This thesis considers the problem of calculating and observing the mixing of modes of positive and negative frequency in inhomogeneous, dispersive media. Scattering of vacuum modes of the electromagnetic field at a moving interface in the refractive index of a dielectric medium is discussed. Kinematics arguments are used to demonstrate that this interface may, in a regime of linear dispersion, act as the analogue of the event horizon of a black hole to modes of the field. Furthermore, a study of the dispersion of the dielectric shows that five distinct configurations of modes of the inhomogeneous medium at the interface exist as a function of frequency. Thus it is shown that the interface is simultaneously a black- and white-hole horizon-like and horizonless emitter. The role, and importance, of negative-frequency modes of the field in mode conversion at the horizon is established and yields a calculation of the spontaneous photonic flux at the interface. An algorithm to calculate the scattering of vacuum modes at the interface is introduced. Spectra of the photonic flux in the moving and laboratory frame, for all modes and all realisable increase in the refractive index at the interface are computed. As a result of the various mode configurations, the spectra are highly structured in intervals with black-hole, white-hole and no horizon. The spectra are dominated by a negative-frequency mode, which is the partner in any Hawking-type emission. An experiment in which an incoming positive-frequency wave is populated with photons is assembled to observe the transfer of energy to outgoing waves of positive and negative frequency at the horizon. The effect of mode conversion at the interface is clearly shown to be a feature of horizon physics. This is a classical version of the quantum experiment that aims at validating the mechanism of Hawking radiation.

Alle optischen Systeme haben den gleichen Zweck: Sie manipulieren Eigenschaften des Lichts, durch Interaktion mit Materie. In dieser Arbeit werden zwei wichtige Teilaspekte aus diesem Kontext untersucht, im linearen und im nicht-linearen Bereich. In Teil I werden die bekannten Bragg-Reflexionen in neuem Licht betrachtet. Bragg Reflexion findet statt, wenn Licht mit einem periodischen Medium interagiert. Die Bragg-Bedingung verknüpft den Gitterabstand in einem Kristall mit der Wellenlänge, die von ihm reflektiert wird. In dieser Arbeit werden die Bragg Reflexionen in gewellten Wellenleitern untersucht. Es wird gezeigt, dass die Bragg-Bedingung nicht ausreicht, um die Streuung in diesen Wellenleitern zu verstehen. Es wird numerisch und analytisch demonstriert, dass unebene Ränder eine neue Reflexionsbedingung schaffen, die über das einfache Bragg-Bild hinausgeht. Dieser Streueffekt, der Square Gradient Bragg-Mechanismus ist aus statistischen Streuansätzen bekannt. Er hängt mit der Krüummung des Randes zusammen und hat einen starken Einfluss auf die Wellenleitung in diesen Systemen. In dieser Arbeit wird die erste allgemeine Theorie für den Square Gradient Bragg Streumechanismus vorgestellt, die es ermöglicht, Voraussagen für einzelne Wellenleiter mit beliebig deformierten Rändern zu treffen. Eine weitere wichtige Eigenschaft des Lichts wird in Teil II dieser Arbeit untersucht: Die Verschränkung zwischen zwei Photonen. Verschränkung ist ein intuitiv nicht verständliches Phänomen, weil es in der uns umgebenden klassischen Welt kein Analogon hat. Insbesondere verletzt es unsere implizite Annahme eines lokalen Realismus, weil voneinander entfernte Teilchen scheinbar instantan miteinander wechselwirken können. In dieser Arbeit wird eine neue und verstimmbare Quelle für verschränkte Photonen entworfen. Die Photonenpaare werden in nicht-linearen Kristallen erzeugt, aber ihre Verschränkung wird rein geometrisch erzwungen. Dieser geometrische Ansatz erlaubt es, die Frequenz der Photonen einzustellen. Hier übertrifft diese neue Quelle ihre Vorgänger, die ausführlich besprochen werden. Die Verschränkung der erzeugten Photonen wird experimentell nachgewiesen. / Any optical experiment, any optical technology is only about one thing: Manipulating the properties of light through interaction with matter. This thesis will address two important issues in this broad context, in the linear and in the non-linear regime. In Part I, the well-known Bragg reflection is revised. Bragg reflection takes place whenever light interacts with a periodic structure. The famous Bragg condition relates the lattice spacing in a crystal to the wavelength which is effectively reflected by that lattice. In this thesis the Bragg reflection in dielectric waveguides is investigated. It is shown that the Bragg condition is not sufficient to describe the scattering situation in waveguides with corrugated boundaries. It is demonstrated, analytically and numerically, that corrugated boundaries cause a new type of reflection condition, which goes beyond the Bragg picture. This scattering mechanism, the Square Gradient Bragg Scattering, is known from statistical scattering approaches. It is connected to the curvature of the boundary and has a strong influence on the wave propagation in these systems. Here the first general theory for Square Gradient Bragg Scattering is presented, which allows for making predictions for single corrugated waveguides with arbitrary boundaries. Another important property of light is investigated in Part II of this thesis: The entanglement of two photons. Entanglement is a counter-intuitive phenomenon, because it has no classical analogy. It especially violates our assumption of local realism, because distant particles seemingly act on each other instantaneously. In this thesis a new tunable and portable source of photon pairs is designed. The photon pairs are created in non-linear crystals, but their entanglement is enforced in a purely geometrical manner. This geometrical approach makes the setup tunable. This is where the new design supersedes its predecessor, which will be discussed in detail. The entanglement of the generated photons is demonstrated experimentally.

