Orientador: Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica / Made available in DSpace on 2018-08-04T08:21:52Z (GMT). No. of bitstreams: 1 ParisioFilho_FernandoRobertodeLuna_D.pdf: 1316597 bytes, checksum: 7f79cd7aefdbaf70bddcdb50acb8e154 (MD5) Previous issue date: 2005 / Resumo: Esta tese aborda diversos aspectos da propagação semiclássica de estados coerentes. Determinamos uma expressão bastante geral para o propagador entre tais estados que, ao contrário das fórmulas existentes na literatura, é válida para pacotes de larguras quaisquer. O resultado, obtido via integração funcional, depende de trajetórias clássicas num espaço de fase complexificado. Aproximações baseadas em órbitas reais são também analisadas e demonstra-se a origem comum dos propagadores gaussianos de Heller e BAKKS. Em seguida, é feito um estudo bastante completo da propagação semiclássica de estados coerentes na representação de posição. Os resultados formais obtidos são aplicados explicitamente para o caso de um pacote gaussiano sob a influência de um potencial repulsivo suave. Para este sistema, a solução das equações de Hamilton e a própria função de onda semiclássica podem ser determinadas analiticamente. O problema das soluções não contribuintes, que se origina da aplicação do método do expoente estacionário, é resolvido através de imposições de consistência física. Os efeitos das cáusticas no espaço de fase, pontos onde a aproximação semiclássica de ordem quadrática diverge, são controlados através de correções envolvendo funções de Airy / Abstract: This thesis addresses di®erent aspects of the semiclassical propagation of coherent states. We have derived a general expression for the propagator connecting these states which, di®erently from previous formulae in the literature, is valid for packets of arbitrary widths. The result, obtained via functional integration, depends on classical trajectories in a complex phase space. Approximations based on real orbits are also analyzed and it is demonstrated that the Heller and BAKKS Gaussian propagators belong to the same category. Next we make a detailed study of the semiclassical propagation of coherent states in the position representation. The obtained formal results are applied to the case of a Gaussian packet under the influence of a smooth repulsive potential. For this system the solution of Hamilton's equations and the semiclassical wave function can be expressed analytically. The problem of non-contributing solutions, which originates from the application of the stationary exponent method, is solved by the introduction of some criteria of physical consistency. The e®ects of caustics in phase space, points where the lowest order semiclassical approximation diverges, are controlled by introducing corrections involving Airy functions / Doutorado / Física / Doutor em Ciências

Les chaînes d'avant pays et les prismes d'accrétion sont des accumulations sédimentaires décollées de la croûte sous-jacente, dans un contexte compressif. En raison de basses températures, la déformation y est frictionnelle et sismogène. Dans la première partie on étudie des échantillons de grès prélevés à proximité de la faille active de Chelungpu, front de déformation du prisme d'accrétion de Taiwan. On montre que l'orientation préférentielle des micro-fractures intra-granulaires existantes ne coïncide pas toujours avec l'orientation des nouvelles micro-fractures produites lors d'essais mécaniques, contredisant des résultats de travaux similaires.La deuxième partie présente l'étude d'une modélisation numérique utilisant l'analyse limite séquentielle d'un prisme frictionnel homogène. On développe cette approche 2D comme une généralisation semi-analytique de la théorie du prisme critique pour suivre la déformation, en intégrant accrétion frontale, adoucissement frictionnel et érosion. Une étude paramétrique systématique révèle le comportement chaotique de la déformation, très sensible aux détails topographiques, mais aussi une organisation statistiquement prévisible des longueurs d'activation du décollement. On distingue par ailleurs une organisation temporelle complexe contrôlée par l'adoucissement frictionnel et les quantités accrétées : par exemple une périodicité d'activation des grandes failles hors-séquence. L'introduction d'une loi d'érosion simple produit un florilège de géométries proches de structures géologiques courantes --- vergence et épaisseur des écailles, duplexes, éventails imbriqués, exhumation. Enfin, une application de la méthode à des expériences de déformation de sables montre la possibilité d'estimer les paramètres de friction in-situ, via des mesures de force. / Chains foreland and accretionary prisms are sedimentary accumulations detached from the underlying crust in a compressive context. Due to low temperatures, deformation is frictional and seismogenic.In the first part we studied sandstone samples collected near the active fault of Chelungpu, deformation front of the Taiwanese accretionary prism. We show that the current preferred orientation of intra-granular microfractures does not always coincide with the orientation of new micro-fractures produced during mechanical testing, contradicting the results of similar work.The second part presents the analysis of numerical modeling using sequential limit analysis of frictional homogeneous prism. We develop this 2D approach as a semi-analytic generalization of the critical prism theory to monitor deformation, including frontal accretion, frictional softening and erosion. A systematic parametric study reveals the chaotic behavior of the deformation --- very sensitive to topographic details --- but also a statistically predictable organization of activation lengths of the décollement. We distinguish also a complex temporal organization controlled by frictional softening and accreted amounts : for example periodicity of activation of large out of sequence faults. The introduction of a simple erosion law produced a plethora of common geological structures --- vergence and thickness of thrusts, duplexes, imbricate fans, exhumation. Finally, an application of the method to sand deformation experiments shows the possibility of estimating in-situ frictional parameters, through force measurements.

