The dissertation is organized into two main parts. The first part considers fractal extension operators. Although extension operators are available for general subsets of Euclidean domains or metric spaces, our extension operator is unique in that it utilizes both the iterative nature of the fractal and finite element approximations to construct the operator. The resulting operator is especially well suited for future numerical work on domains with prefractal boundaries. In the dissertation we prove the existence of a linear extension operator, Π from the space of Hölder continuous functions on a fractal set S to the space of Hölder continuous functions on a larger domain Ω. Moreover this same extension operator maps functions of finite energy on the fractal to H1 functions on the larger domain Ω. In the second part, we consider boundary value problems in domains with fractal boundaries. First we consider the Sierpinski prefractal and how we might apply the technique of singular homogenization to thin layers constructed on the prefractal. We will also discuss numerical approximation in domains with fractal boundaries and introduce a finite element mesh developed for studying problems in domains with prefractal Koch boundaries. This mesh exploits the self-similarity of the Koch curve for arbitrary rational values of α and its construction is crucial for future numerical study of problems in domains with prefractal Koch curve boundaries. We also show a technique for mesh refinement so that singularities in the domain can be handled and present sample numerical results for the transmission problem.

The purpose of this paper is to construct sets, measures and energy forms of certain mixed nested fractals which are spatially homogeneous but not strictly self-similar. We start with the constructions of regular nested fractals, such as Sierpinski gaskets and Koch curves, by employing the iterated map system. Then we show that under the open set condition, the unique invariant (self-similar) measure consists with the normalized Hausdorff measure ristricted on the invariant set. The energy forms construced on regular Sierpinski gaskets and Koch curves is also proved to be a closed form. Next, we use the similar idea, by extending the iterated maps system into a general case, to construct the mixture sets, as well as measures and energy forms. It can be seen that the elements so constructed will not have any strict self-similarity, but them indeed satisfy some weak self-similar properties.

Leakages from seals are one of the important factors that are taken into consideration while designing any machining element. This is because leakages can affect the performance of any component and can also turn into a catastrophe. If looked into it, many parameters can be pointed out that can enhance leakages within the system, some of them may be pressure, temperature, clamping force and bolt distance etc. But the main parameter is the surface roughness, higher the roughness more the leakage and vice-versa. Thus, in this thesis an attempt has been made how the surface roughness can affect the performance of the sealing concept for metal bounded gasket with above four mentioned parameters. Also how leak proof surface can be defined using standard tribological parameters is the aim of this thesis. This report includes the results for methodologies implemented during the thesis and track down the leakages. The leaked surfaces were carefully studied and analyzed using different standards compared with the non leaked surfaces’ roughness parameters. / Läckagerisk från tätande förband är en av de viktigaste faktorerna som beaktas vid utformning av konstruktionsartiklar. Detta på grund av att konsekvenserna kan bli förödande. Det tätande förbandet påverkas av många olika parametrar såsom till exempel tryck, temperatur, klämkraft, skruvavstånd och val av packning. En viktig faktor är ytans beskaffenhet; Generellt läcker en grov yta och vågig yta mer än en fin och plan yta. Således har i denna avhandling ytans beskaffenhet studerats tillsammans med en packning av typen metallburen gummipackning för att påvisa täthetfunktionen som en funktion av tryck, temperatur, klämkraft och skruvavstånd. Denna rapport innehåller resultat och analys av olika standardmetoder för de ytor som ingick i utredningen.

Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Z d but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff di- mension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts. / Mathematics

This thesis deals with the replacement of the lid gasket of the primary collector of the steam generator VVER 1000. Original sealing by nickel rings is replaced by kammprofile gasket with expanded graphite layers. The thesis compare the properties of both types of gaskets and the new and the original configuration of flange joint which have been calculated according to EN 1591. The results are compared and conclusions arising therefrom are presented. The work includes results of FEM analysis of the new configuration of the flange joint. There is also a description of the main components of the nuclear power plants VVER 1000 primary circuit in the introductory part which focused on the construction and operation of the steam generator and its primary collector.