Curved and skewed I-girder bridges exhibit torsional displacements of the individual girders and of the overall bridge cross-section under dead loads. As a result, the girder webs can be plumb in only one configuration. If the structure is built such that the webs are plumb in the ideal no-load position, they generally cannot be plumb under the action of the structure's steel or total dead load; hence, twisting of the girders is unavoidable under dead loads. The deflected geometry resulting from these torsional displacements can impact the fit-up of the members, the erection requirements (crane positions and capacities, the number of temporary supports, tie down requirements, etc.), the bearing cost and type, and the overall strength of the structure. Furthermore, significant layover may be visually objectionable, particularly at piers and abutments. If the torsional deflections are large enough, then the cross-frames are typically detailed to compensate for them, either partially or fully. As specified in Article C6.7.2 of the AASHTO LRFD Specifications, different types of cross-frame detailing methods are used to achieve theoretically plumb webs under the no-load, steel dead load, or total dead load conditions. Each of the cross-frame detailing methods has ramifications on the behavior and constructability of a bridge. Currently, there is much confusion and divergence of opinion in the bridge industry regarding the stage at which steel I girder webs should be ideally plumb and the consequences of out-of-plumbness at other stages. Furthermore, concerns are often raised about potential fit-up problems during steel erection as well as the control of the final deck geometry (e.g., cross-slopes and joint alignment). These influences and ramifications of cross-frame detailing need to be investigated and explained so that resulting field problems leading to needless construction delays and legal claims can be avoided. This dissertation addresses the influence of cross-frame detailing on curved and/or skewed steel I girder bridges during steel erection and concrete deck placement by conducting comprehensive analytical studies. Procedures to determine the lack-of-fit forces due to dead load fit (DLF) detailing are developed to assess the impact of different types of cross-frame detailing. The studies include benchmarking of refined analytical models against selected full scale experimental tests and field measurements. These analytical models are then utilized to study a variety of practical combinations and permutations of bridge parameters pertaining to horizontal curvature and skew effects. This research develops and clarifies procedures and provides new knowledge with respect to the impact of cross-frame detailing methods on: 1) constructed bridge geometries, 2) cross-frame forces, 3) girder stresses, 4) system strengths, 5) potential uplift at bearings, and 6) fit-up during erection. These developments provide the basis for the development of refined guidelines for: 1) practices to alleviate fit-up difficulties during erection, 2) selection of cross-frame detailing methods as a function of I-girder bridge geometry characteristics, and 3) procedures to calculate the locked-in forces due to DLF cross-frame detailing.