Des Histoires de passage : en regroupant sous ce titre des extraits de ses diverses proses, Philippe Jaccottet, poète de Suisse romande, né en 1925, souligne lui-même l’importance essentielle que revêt dans son œuvre la notion de passage. Cette recherche se propose de montrer qu’elle porte une thématique, définit une poétique, ouvre sur une ontologie. Dépassant l’opposition entre l’attrait pour les passages libres visibles dans le paysage et l’aversion face à l’obstacle - muraille de la montagne ou de la mort, notamment, qui suscite le vœu d’une magique abolition - la sensibilité de Jaccottet met en œuvre une relation complexe entre ces contraires et révèle une profonde fascination pour le point de passage en soi : le seuil. L’expérience poétique comble ces aspirations puisque qu’en certains « instants privilégiés », elle révèle à « l’autre regard » un monde ouvert et unifié, sans barrières ni hiatus. Elle trouve son accomplissement dans un usage particulier de la métaphore, figure même du passage, qui permet entre les choses une circulation continue. Métamorphose du monde, la poésie s’avère alors liée au sacré : elle « donne sur » « autre chose », est passage ou pressentiment d’un passage vers un au-delà dont la nature ne peut être dite ni philosophique, ni religieuse, ni même à proprement parler mystique. Entraperçu dans l’ici, il reste un inaccessible, un indicible que l’écriture désigne comme tel, ouvrant vers lui une perspective à l’infini. Le passage serait donc dans le passage même, cette ontologie induisant alors une dialectique de la limite et de l’illimité. / By gathering together extracts from his prose writings under the title Des Histoires de passage [Stories of passage], the Swiss-French poet Philippe Jaccottet, born in 1925, highlights the vital importance of the notion of passage in his work. This research proposes to demonstrate that this notion expresses a set of themes, defines a poetic theory and offers an ontological analysis. Reaching beyond the contrast between an attraction to visible passageways in a landscape and an aversion to obstacles [such as a steep mountainside or death, which inspire hope for a « magical » eradication], Jaccottet’s sensibility develops a complex interplay between these conflicting concepts and reveals a profound fascination for the point of passage itself : the threshold. Poetic experience gratifies such aspirations, since at certain « privileged » moments it reveals to the poet’s « other vision » a world that is open and unified, without barriers or hiatuses. This is achieved here through a particular use of metaphor, itself an active participant in the passage, which allows for a continuous circulation between elements. As a metamorphosis of the world, poetry reveals its connection to the sacred : it « gives onto » « something else » ; it is a pathway, or envisioned pathway, towards a « beyond » which cannot be defined as philosophical, religious, or even, strictly speaking, mystical. Glimpsed in the here and now, the beyond remains inaccessible and indescribable, identified as such through writing, which opens up towards it an infinite vista. The passage is thus within the passage itself, constituting an ontology that leads to a dialectic of limits and the unlimited.

