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Periodically perforated sheets(PS) are ubiquitous in nature as well as in engineered artifacts developed for aerospace, automotive, marine, nuclear and structural applications. PS are indispensable for saving weight and cost for aircraft; for enhancing safety and integrity of heat exchangers used in nuclear and thermal power stations. Ancient PS grills and lattice frames dating back to 1000 BC continue to inspire contemporary art and architecture, buildings and furniture. PS design and analysis, however, is a complex affair stemming from the inherent configurational anisotropy induced by periodicity. In addition, complex boundary conditions complicate the analysis. Unlike atoms in crystalline media, both shape and periodicity of perforations control this anisotropic nature. This thesis explores theoretical and numerical strategies for evaluating the effective anisotropic elastic moduli of PS. Following an experimental prelude for visualizing the PS stress field in a photoelastic sheet and a brief review of PS theory, this thesis proposes a novel theoretical numerical hybrid method for determining the Airy stress function constants. The proposed hybrid method can be exploited experimentally using automated vision based imaging technologies to measure the boundary displacements noninvasively. For determining the Airy constants periodic boundary conditions to the unit cell are applied, the displacement components around the PS hole boundary are obtained using FEM. Using these constants the PS stress field is reconstructed to assess the efficacy of the proposed hybrid method. It is observed that in general while the actual and the reconstructed stress fields agree reasonably well, more refined boundary data obtained either numerically or experimentally can enhance the accuracy further. The thesis then makes an extensive presentation of anisotropic moduli in a variety of PS designs configured on rectangular or square layouts. Conventional as well as some exotic patterns with cusps and satellite holes are examined, and the results are presented graphically to aid the designer. Finally, some special topics pertaining PS design and analysis are discussed to help overcome the inherent limitations of solutions based on applying periodic boundary conditions. In this vein, strategies for achieving a functionally graded PS are presented by altering the pitch and hole size. These strategies assume importance near boundaries as well as near concentrated forces inducing stress gradients. Other special topics include the applicability of tensor transformation rule to PS anisotropy. The effective bulk modulus which remains a scalar invariant is exploited to assess the validity of tensor transformation in a square PS. The rule of mixture widely used in homogenization of composite media is also discussed briefly. Thus, this thesis makes an attempt to demonstrate the power of blending micromechanics with experiments and FEM to aid in PS design and analysis.

The presented diploma thesis deals with the problem of determining the stress singularity exponent of the V-notch. This task can be divided into two parts. The first deals with the theoretical background, that means the basic relations of mechanics and the basic concepts of fracture mechanics. The second part deals with the elaboration of the Williams method and the creation of a program for calculating the stress singularity exponent.