Gegenwärtige Bestrebungen materialwissenschaftlicher Forschung beschäftigen sich unter anderem mit der Überführung zweidimensionaler Elemente elektronischer, optischer, plasmonischer oder magnetischer Funktionalität in den dreidimensionalen (3D) Raum. Dieser Ansatz vermag mittels Krümmung und struktureller Topologie bereits vorhandene Eigenschaften abzuändern beziehungsweise neue Funktionalitäten bereitzustellen. Vor allem Vektoreigenschaften wie die Magnetisierung kondensierter Materie lassen sich aufgrund der Brechung der Inversionssymmetrie in gekrümmten Flächen stark beeinflussen. Neben der Entwicklung diverser Vorgänge zur Herstellung 3D magnetischer Gegenstände sind geeignete Untersuchungsmethoden wie beispielsweise tomografische Abbildungen der Magnetisierung von Nöten, die maßgeblich die physikalischen Eigenschaften bestimmen. Die vorliegende Dissertationsschrift befasst sich mit der Abbildung von magnetischen Domänen in 3D gekrümmten Dünnschichten beruhend auf dem Effekt des zirkularen magnetischen Röntgendichroismus (XMCD). Die in diesem Zusammenhang entwickelte magnetische Röntgentomografie (MXT) basierend auf weicher Röntgenmikroskopie stellt eine zu Elektronenholografie und Neutronentomografie komplementäre Methodik dar, welche großes Anwendungspotential in der elementspezifischen Untersuchung magnetischer gekrümmter Flächen mit örtlicher Auflösung im Nanometerbereich aufweist. Die Schwierigkeit der Interpretation von Abbildungen magnetischer Strukturen in gekrümmten Flächen rührt von der Dreidimensionalität und der Vektoreigenschaft der Magnetisierung her. Die hierzu notwendigen Kenntnisse sind anhand von zwei topologisch verschiedenen Flächen in Form hemisphärischer Kappen und hohler Zylinder erschlossen worden. Die praktische Anwendung von MXT ist abschließend anhand der Rekonstruktion magnetischer Domänen in aufgerollten Dünnschichten mit zylindrischer Form verdeutlicht. / One of the foci of modern materials sciences is set on expanding conventional two-dimensional electronic, photonic, plasmonic and magnetic devices into the third dimension. This approach provides means to modify conventional or to launch novel functionalities by tailoring curvature and three-dimensional (3D) shape. The degree of effect is particularly high for vector properties like the magnetization due to an emergent inversion symmetry breaking. Aside from capabilities to design and synthesize 3D magnetic architectures, proper characterization methods, such as magnetic tomographic imaging techniques, need to be developed to obtain a thorough understanding of the system’s response under external stimuli. The main objective of this thesis is to develop a visualization technique that provides nanometer spatial resolution to image the peculiarities of the magnetic domain patterns on extended 3D curved surfaces. The proposed and realized concept of magnetic soft X-ray tomography (MXT), based on the X-ray magnetic circular dichroism (XMCD) effect with soft X-ray microscopies, has the potential to become a powerful tool to investigate element specifically an entirely new class of 3D magnetic objects with virtually any shape and magnetization. Imaging curved surfaces meets the challenge of three-dimensionality and requires a profound understanding of the recorded XMCD contrast. These experiences are gained by visualizing magnetic domain patterns on two distinct 3D curved surfaces, namely magnetic cap structures and rolled-up magnetic nanomembranes with cylindrical shape. The capability of MXT is demonstrated by reconstructing the magnetic domain patterns on 3D curved surfaces resembling hollow cylindrical objects.

Em geral, as formulações disponíveis na literatura para a análise de cascas laminadas reforçadas com fibras substituem o meio original heterogêneo por um homogêneo equivalente, que dificulta a identificação das tensões fibra-matriz, ou requerem que a malha de elementos finitos seja disposta de modo que os nós dos elementos finitos de fibra coincidam com os nós dos elementos finitos de casca, que é uma exigência bastante restritiva e que aumenta o número de graus de liberdade do sistema de equações resultante. Neste sentido, o objetivo geral desta tese consiste em desenvolver uma formulação para a inclusão de fibras longas e curtas aleatórias nas diversas lâminas de cascas laminadas anisotrópicas com não linearidade geométrica utilizando o método dos elementos finitos sem aumentar o número de graus de liberdade do sistema de equações resultante e sem a necessidade de coincidência de nós na discretização das fibras e da matriz. Nesta formulação, o elemento finito triangular de casca laminada utilizado para discretizar a matriz possui dez nós e sete graus de liberdade por nó, sendo três translações, três componentes do vetor generalizado e a taxa de variação linear da deformação ao longo da espessura. As fibras curvas, curtas aleatórias ou longas, são introduzidas, em qualquer camada do laminado, por meio de relações cinemáticas que garantem sua aderência à matriz sem a introdução de novos graus de liberdade no sistema de equações resultante. Para discretizá-las são utilizados elementos finitos unidimensionais de ordem qualquer com três graus de liberdade por nó e que