Abstract Digital delta-sigma modulators are used in a broad range of modern electronic sub-systems, including oversampled digital-to-analogue converters, class-D amplifiers and fractional-N frequency synthesizers. This work addresses a well known problem of unwanted spurious tones in the modulator’s output spectrum. When a delta-sigma modulator works with a constant input, the output signal can be periodic, where short periods lead to strong deterministic tones. In this work we propose means for guaranteeing that the output period will never be shorter than a prescribed minimum value for all constant inputs. This allows a relationship to be formulated between the modulator’s bus width and the spurious-free range, thereby making it possible to trade output spectrum quality for hardware consumption. The second problem addressed in this thesis is related to the finite accuracy of frequencies generated in delta-sigma fractional-N frequency synthesis. The synthesized frequencies are usually approximated with an accuracy that is dependent on the modulator’s bus width. We propose a solution which allows frequencies to be generated exactly and removes the problem of a constant phase drift. This solution, which is applicable to a broad range of digital delta-sigma modulator architectures, replaces the traditionally used truncation quantizer with a variable modulus quantizer. The modulus, provided by a separate input, defines the denominator of the rational output mean. The thesis concludes with a practical example of a delta-sigma modulator used in a fractional-N frequency synthesizer designed to meet the strict accuracy requirements of a GSM base station transceiver. Here we optimize and compare a traditional modulator and a variable modulus design in order to minimize hardware consumption. The example illustrates the use made of the relationship between the spurious-free range and the modulator’s bus width, and the practical use of the variable modulus functionality.

This thesis presents a study of the centre bifurcation and chaotic behaviour of three dimensional Lotka-Volterra systems. In two dimensional systems, Christopher (2005) considered a simple computational approach to estimate the cyclicity bifurcating from the centre. We generalized the technique to estimate the cyclicity of the centre in three dimensional systems. A lower bounds is given for the cyclicity of a hopf point in the three dimensional Lotka-Volterra systems via centre bifurcations. Sufficient conditions for the existence of a centre are obtained via the Darboux method using inverse Jacobi multiplier functions. For a given centre, the cyclicity is bounded from below by considering the linear parts of the corresponding Liapunov quantities of the perturbed system. Although the number obtained is not new, the technique is fast and can easily be adapted to other systems. The same technique is applied to estimate the cyclicity of a three dimensional system with a plane of singularities. As a result, eight limit cycles are shown to bifurcate from the centre by considering the quadratic parts of the corresponding Liapunov quantities of the perturbed system. This thesis also examines the chaotic behaviour of three dimensional Lotka-Volterra systems. For studying the chaotic behaviour, a geometric method is used. We construct an example of a three dimensional Lotka-Volterra system with a saddle-focus critical point of Shilnikov type as well as a loop. A construction of the heteroclinic cycle that joins the critical point with two other critical points of type planar saddle and axial saddle is undertaken. Furthermore, the local behaviour of trajectories in a small neighbourhood of the critical points is investigated. The dynamics of the Poincare map around the heteroclinic cycle can exhibit chaos by demonstrating the existence of a horseshoe map. The proof uses a Shilnikov-type structure adapted to the geometry of these systems. For a good understanding of the global dynamics of the system, the behaviour at infinity is also examined. This helps us to draw the global phase portrait of the system. The last part of this thesis is devoted to a study of the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems. Explicit conditions for the existence of two first integrals for the system and a line of singularity with zero eigenvalue are given. We characteristic the parameters for which a zero-Hopf equilibrium point takes place at any points on the line. We prove that there are three 3-parameter families exhibiting such equilibria. First order of averaging theory is also applied but we show that it gives no information about the possible periodic orbits bifurcating from the zero-Hopf equilibria.

