The final thesis is focused on a design of an apartment house and processing of the design documentation. Designed building is situated on the periphery of the town Chrudim in the locality of the housing estate Na Větrníku. It’s a detached house with five floors and a basement. Building has a rectangular plan with dimensions 30,92 × 17,17 m. The foundation of the building is designed as a combination of piles and strips. The vertical constructions will be made of the clay blocks. The floor structures are designed as cast-in-place reinforced concrete floors. The apartment house has a saddle roof with a slope 15°. There are 25 apartments in the building and the mass garages for 15 cars, which are situated in the basement. The garages will serve to the residents of the house.

The thesis focuses on a project of a mountain hotel. Hotel is located in the area Jeseník, altitude of 550 m. It is detached hotel with a rectangular ground plan with one underground floor and four above ground floors. In the basement is the engine room ventilation, bikes room and in the second part of the underground is wellness center. On the first floor is a restaurant. In the other floors are hotel rooms for 1 to 3 person. On the fourth floor are two apartments. The hotel is based on the monolithic footings.In the basement the vertical supporting are from concrete. Other vertical supporting are built from bricks Porotherm 30, which is insulated and ventilated facade with laggin 150 mm. Supporting horizontal structures are made of monolithic reinforced concrete. The building is covered with a double skin roof structure made of wooden trusses.

This diploma thesis is focused on design of project documentation apartment residence with wellness centre in Beskydy Mountains. It is a three floors apartment residence with wellness centre with basement, with is located in sloping plot in the village of Staré Hamry in Frýdek-Místek. Nearby are 2 ski lifts and 3 ski slopes. The whole area is very used by tourist in summer and winter season. In building is 13 apartments and they are designed to be suitable for a longer stay with one apartment is designed for people with limited mobility. Residence is possible make accommodation for 36 people. In wellness part are designed swimming pool, whirlpool, finish and infra saunas. The main disposal idea was separate an accommodation part from wellness part. The supporting system consists of two structural systems. As a main building material was in basement part used a permanent formwork from vibropressed concrete blocks and in upper floor are used ceramic block Porotherm with voids filed by hydrophobic mineral wool. Loadbearing interior basement part consist of reinforced concrete columns with make a space for parking space for cars. Ceiling construction consists of prestressed hollow core slab Spiroll. Roof is designed as a saddle roof. The main result is the correct design of the building with a correct layout design, correct structural design, architectural, energy saving and safety in use of the building.

The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.:1. Introduction 2. Basics 3. Mixed variational formulation 4. Solution method 5. Error estimation 6. LBB conditions 7. Improvement suggestions

The diploma thesis deals with the project documentation of the accommodation facility - a mountain pension in the village of Rudná pod Pradědem. The building has an irregular floor plan and is divided into two parts. One part of the building is used for accommodation with a capacity of 16 people. It has two floors and consists of a flat, green roof. In the second part of the building, on the first floor there is a cafe, massages and infrared sauna. In the basement there is a technical background of the building. Office space and accommodation unit are located in the attic of the building. It consists of a saddle roof. The building is based on simple concrete foundation strips. The vertical load-bearing structures are made of ceramic blocks and blocks of lost formwork in the basement. Ceiling structures are designed as reinforced concrete, monolithic. The building is designed on a sloping terrain.

The aim of the master project is to design a building of an energy-efficient boarding house. It is a three-storey building made of sand-lime masonry with a combination of a saddle roof and a flat green roof. The capacity of the building is 20 visitors. The basement contains a small wellness centre, kitchen storage, general storage, and a utility room. The first floor contains main entrance, a canteen, staff premises, and an accessible guest room. The second floor contains 7 guest rooms and a cleaning room. The third floor contains a meeting room with a kitchenette and toilets, one guest room and entrance to the green roof terrace. Whole building is ventilated by four air conditioning units. The building is heated by floor heating and radiators supplied with a geothermal heat pump and solar thermal panels. Solar thermal panels were analysed.

The thesis describes design of an L-shaped two-storey office building in Chotěboř, which can work with saving energy and be careful to nature. Using renewable materials and new technical equipments. At the end of the design, there should be a building that will be architecturally interesting, energy-efficient and use renewable resources. It is a two-storey building, which is designed for office working and one part of building can be used for teaching science. Main roof on administration part has saddle shape, second roof on part which science centre has flat roof. Both roofs are intensive green roof overgrown with plants. For day illumination, there are design French windows with openings parts. Most of the first floor and the whole second floor belongs to offices and auxiliary staff rooms, toilets, etc. First floor also includes a small training centre with one classroom and necessary facilities (toilet, staff room, etc.). The load-bearing structures (foundations, walls, columns, floor and roof slabs, etc.) are designed from cast-in-place reinforced concrete. Load bearing vertical elements are walls, columns, and posts. Part of the first floor exceeding the layout of the second floor is covered with a flat green roof. Second floor is covered with a saddle green roof. All drawings and 3D rendering were done using ArchiCAD software.