consideram consistentemente a não linearidade geométrica. Todas as grandezas envolvidas são escritas em relação à configuração inicial do corpo, caracterizando a descrição Lagrangeana total ou material do movimento. Para modelar o comportamento do material adota-se a Lei Constitutiva de Saint-Venant-Kirchhoff que relaciona de forma linear o tensor de tensões de Piolla-Kirchhoff de segunda espécie e o tensor de deformações de Green-Lagrange. O equilíbrio é encontrado a partir do Princípio da Mínima Energia Potencial Total e o sistema não linear de equações resultante é resolvido utilizando-se o procedimento iterativo de Newton-Raphson. As ações externas podem ser introduzidas ao sistema de forma total ou incremental e a contribuição das fibras para a energia do sistema é adicionada na matriz global do problema. Os exemplos numéricos testados validam e demonstram as potencialidades da formulação proposta. / In general, the Finite Element (FE) formulations available in the literature for the analysis of fibre reinforced laminated shells replace the original heterogeneous medium by an equivalent homogeneous one, which makes difficult the identification of fiber-matrix stress distribution, or require that the finite element mesh is arranged in a way that the fibre finite element nodes coincide with the shell finite element ones, which is a very restrictive requirement and increases the number of degrees of freedom of the resulting system of equations. In this sense, the objective of this thesis is to develop a formulation for the inclusion of long and random short fibres in any layer of FE laminated anisotropic shells developing large displacement and rotations without increasing the number of degrees of freedom and the necessity of matching nodes in the discretization of the fibre and the matrix. In this formulation, the triangular laminated shell finite element used to discretize the matrix has ten nodes and seven degrees of freedom per node, that are, three translations, three components of a generalized vector and the linear rate of strain variation along the thickness. The curved fibres, long or random short, are introduced in any layer of the laminate shell by means of kinematic relation to ensure its adherence to the matrix without introducing new degrees of freedom in the resulting system of equations. To discretize them, any order one-dimensional finite elements with three degrees of freedom per node are used. These fibres elements are consistently considered by Geometric nonlinearity. All involved variables are written with respect to the initial configuration of the body, characterizing the Total Lagrangian description. To model the behavior of the material we use the Saint-VenantKirchhoff Constitutive Law that relates linearly the second Piolla-Kirchhoff stress tensor and Green-Lagrange strain tensor. The equilibrium is achieved from the Principle of Minimum Potential Energy and the non-linear system of equations is solved by the Newton-Raphson iterative procedure. External loads may be introduced to the system by one or various steps and the contribution of fibres to the energy of the system is added to the global matrix of the problem. The numerical examples validate and demonstrate the potential of the proposed formulation.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-15T19:23:47Z No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T14:37:09Z (GMT) No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) / Made available in DSpace on 2018-05-22T14:37:09Z (GMT). No. of bitstreams: 1 tiberiodepaulanetto.pdf: 1926871 bytes, checksum: 17bceffda5c85de37a0d50a14f4f3f04 (MD5) Previous issue date: 2017-02-22 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese, exploram-se diferentes aspectos e aplicações das teorias gravitacionais com correções quânticas. O texto é dividido em três partes principais. Na primeira parte, são consideradas as soluções linearizadas em diferentes teorias de gravitação com derivadas superiores. O potencial Newtoniano é calculado nos modelos locais, super-renormalizáveis no nível quântico, e mostra-se que a singularidade Newtoniana é cancelada devido a contribuição dos modos massivos extras. Logo depois, o colapso gravitacional de uma pequena massa é estudado na gravitação não-local livre de fantasmas, sendo o principal resultado a ausência da singularidade na solução do campo gravitacional e a possibilidade da não formação do miniburaco negro como resultado do colapso. Na segunda parte, algumas questões sobre a inflação induzida pela anomalia conforme são estudadas. É discutida a possibilidade da transição entre os períodos de inflação estável para instável. É mostrado que esta transição é automática se as correções quânticas nesse período forem desprezadas. Em seguida, considera-se o efeito de termos que violam as simetrias de CPT e Lorentz na inflação induzida pela anomalia conforme. É demonstrado que os novos termos responsáveis por violar essas simetrias não afetam a dinâmica do fator de escala da métrica. Por fim, na terceira parte as correções quânticas para o modelo dos Galileons e para as teorias dos campos massivos tensoriais antissimétricos são obtidas. É mostrado que o propagador da teoria dos Galileons