Learning is a mechanism intrinsic to all sentient biological systems. Despite the diverse range of paradigms that exist, it appears that an artificial system has yet to be developed that can emulate learning with a comparable degree of accuracy or efficiency to the human brain. With the development of new approaches comes the opportunity to reduce this disparity in performance. A model presented by Janson and Marsden [arXiv:1107.0674 (2011)] (Memory foam model) redefines the critical features that an intelligent system should demonstrate. Rather than focussing on the topological constraints of the rigid neuron structure, the emphasis is placed on the on-line, unsupervised, classification, retention and recognition of stimuli. In contrast to traditional AI approaches, the system s memory is not plagued by spurious attractors or the curse of dimensionality. The ability to continuously learn, whilst simultaneously recognising aspects of a stimuli ensures that this model more closely embodies the operations occurring in the brain than many other AI approaches. Here we consider the pertinent deficiencies of classical artificial learning models before introducing and developing this memory foam self-shaping system. As this model is relatively new, its limitations are not yet apparent. These must be established by testing the model in various complex environments. Here we consider its ability to learn and recognize the RGB colours composing cartoons as observed via a web-camera. The self-shaping vector field of the system is shown to adjust its composition to reflect the distribution of three-dimensional inputs. The model builds a memory of its experiences and is shown to recognize unfamiliar colours by locating the most appropriate class with which to associate a stimuli. In addition, we discuss a method to map a three-dimensional RGB input onto a line spectrum of colours. The corresponding reduction of the models dimensions is shown to dramatically improve computational speed, however, the model is then restricted to a much smaller set of representable colours. This models prototype offers a gradient description of recognition, it is evident that a more complex, non-linear alternative may be used to better characterize the classes of the system. It is postulated that non-linear attractors may be utilized to convey the concept of hierarchy that relates the different classes of the system. We relate the dynamics of the van der Pol oscillator to this plastic self-shaping system, first demonstrating the recognition of stimuli with limit cycle trajectories. The location and frequency of each cycle is dependent on the topology of the systems energy potential. For a one-dimensional stimuli the dynamics are restricted to the cycle, the extension of the model to an N dimensional stimuli is approached via the coupling of N oscillators. Here we study systems of up to three mutually coupled oscillators and relate limit cycles, fixed points and quasi-periodic orbits to the recognition of stimuli.

[pt] Este trabalho apresenta uma formulação puramente baseada em plasticidade para ser aplicada à otimização topológica. A principal ideia da otimização topológica em mecânica dos sólidos é encontrar a distribuição de material dentro do domínio de forma a otimizar uma medida de performance e satisfazer um conjunto de restrições. Uma possibilidade é minimizar a flexibilidade da estrutura satisfazendo que o volume seja menor do que um determinado valor. Essa é a formulação clássica da otimização topológica, que é vastamente utilizada na literatura. Não obstante fornecer resultados interessantes, condições adicionais devem ser levadas em consideração para viabilizar sua aplicação prática. O projeto estrutural aborda dois aspectos principais: (i) a estrutura não deve colapsar, suportando os carregamentos aplicados (critério de segurança); e (ii) deverá se sujeitar a um valor máximo aceitável de deformação (critério de aceitabilidade). Consequentemente, a otimização topológica clássica deve ser modificada de forma a encontrar a distribuição de material correspondente ao menor volume possível tal que o critério de segurança seja verificado. O referido critério de segurança pode ser definido como limitar as tensões elásticas ao critério de plastificação em todo o domínio. Esta definição resultou em um novo ramo de pesquisa: a otimização topológica com restrições de tensões. Por outro lado, entende-se que o projeto estrutural plástico é preferível quando um projeto ótimo é almejado, uma vez que permite um maior aproveitamento da resistência do material. Dessa forma, este trabalho aborda a incorporação do projeto estrutural plástico à otimização topológica como método mais vantajoso do que a otimização topológica clássica e a com restrições de tensões. A formulação proposta é uma extensão da análise limite, que fornece uma estimativa da carga de colapso de uma estrutura diretamente por meio da programação matemática, assegurando a eficiência computacional da metodologia proposta. De forma a verificar a otimização topológica plástica e comparar a topologia final com as obtidas através da otimização topológica clássica e da com restrição de tensões, são apresentados exemplos numéricos. / [en] This work presents a full plastic formulation to be applied within topology optimization. The main idea of topology optimization in solid mechanics is to find the material distribution within the domain so that it optimizes a performance measure and satisfies a set of constraints. One might seek to minimize the compliance satisfying that the volume is less than a given value. The aforementioned formulation is the standard topology optimization which has been used widely in literature. Although it provides interesting results, additional requirements must be taken into account when practical application is concerned. Structures are designed considering two main aspects: (i) the structure must not collapse, supporting the applied loads (safety criterion); and (ii) its displacements must be lower than a prescribed bound (serviceability criterion). Consequently, the standard formulation shall be modified, finding the material distribution corresponding to the minimum volume such that the safety criterion is met. Said safety criterion may be defined as restraining the elastic stresses to the yield criterion in the entire domain. This definition has resulted in a new branch in this research field: the stress constrained topology optimization. On the other hand, it is understood that the plastic design criterion is preferable when optimization is intended, since it fully exploits the material strength. Therefore, this work addresses the incorporation of the plastic design criterion into topology optimization as a more advantageous method than standard and stress constrained topology optimization methods. The proposed formulation is an extension of limit analysis, which provides an estimative of the collapse load of a structure directly through mathematical programming, ensuring computational efficiency to the proposed methodology. Lastly, numerical examples are shown to verify plastic topology optimization and the final topology is compared with those provided by standard and stress constrained topology optimization methods.