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)

Dans ce mémoire, nous étudions le problème centre-foyer sur un système polynomial. Nous développons ainsi deux mécanismes permettant de conclure qu’un point singulier monodromique dans ce système non-linéaire polynomial est un centre. Le premier mécanisme est la méthode de Darboux. Cette méthode utilise des courbes algébriques invariantes dans la construction d’une intégrale première. La deuxième méthode analyse la réversibilité algébrique ou analytique du système. Un système possédant une singularité monodromique et étant algébriquement ou analytiquement réversible à ce point sera nécessairement un centre. Comme application, dans le dernier chapitre, nous considérons le modèle de Gauss généralisé avec récolte de proies. / In this thesis, we study the center-focus problem in a polynomial system. We describe two mechanisms to conclude that a monodromic singular point in this polynomial system is a center. The first one is the method of Darboux. In this method, one uses invariant algebraic curves to build a first integral. The second method is the algebraic (and analytic) reversibility. A monodromic singularity, which is algebraically or analytically reversible at the singular point, is necessarily a center. As an application, in the last chapter, we consider the generalized Gause model with prey harvesting and a generalized Holling response function of type III.

La thèse est composée d’un chapitre de préliminaires et de deux articles sur le sujet du déploiement de singularités d’équations différentielles ordinaires analytiques dans le plan complexe. L’article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity traite le problème de l’équivalence analytique de familles paramétriques de systèmes linéaires en dimension 2 qui déploient une singularité résonante générique de rang de Poincaré 1 dont la matrice principale est composée d’un seul bloc de Jordan. La question: quand deux telles familles sontelles équivalentes au moyen d’un changement analytique de coordonnées au voisinage d’une singularité? est complètement résolue et l’espace des modules des classes d’équivalence analytiques est décrit en termes d’un ensemble d’invariants formels et d’un invariant analytique, obtenu à partir de la trace de la monodromie. Des déploiements universels sont donnés pour toutes ces singularités. Dans l’article Confluence of singularities of non-linear differential equations via Borel–Laplace transformations on cherche des solutions bornées de systèmes paramétriques des équations non-linéaires de la variété centre de dimension 1 d’une singularité col-noeud déployée dans une famille de champs vectoriels complexes. En général, un système d’ÉDO analytiques avec une singularité double possède une unique solution formelle divergente au voisinage de la singularité, à laquelle on peut associer des vraies solutions sur certains secteurs dans le plan complexe en utilisant les transformations de Borel–Laplace. L’article montre comment généraliser cette méthode et déployer les solutions sectorielles. On construit des solutions de systèmes paramétriques, avec deux singularités régulières déployant une singularité irrégulière double, qui sont bornées sur des domaines «spirals» attachés aux deux points singuliers, et qui, à la limite, convergent vers une paire de solutions sectorielles couvrant un voisinage de la singularité confluente. La méthode apporte une description unifiée pour toutes les valeurs du paramètre. / The thesis is composed of a chapter of preliminaries and two articles on the theme of unfolding of singularities of analytic differential equations in a complex domain. They are both related to the problem of local analytic classification of parametric families of linear systems: When two parametric families of linear systems are equivalent by means of an analytic change of coordinates in a neighborhood of the singularity? The article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity deals with the question of analytic equivalence of parametric families of systems of linear differential equations in dimension 2 unfolding a generic resonant singularity of Poincaré rank 1 whose leading matrix is a Jordan bloc. The problem is completely solved and the moduli space of analytic equivalence classes is described in terms of a set of formal invariants and a single analytic invariant obtained from the trace of the monodromy. Universal unfoldings are provided for all such singularities. The article Confluence of singularities of non-linear differential equations via Borel-Laplace transformations investigates bounded solutions of systems of differential equations describing a 1-dimensional center manifold of an unfolded saddle-node singularity in a family of complex vector fields. Generally, a system of analytic ODE at a double singular point possesses a unique formal solution in terms of a divergent power series. The classical Borel summation method associates to it true solutions that are asymptotic to the series on certain sectors in the complex plane. The article shows how to unfold the Borel and Laplace integral transformations of the summation procedure. A new kind of solutions of parameter dependent systems of ODE with two simple (regular) singular points unfolding a double (irregular) singularity are constructed, which are bounded on certain “spiraling” domains attached to both singular points, and which at the limit converge uniformly to a pair of the classical sectorial solutions. The method provides a unified treatment for all values of parameter.