Cette thèse est dédiée à l'extension du Tracé de Rayons Vectoriels Complexes (TRVC) développé au laboratoire et son application à la caractérisation des particules non-sphériques. Dans divers domaines de recherche, tels que la mécanique des fluides et la combustion, nous devons mesurer les caractéristiques des particules. Parmi les différents types de techniques de mesure, la métrologie optique est largement utilisée grâce à sa précision et sa fiabilité. Cependant, la forme des particules est souvent considérée comme sphérique principalement à cause du manque de moyens pour prédire avec précision l'interaction de la lumière avec de grandes particules non-sphériques. TRVC a été développé pour répondre à ces besoins. Il est basé sur le modèle de rayons mais une amélioration radicale a été apportée dans ce nouveau modèle par l'introduction d'une nouvelle propriété dans la notion de rayons lumineux - la courbure de front d'onde. Dans cette thèse, le modèle est appliqué à réexaminer la théorie d'Airy. Il a été montré que TRVC prédit mieux les intensités et les positions des lobes secondaires dans les arcs-en-ciel d'une particule sphérique que la théorie d'Airy. Ensuite, TRVC est appliqué à l'étude des propriétés des arcs-en-ciel formés par les ellipsoïdes allongé et aplati. Il est montré que TRVC peut prédire analytiquement les positions et les intensités de lobes secondaires dans les arcs-en-ciel d’une particule sphéroïdale lorsqu’elle est éclairée par une onde plane dans le plan symétrique. Les pics dus à l'effet focal d'une particule sphéroïdale aplatie ont également été évalués analytiquement en utilisantle facteur de divergence de TRVC. Un système de mesure est aussi mis en place dans le laboratoire pour la diffusion de la lumière par des gouttes pendantes. Il a été montré que le rapport des intensités des deux premiers arcs-en-ciel est sensible à l'ellipticité d'un sphéroïde équivalent. Ceci ouvre un champ d'application potentiel pour caractériser la déformation d'une goutte pendante. / This thesis is dedicated to the extension of Vectorial Complex Ray Model (VCRM)developed in the laboratory and its application in the characterization of large nonspherical particles. In various research domains, such as the uid mechanics and the combustion field, we need to measure the characteristics of the particles. Among di_erent kinds of measurement techniques, the optical metrology is largely employed due to its advantage of being accurate, reliable and non-intrusive. However, in many optical techniques, the shape of the particles is assumed to be spherical. The main reason of this limit is due to the lack of theoretical model to describe with precision the interaction of light with large non-spherical particles. The Vectorial Complex Ray Model has been developed to reply this demand. It is based on the ray model but a radical improvement has been done by introducing a new property the wave front curvatures in the ray model. In this thesis, the model is firstly applied to reexamine the Airy theory. It is shown that even in the case of spherical particle VCRM predicts better the intensity and positions of supernumerary bows of rainbow than the Airy theory. Then VCRM is applied to investigate the properties of the rainbows formed by a spheroidal (prolate or oblate) particle. It is shown that VCRM can predict analytically the positions and the intensity of supernumerary bows and the peaks due to the focal effect when it is illuminated by a plane wave in the symmetrical plane.The theoretical research results have been also applied to the experimental characterization of a pendant drop. The intensity ratio of the two first orders of rainbow is shown sensible to the aspect ratio of the equivalent spheroid and it opens a potential to develop a measurement technique to characterize the deformation of pendant drop.

Masters thesis of Liam Farrell, under the supervision of Dr. Duncan O'Dell. Successfully defended on August 26, 2021. / Caustics are regions created by the natural focusing of waves. Some examples include rainbows, spherical aberration, and sonic booms. The intensity of a caustic is singular in the classical ray theory, but can be smoothed out by taking into account the interference of waves. Caustics are generic in nature and are universally described by the mathematical theory known as catastrophe theory, which has successfully been applied to physically describe a wide variety of phenomena. Interestingly, caustics can exist in quantum mechanical systems in the form of phase singularities. Since phase is such a central concept in wave theory, this heralds the breakdown of the wave description of quantum mechanics and is in fact an example of a quantum catastrophe. Similarly to classical catastrophes, quantum catastrophes require some previously ignored property or degree of freedom to be taken into account in order to smooth the phase divergence. Different forms of spontaneous pair-production appear to suffer logarithmic phase singularities, specifically Hawking radiation from gravitational black holes. This is known as the trans-Planckian problem. We will investigate Hawking radiation formed in an analogue black hole consisting of a flowing ultra-cold Bose-Einstein condensate. By moving from an approximate hydrodynamical continuum description to a quantum mechanical discrete theory, the phase singularity is cured. We describe this process, and make connections to a new theory of logarithmic catastrophes. We show that our analogue Hawking radiation is mathematically described by a logarithmic Airy catastrophe, which further establishes the plausibility of pair-production being a quantum catastrophe / Thesis / Master of Science (MSc)

