Finally, we consider the polymer quantization of the free electromagnetic field, which results in an abelian theory which is very similar to LQG. In this context, it is possible to apply the same framework that was developed for the previous case.

Low-resolution, coarse-grained models are powerful computational tools to investigate the behavior of biological systems over time and length scales that are not accessible to all-atom Molecular Dynamics simulations. While several algorithms exist that aim at constructing accurate coarse-grained potentials, few works focus on the choice of the reduced representation, or mapping, to be employed to describe the high-resolution system with a lower number of degrees of freedom. This thesis proposes a series of approaches to investigate and characterise the representation problem in coarse-grained modelling of proteins. This is achieved by employing a collection of diverse methods, including statistical mechanics, machine learning algorithms and information-theoretical tools. The central mathematical object of this work is the mapping entropy, a Kullback-Leibler divergence that measures the intrinsic quality of a given reduced representation. When this quantity is minimised, we obtain the maximally informative coarse-grained mappings of a biomolecule, which cover the structure with an uneven level of detail. Tests conducted over a set of well-known proteins show that regions preserved with high probability are often related to important functional mechanisms of the molecule. Applications of the mapping entropy outside of the field of structural biology show promising results, leading to the identification of those combinations of features that retain the maximum amount of information about the high-resolution system. Additionally, a purely structural notion of scalar product and distance between coarse-grained mappings is introduced, which allow to analyse the metric and topological properties of the mapping space. The thorough exploration of such space leads to the discovery of qualitatively different reduced representations of the biomolecule of interest.

The investigation of real-time dynamics of charged and neutral quantum excitation propagating through macromolecular systems is receiving growing attention due to its potentially countless applications in nano-scale (opto-)electronics and in biophysics. Several key issues have not been fully clarified yet, including the role played by molecular thermal fluctuations and the possible correlations between the degree of quantum coherence and the efficiency of the transport process. In order to gain some insight, we developed a rigorous and systematic framework describing quantum transport, based on a field-theoretic formalism.

Recent technological advances in quantum simulators have proven that synthetic materials are very well suited to study and realise many condensed matter models. However, many of these synthetic systems are characterized by neutral particles that do not couple to real gauge fields. In order to simulate interesting electromagnetic phenomena, such as the topological insulators, or the Landau levels, there is the need for the implementation of artificial gauge fields. In particular, the topological insulators are very interesting both from the point of view of fundamental physics and concrete applications. They are bulk insulating materials that carry a certain number of edge states which are topologically protected against small perturbations of the system. An example of a topological insulator is the integer quantum Hall effect. While there have been many works studying topological physics with quantum artificial systems, little attention was dedicated to the interplay of topology and the purely classical world. Only in the last couple of years, pioneering efforts to encode a non-trivial topology in the dynamical matrix or into the Hamiltonian of a system have proven that the hallmarks of a topological insulator are not the prerogative of quantum mechanics, but can be also observed with a classical system governed by Newton’s equations. The first part of this thesis is therefore based on our studies dedicated to the implementation of a classical analogue of the integer quantum Hall system, by realizing the Harper-Hofstadter model for classical frequency-modulated coupled harmonic oscillators. The achievement of an artificial gauge field allows also for the deeper study of magnetic effects such as Landau levels. In graphene, an inhomogeneous strain of the lattice is equivalent to an artificial pseudo-magnetic field, and the low-energy spectrum shows the formation of relativistic pseudo-Landau levels. The second part of the thesis is therefore focussed on the photonics honeycomb lattice geometry and our theoretical proposal for a configuration based on an intrinsically driven-dissipative system in which to probe the physics of the Landau levels, and especially the spatial structure of their wavefunctions. Finally, we have also studied spin-orbit coupling in a mechanical system of masses and springs induced by pre-tensioned springs that split the longitudinal and transverse couplings in the honeycomb geometry. We have presented the experimental results of a simple mechanical benzene composed of six pendula connected with pre-tensioned springs, to verify that the eigenmodes of this system are well described by our theory in the presence of spin-orbit coupling.