<p>Within the telecommunication business there are a lot of different hardware designs made for outside locations. Many of these outdoor products contain sensitive electronic equipment and all of these designs must be able to function in extreme environments. They might be mounted on the ground, on a wall or on masts at varying altitudes. They need to be enclosed and protected against blizzards, moisture, sandstorms, earthquakes, dust and similar contaminations or nature phenomena in order to assure a reliable and proper function of the device.</p><p>To delimit this thesis the focus is completely set on outdoor enclosures with hinged doors. The sealing solution for the enclosure door is crucial because it is the weakest link in the environmental protection. The aim with this thesis is to find a robust yet versatile sealing solution for Ericsson outdoor cabinets.</p><p>The sealing solution does not only concern the gasket design, it is in fact the entire principle when it comes to seal the door. Interesting features are choice of locking system, the positions of the hinges and other details which might affect the sealing of the enclosure door.</p><p>The project includes the whole product development process from pre-study to concept development and evaluation of proposal design. The pre-study contain extensive literature research, benchmark and a state of the art investigation. A number of concepts are generated, screened, compared and ranked with systematic concept development methods. At last, one final concept is selected for further development. The chosen sealing solution is refined and a functional model is made. A simple prototype of the sealing solution is designed, manufactured and tested to validate the functionality of the concept.</p><p>An economical analysis is performed in order to approximate the manufacturing cost of the gasket proposed in the sealing solution and to compare the unit price for different batch sizes. The water intrusion test indicates that the solution seems promising and that the result is a simple and robust sealing solution that easily can be implemented on various enclosure types.</p> / <p>Inom telecom-industrin finns det många typer av hårdvara som är konstruerad för att placeras utomhus. Många av dessa utomhusprodukter innehåller känslig elektronisk utrustning och alla dessa konstruktioner måste fungera i extrema miljöer. De kan monteras på marken, på väggar eller på master på olika höjder. De måste vara täta och skyddade mot snöstormar, fukt, sandstormar, jordbävningar, damm och liknande föroreningar eller naturfenomen för att säkerställa en tillförlitlig och korrekt funktion hos anordningen.</p><p>För att begränsa detta examensarbete är fokus helt inställt på utomhusskåp med gångjärnsupphända dörrar. Tätningslösningen för skåpdörren är kritisk eftersom den utgör den svagaste länken i väderskyddet. Målet med detta examensarbete är att hitta en robust men samtidigt mångsidig lösning för Ericssons utomhuskabinet.</p><p>Tätningslösningen handlar inte enbart om packningsutformningen utan den täcker faktiskt hela principen för hur dörren tätas. Intressanta delar är val av lås-lösning, placeringen av gångjärnen och andra detaljer som kan påverka tätningen av skåpsdörren.</p><p>Projektet behandlar hela produktutvecklingsprocessen från förstudie till konceptutveckling och utvärdering av föreslagen konstruktion. Förstudien innehöll en utförlig litteraturstudie, en ”benchmark” och en ”state of the art” undersökning. Ett antal koncept genererades, kontrollerades, jämfördes och rankades med hjälp av systematiska konceptutvecklingsmetoder. Till sist valdes ett slutgiltigt koncept ut för vidare utveckling. Den valda tätningslösningen förfinades och en funktionsmodell byggdes. En enkel prototyp av tätningslösningen konstruerades, tillverkades och testades för att validera funktionen hos konceptet.</p><p>En ekonomisk analys utfördes för att uppskatta tillverkningskostnaden för den föreslagna packningen i tätningslösningen och för att jämföra enhetspriset för olika seriestorlekar. Ett vattentäthetstest visar att lösningen verkar lovande och att resultatet är en enkel och robust tätningslösning som på ett enkelt sätt kan implementeras på olika skåpstyper.</p>