Auf dielektrische Substrate wurden Schichten aus Gold thermisch aufgedampft. Die Schichten wurden neben anderen Methoden wie AFM oder der Messung der Schichtleitfähigkeiten hauptsächlich mit Hilfe der spektroskopischen IR-Ellipsometrie (SIRE) in einem Schichtdickenbereich von 4 bis 60 nm systematisch untersucht. Aus den primär ermittelten ellipsometrischen Parametern tan(Psi) und Delta lassen sich der Brechungsindex n und der Absorptionsindex k bestimmen und auch weitere Größen wie z.B. der elektrische Widerstand bzw. die elektrische Leitfähigkeit errechnen. Die untersuchten Schichten lassen sich anhand der optischen, topographischen und elektrischen Eigenschaften in drei Gruppen einteilen: Dielektrische, aus isolierten Goldinseln bestehende Filme (4 bis 6 nm), Schichten in einem Übergangsbereich (8 bis ca. 16 nm), metallische Schichten (ab ca. 16 nm). Die dielektrischen Goldinselfilme zeigen optische Eigenschaften, die bislang für keine anderen Proben beschrieben worden sind. Der Brechungsindex n ist hoch (4 bis 9 bei 2400/cm) und der Absorptionsindex k klein (0 bis 4 bei 2400/cm). Beide Indizes sind spektral weitgehend konstant. Daß diese Filme dielektrische Eigenschaften besitzen, steht in direktem Widerspruch zur allgemeinen SEIRA-Literatur. Die Inselstruktur der dielektrischen Filme verursacht einen Verstärkungseffekt, der als Oberflächenverstärkte Infrarotabsorption (surface-enhanced infrared absorption - SEIRA) bekannt ist. Es zeigte sich, daß die optischen Konstanten der Filme einen erheblichen Einfluß auf die SEIRA-Verstärkung ausüben. Um Inselfilme mit reproduzierbaren optischen Eigenschaften herstellen zu können, wurde ein lithographisches Verfahren entwickelt. Auf einer geschlossenen, homogenen Goldschicht wurden monodisperse Nanopartikel aus Polystyrol (PS) in einer Monolage deponiert. Die PS-Nanopartikel dienten in einem trockenen Ätzprozeß im Ar-Plasma als lithographische Maske, um die darunterliegende Au-Schicht zu strukturieren. / Thin films were produced on dielectric substrates by thermal evaporation of gold in a high vacuum chamber. These films were investigated systematically in a range between 4 and 60 nm thickness. The method mainly applied was the spectroscopic IR-ellipsometry (SIRE), in addition to other methods like AFM or sheet resistance measurement. The primary results are the ellipsometric parameters tan(Psi) and Delta. They were used to determine the refractive index n and the absorption index k. Electrical parameters can also be calculated. Depending on the optical, topographical and electrical properties the population of different layers can be divided into three parts: dielectric films with isolated gold islands (4 to 6 nm), layers in a transient area (8 to ca. 16 nm), metal films (ca. 16 to 60 nm). The optical properties shown by dielectric gold island films were never before described for other samples. The refractive index n is high (4 to 9 at 2400/cm) and the absorption index small (0 to 4 at 2400/cm). Both indices are nearly constant in the spectral range. Directly in contrast to the SEIRA-literature the island films show dielectric properties. The island structure of the dielectric films gives rise to an enhancement effect called surface-enhanced infrared absorption (SEIRA). It could be shown that the optical constants of the island films have a considerable influence on the enhancement factors. A lithographic method was developed in order to find a way for manufacturing island films with reproducible optical properties. Monodispers polystyrene nanoparticles were deposited in a monolayer on a dense gold layer on a dielectric substrate. The layer of nanoparticles was used as a mask for a dry etch process in a reactive Ar-plasma.

The diploma thesis deals with the design of three length standards, which will serve to ensure metrological traceability between Rigaku nano3DX, SIOS NMM-1, Zeiss UPMC Carat 850 and other devices located at ÚVSSR BUT and CEITEC Brno. The first part of the thesis focuses on the theoretical acquaintance with concepts closely related to the issue of ensuring metrological traceability. In addition, this section deals with computed tomography and the description of individual devices. The second part of the thesis is devoted to design, production process and testing of individual standards. The last part describes the ensuring the calibration of the smallest standard, the so-called Nano standard and the calculation of the uncertainty of measuring its calibrated length. At the end of the thesis, the outputs of these activities are evaluated.