In this work an improved methodology for the study of hydrogen storage material (HSM) is presented, for the characterization of smaller samples of HSM at increased accuracy. It includes: the realization of innovative differential instrument; a novel approach to the detailed micro kinetic modelling; increase the comprehension of absorption and desorption mechanisms; support research efforts in this topic. As side results, a macro and lumped model for the design of generic hydrogen storage tank are developed and validated. The study of a novel IDA (Isochoric Differential apparatus) is presented, describing all the steps from the initial theoretical approach, to the detailed design and the definition of an experimental proceeding. It includes the necessary technical improvements to increase the measure uncertainty compared to the classical SIevert. Novel microkinetic modelling for HSM is explained as variation of classic nucleation and growth model (JMAK model). The nuclei’s growth is assumed to be limited by surface or even by radius of powder’s particles. Micro modelling is applied on Mg-based material, introducing high accurate kinetic measures obtained by IDA. This leads to extrapolate information about kinetic parameters and kinetic mechanisms of hydrogen sorption. The obtained micro modelling is used as core for the development of a model at a higher scale (macro) which keeps in consideration also heat and hydrogen diffusion in porous materials typical in hydrogen storage tank. Experimental data collected by a prototipal realization of hydrogen storage tank are used to validate macro modelling. Moreover, a lumped model is developed with the scope to built a numerical tool able to give preliminary indications on proper design/layout of hydrogen storage tank, based on hydrogen flow, temperature or pressure requirements. Lumped modelling is finally compared with results by the numerical simulation of validated macro model. Finally, micro kinetic model is applied on high accuracy sorption data (by IDA) on innovative catalysed Mg-material. Material is produced by a novel approach, where catalyst, Nb2O5, is deposited by PVD techniques at extremely low concentration on the surface of powder to exploit its higher catalyst proprieties.

The aim of this thesis is to study renormalization of Wick polynomials of quantum Boson fields in locally covariant algebraic quantum field theory in curved spacetime. Vector fields are described as sections of natural vector bundles over globally hyperbolic spacetimes and quantized in a locally covariant framework through the known functorial machinery in terms of local *-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles: The most obvious one is the metric of the spacetime itself, but we encompass also the case of generic spacetime tensors as background fields. In our framework also physical quantities like the mass of the field or the coupling to the curvature are viewed as background fields. Wick powers of the quantized vector field are then axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is then specialized to the case of spacetime tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields. Our main technical tools are based on the Peetre-Slov\'ak theorem characterizing differential operators and on the classification of smooth invariants on representations of reductive Lie groups.

Time-resolved fluorescence measurements enable the study of structure of molecular systems and dynamical processes inside them. This is possible because of a very high sensitivity of fluorescence lifetime to the physical and chemical properties of micro-environment in which fluorophores are situated. However, proper detection of the fluorescence lifetime is a challenging task, due to the fact that the fluorescence decay time of commonly used fluorophores lies in a nanosecond range. This puts strict requirements on the parameters of the fluorescence detectors. The features of single-photon avalanche diodes (SPAD) make these optical detectors a good alternative to conventional photomultiplier tubes and micro-channel plates. CMOS technology allows cointegration of a SPAD and electronic circuits on the same substrate and provides advantages in time resolution and noise characteristics. Monolithic integration of signal processing circuits and detectors on the same chip allows using such detectors without additional external hardware. New SPAD sensors with improved characteristics are produced every year. However, the designers consider various performance metrics while the importance of each particular detector characteristic depends on its application. Therefore, the validation and optimization of SPAD characteristics should be performed in a close connection with the analysis of a specific system, wherein this detector will be used. This work was aimed at developing of a model able to describe a typical fluorescence experiment with SPAD-based detector. The model simulates all essential parts of the fluorescence experiment starting from the light emission, through photo-physical processes occurring inside a bio-sample, to a detector itself and read-out electronics. The ability of the developed model to simulate various light sources (laser and micro-LED), fluorescence measurement techniques (time-correlated single photon counting and time-gating) was verified. The simulated results were in good agreement with the experimental data and the model proved its flexibility. Furthermore, the model provided the explanation of the distortions in experimental fluorescent curves measured under a very high ambient light when pile-up effects appear. Finally, a set of virtual experiments were established to investigate the influence of noisy pixels in SPAD array on a lifetime estimation and to study the feasibility of time-filtering instead of conventional optical filtering. Simulation results are in good agreement with data available in literature.

In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.