Within the telecommunication business there are a lot of different hardware designs made for outside locations. Many of these outdoor products contain sensitive electronic equipment and all of these designs must be able to function in extreme environments. They might be mounted on the ground, on a wall or on masts at varying altitudes. They need to be enclosed and protected against blizzards, moisture, sandstorms, earthquakes, dust and similar contaminations or nature phenomena in order to assure a reliable and proper function of the device. To delimit this thesis the focus is completely set on outdoor enclosures with hinged doors. The sealing solution for the enclosure door is crucial because it is the weakest link in the environmental protection. The aim with this thesis is to find a robust yet versatile sealing solution for Ericsson outdoor cabinets. The sealing solution does not only concern the gasket design, it is in fact the entire principle when it comes to seal the door. Interesting features are choice of locking system, the positions of the hinges and other details which might affect the sealing of the enclosure door. The project includes the whole product development process from pre-study to concept development and evaluation of proposal design. The pre-study contain extensive literature research, benchmark and a state of the art investigation. A number of concepts are generated, screened, compared and ranked with systematic concept development methods. At last, one final concept is selected for further development. The chosen sealing solution is refined and a functional model is made. A simple prototype of the sealing solution is designed, manufactured and tested to validate the functionality of the concept. An economical analysis is performed in order to approximate the manufacturing cost of the gasket proposed in the sealing solution and to compare the unit price for different batch sizes. The water intrusion test indicates that the solution seems promising and that the result is a simple and robust sealing solution that easily can be implemented on various enclosure types. / Inom telecom-industrin finns det många typer av hårdvara som är konstruerad för att placeras utomhus. Många av dessa utomhusprodukter innehåller känslig elektronisk utrustning och alla dessa konstruktioner måste fungera i extrema miljöer. De kan monteras på marken, på väggar eller på master på olika höjder. De måste vara täta och skyddade mot snöstormar, fukt, sandstormar, jordbävningar, damm och liknande föroreningar eller naturfenomen för att säkerställa en tillförlitlig och korrekt funktion hos anordningen. För att begränsa detta examensarbete är fokus helt inställt på utomhusskåp med gångjärnsupphända dörrar. Tätningslösningen för skåpdörren är kritisk eftersom den utgör den svagaste länken i väderskyddet. Målet med detta examensarbete är att hitta en robust men samtidigt mångsidig lösning för Ericssons utomhuskabinet. Tätningslösningen handlar inte enbart om packningsutformningen utan den täcker faktiskt hela principen för hur dörren tätas. Intressanta delar är val av lås-lösning, placeringen av gångjärnen och andra detaljer som kan påverka tätningen av skåpsdörren. Projektet behandlar hela produktutvecklingsprocessen från förstudie till konceptutveckling och utvärdering av föreslagen konstruktion. Förstudien innehöll en utförlig litteraturstudie, en ”benchmark” och en ”state of the art” undersökning. Ett antal koncept genererades, kontrollerades, jämfördes och rankades med hjälp av systematiska konceptutvecklingsmetoder. Till sist valdes ett slutgiltigt koncept ut för vidare utveckling. Den valda tätningslösningen förfinades och en funktionsmodell byggdes. En enkel prototyp av tätningslösningen konstruerades, tillverkades och testades för att validera funktionen hos konceptet. En ekonomisk analys utfördes för att uppskatta tillverkningskostnaden för den föreslagna packningen i tätningslösningen och för att jämföra enhetspriset för olika seriestorlekar. Ett vattentäthetstest visar att lösningen verkar lovande och att resultatet är en enkel och robust tätningslösning som på ett enkelt sätt kan implementeras på olika skåpstyper.

This Master’s thesis deals with flange joints. A suitably designed flange joint (FJ) construction and installation is necessary to ensure the reliability of piping systems and machinery where these joints are used. The thesis describes the procedures of their design and assessment in terms of tightness, strength and durability. It focuses on the stiffness calculation of all components of FJ – primarily the stiffness of flanges, bolts and seals. The main part of the work was to create a computational program by using the Python language to determine the appropriate preload force in the bolts. The program uses the procedures described in the ČSN EN 1591-1 standard. The thesis describes computational algorithms of this program, verification of the program and its use in the assessment of FJ on a specific technical work – pressure vessel with adjacent piping. Verification was performed by comparing the acting force to the seals obtained from the computational program and the stress-strain analysis using the finite element method (FEM), where the load model in this stress-strain analysis included the preload force obtained from the computational program. The application of the pressure vessel computational program consisted in determining the preload forces for all FJs of this assembly. The last part describes the assessment of the most loaded FJ. Again, stress-strain state was evaluated using FEM and FJ was assessed for tightness, strength and durability using the NTD A.S.I. standard.

This master thesis focuses on the issue of tightness evaluation of gasketed tubesheet in U tube exchangers, which meets strength requirements of ČSN EN 13 445-3 and ČSN EN 1591-1 standards. It deals with the forces acting on the gasket when measuring the effects acting on the entire heat exchanger. A separate part is devoted to the calculation of the heat profile in the heat exchanger and verification of the strength of the heat exchanger. The final part introduces model of a heat exchanger, on which a possible approach to solving the tightness of the tubesheet in heat exchangers is presented. In thesis temperature field evaluation was conducted, the results of which were used in stress strain analysis, in order to obtain gasket contact pressure. Extreme gasket contact pressures were used to estimate leak rate limits.

This diploma work is engaged in replacement of gasket main dividing plane of reactor coolant pumps in nuclear power plant Paks. Of the newly suggested gasket is kammprofile gasket with expanded graphite layer. This work contain suggestion and calculation of new sealing a knot and calculation existing sealing the knot. Results are confrontacion and sequentially is discussed influence on main dividing plane HCČ 317 by use the new and the existing gasket. In this work is contained description brief of legislation. This legislation must keep by design components dedicated for nuclear equipment. Next this work contain view of the most important sealing knots used in primary system of Nuclear Power Plant type VVER 440.