recebe correções quânticas com derivadas superiores e que o teorema de não-renormalização do modelo dos Galileons permanece, de uma maneira generalizada, válido na região das baixas energias. Depois, por meio de cálculos explícitos das correções quânticas semiclássicas não-locais é confirmada a equivalência quântica entre os modelos dos campos tensoriais antissimétricos massivos com a teoria de Proca e com o modelo do campo escalar massivo mínimo. / In this thesis, different aspects and applications of gravitational theories with quan-tum corrections are explored. The text is divided into three main parts. In the first part, the linearized solutions in different gravity theories with higher derivatives are considered. The Newtonian potential is calculated in the local models, super-renormalizable at the quantum level, and it is shown that the Newtonian singularity is cancelled due to the contributions of the extra massive modes. Then the gravitational collapse of a small mass is studied in non-local ghost-free gravity, being the main result the absence of singularity in the gravitational field solution and the possibility of non-mini black hole formation as the collapse result. In the second part, some issues about anomaly-induced inflation are studied. It is discussed the possibility of the transition between stable to unstable periods of inflation. It is shown that this transition is automatic if the quantum corrections in this period are neglected. In the following, we consider the effect of CPT and Lorentz-violating terms in the conformal anomaly-induced inflation. It is shown the new terms responsible to violate these symmetries do not affect the dynamics of the metric scale factor. Finally, in the third part, the quantum corrections for the Galileon model and for the theory of the massive antisymmetric tensor fields are obtained. It is shown that the propaga-tor of Galilean theory receives quantum corrections with higher derivatives and that the non-renormalization theorem for Galileon models remains, in a generalized way, valid in the low-energy region. Then, by means of explicit calculations of non-local semiclassical quantum corrections, the quantum equivalence between the massive antisymmetric tensor field models with the Proca theory and minimal massive scalar field model is confirmed.

The Diploma thesis deals with design and static assessment of timber footbridge structural system for pedestrians and cyclist across the Trebuvka river in Lostice on the site of the existing footbridge. Structural system is designed in two alternatives and assessed according to the current standards. Spans of the bridge are 2x18 m and 1x6 m. The main beams are made of glued laminated timber, other parts of the structure are made of timber and steel elements. First alternative is designed as a simple half-through truss beam, second alternative as continuous beam with variable height where the deck is sitting on top of the girders.

The subject of this thesis is the design and analysis of five-span bridge construction across the railway on the route Zábřeh - Šumperk and the Morava river. There will be made separated bridge for each direction, only right bridge is considered in the thesis. Object is located to 1st class road I/44 on the route between Mohelnice and Jeseník. Three variants were designed - two prestressed chamber girders, one prestressed chamber girder with prefabricated consoles and construction of concrete slab mixed with two steel girders. After these variants were weigh up and the first one, with the length of cantilevered construction 235,6 m and maximum lenght of span 60 m, was chosen for analysis. Calculation of load effects was made by software Scia Engineering 2013 and the analysis was made according to current standards by manual calculation depending on limit states and their influence on the design as well. Drawing documentation and visualization are also part of the thesis.

This Master’s thesis is focused on the design and structural analysis of load-bearing structure of a multipurpose hall that is strained by the permanent load, working load and climatic load. The hall has the shape of an elliptical dome. Maximum margin of the structure is 60,0m and maximum height is 18,0m. Main carrier elements of the structure are radially arranged curved beams made of glued laminated timber, class SA(GL24).

Master´s thesis deals with design and complex static assessment of timber roofed footbridge structural system. The calculation part is divided into three main chapters, that are dedicated to determine load impacts on structure, to particular structural and roof members assessment and also to design details of connections. The lower part of structure is formed by flat arched main beams of glued laminated timber, floor beams, stringers and under-deck bracing. The upper part of footbridge is formed by structure of gabled roof and additional bracings. Transversal frames of footbridge copy the shape of arch and they are arranged orthogonally to its axis. They form a radial fan with commom centre in the longitudinal direction. The static scheme of structure is thought as a statically undefinite system thanks to the bedrock surrounding the footbridge.