In this paper, metal-enhanced fluorescence (MEF) technique is used to lower the detection limit of carcinoembryonic antigen (CEA) which is able to be utilized in forecasting the risk of having certain kinds of cancers, especially colon and rectal cancer. By incubating silver nanocubes (Ag NCs) on the surface of the chips, the detection limit goes down to below 1ng/mL of CEA. Also, when combining MEF with surface acoustic wave (SAW) devices, the incubation time between antigen and antibody will decrease significantly with the fluorescence signal keeping similar or higher level.

Standard optical microscopes cannot resolve images below 200 nm within the visible wavelengths due to optical diffraction limit. This Thesis reports an investigation into super-resolution imaging beyond the optical diffraction limit by microsphere optical nano-scopy (MONS) and submerged microsphere optical nano-scopy (SMON). The effect of microsphere size, material and the liquid type as well as light illumination conditions and focal plane positions on imaging resolution and magnification have been studied for imaging both biological (viruses and cells) and non-biological (Blu-ray disk patterns and nano-pores of anodised aluminium oxide) samples. In particular, sub-surface imaging of nano-structures (data-recorded Blu-ray) that cannot even be seen by a scanning electron microscope (SEM) has been demonstrated using the SMON technique. Adenoviruses of 75 nm in size have been observed with white light optical microscopy for the first time. High refractive index microsphere materials such as BaTiO3 (refractive index n = 1.9) and TiO2-BaO-ZnO (refractive index n = 2.2) were investigated for the first time for the imaging. The super-resolution imaging of sub-diffraction-limited objects is strongly influenced by the relationship between the far-field propagating wave and the near-field evanescent waves. The diffraction limit free evanescent waves are the key to achieving super-resolution imaging. This work shows that the MONS and SMON techniques can generate super-resolution through converting evanescent waves into propagating wave. The optical interactions with the microspheres were simulated using special software (DSIMie) and finite different in time domain numerical analysis software (CST Microwave Studio). The optical field structures are observed in the near-field of a microsphere. The photonic nanojets waist and the distance between single dielectric microsphere and maximum intensity position were calculated. The theoretical modelling was calculated for comparisons with experimental measurements in order to develop and discover super-resolution potential.

This thesis deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that in the hydrodynamic limit, the particle densities of a one-dimensional zero range process on a periodic lattice converge to the solution of a nonlinear diffusion equation. This method allows for the first time an explicit uniform-in-time bound on the rate of convergence in the hydrodynamic limit. We also discuss how to extend this method to the multi-dimensional case. Furthermore we present an argument, which seems to be new in the context of hydrodynamic limits, how to deduce the convergence of the microscopic entropy and Fisher information towards the corresponding macroscopic quantities from the validity of the hydrodynamic limit and the initial convergence of the entropy. The second part deals with problems arising in the analysis of nonlinear Schrödinger equations of Gross-Pitaevskii type. First, we consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in the literature. Moreover, we find that the rotation term has a considerable influence in proving finite time blow-up in the focusing case. Finally, a mathematical framework for optimal bilinear control of nonlinear Schrödinger equations arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical work load over the control process is taken into account rather then often used L^2- or H^1-norms for the cost of the control action. We prove well-posedness of the problem and existence of an optimal control. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton type iteration, and used to solve several coherent quantum control problems.