This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the auto-catalyst. The diffusion coefficients for A and B are given by DA and DB. These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, v* and v*, depending on DB/DA, where for speeds v ≥ v*, a traveling wave solution exists, while for speeds v < v*, a solution does not exist. Moreover, if DB ≤ DA, and v* and v* are similar to one another and in the order of DB/DA when it is small. On the other hand, when DA ≤ DB there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining the dynamics of general solutions. To fill in the gap of the theoretical study, we use numerical methods to determine vmin for various cases. The numerical algorithm used is the fourth-order Runge-Kutta method (RK4).

<p> This thesis demonstrates the effectiveness of matrix methods in algebraic number fields, the integral closure of pure cubic fields and the use of the Hessian and discriminant to determine integral closure. </p> / Thesis / Master of Science (MSc)

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Ce travail porte sur la caractérisation structurale et optique d'échantillons de SiC. Les échantillons étudiés ont été répartis en trois groupes : des échantillons massifs, des couches épitaxiales épaisses et enfin des couches minces. La croissance des échantillons massifs a été réalisée avec la technique CF-PVT, utilisant une géométrie « d'étranglement ». L'objectif était de filtrer les défauts afin de créer des germes de 3C de haute pureté. La croissance de des couches épaisses par sublimation avait comme objectif la maitrise d'un dopage résiduel faible de type n et p pour des applications composants. Enfin, dans le but de réaliser des composants de type LED blanche des impuretés Ga ont été introduites dans des couches minces épitaxiées par VLS afin de créer des échantillons fortement dopé de type p. Tous ces échantillons ont été étudiés par photoluminescence, micro-Raman, SIMS et microscopie électronique à transmission. Il a été possible de déterminer la concentration d'impuretés et d'identifier le caractère n ou p de ces échantillons. L'analyse des échantillons a été faite en utilisant à la fois l'observation des défauts structurels et les informations obtenues à partir des techniques de caractérisation optique. Nous avons pu obtenir des informations sur les paramètres physiques de 3C-SiC, comme l'énergie de liaison de Ga et Al, la structure fine des excitons liés à l'Al et celle des paires donneurs accepteurs Al-N et Ga-N. Enfin l'apparition d'un nouveau défaut de structure appelée le « fourfold twin » a été observée. / The main topic of this thesis is the structural and optical characterization of SiC samples. The samples were divided in three groups: bulk, thick and thin epilayers. The bulk samples were grown with the CF-PVT technique and used a modified crystal holder geometry. The objective was to filter the defects to and create high purity and quality seeds of 3C-SiC. The thick epilayers were grown with the sublimation epitaxy technique, trying to demonstrate the creation of low impurity n and p type layers for device applications. Finally the thin epilayers were grown with the vapour-liquid-solid technique and doped with Ga impurities in an effort to create either heavily p-type doped samples and components for white LED applications. The samples were studied with low temperature photoluminescence, micro-Raman, SIMS and transmission electron microscopy. With the help of these techniques it was possible to determine the impurity concentration and identif y the n or p character of these samples. A qualitative analysis of the quality of the samples was done using both the observation of the structural defects and the information from the optical characterization techniques. We were able to acquire information about physical parameters of 3C-SiC like the binding energy of Ga and Al, the Al bound exciton fine structure and the Al-N and Ga-N donor acceptor pair fine structure. The appearance of a new structural defect called the fourfold twin was observed and presented.

This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.

L'objectif principal de la présente dissertation est d'étudier le rôle des fissures pointues sur le comportement mécanique des cristaux sous charge à l'échelle atomique. La question d'intérêt est la façon dont un cristal pur, qui contient une seule fissure en équilibre mécanique, se déforme. Deux métaux ont été considérés: l'aluminium, qui est ductile à toute température, et le fer, transformé de ductile en fragile à une température décroissante inférieure à T=77K. Les forces de cohésion dans les deux métaux ont été modélisées via les potentiels phénoménologiques "n-body". A (010)[001] mode I nano-crack a été introduit dans le réseau cristallin parfait de chacun des métaux étudiés en utilisant des déplacements appropriés attribués par l'élasticité anisotrope. A T=0K, des configurations de fissures à l'équilibre ont été obtenues par minimisation d'énergie avec un type mixte de conditions aux limites. Les deux modèles ont révélé que les configurations de fissures restaient stables sous une gamme finie de contraintes appliquées en raison de l'effet de piégeage en treillis. La présente thèse propose une nouvelle approche pour interpréter le comportement mécanique intrinsèque des deux systèmes métalliques sous le chargement. En particulier, la réponse ductile ou fragile d'un système cristallin peut être déterminée en examinant si la barrière de piégeage en treillis d'une fissure préexistante est suffisante pour provoquer le glissement de dislocations statiques préexistantes. Les résultats des simulations ainsi que les données expérimentales démontrent que, selon le modèle proposé, l'aluminium et le fer sont ductiles et fragiles à T=0K, respectivement. / The principal aim of the present dissertation is to investigate the role of sharp cracks on the mechanical behaviour of crystals under load at the atomic scale. The question of interest is how a pure crystal, which contains a single crack in mechanical equilibrium, deforms. Two metals were considered: aluminium, ductile at any temperature below its melting point, and iron, being transformed from ductile to brittle upon decreasing temperature below T=77K. Cohesive forces in both metals were modeled via phenomenological n-body potentials. A (010)[001] mode I nano-crack was introduced in the perfect crystalline lattice of each of the studied metals by using appropriate displacements ascribed by anisotropic elasticity. At T=0K, equilibrium crack configurations were obtained via energy minimization with a mixed type of boundary conditions. Both models revealed that the crack configurations remained stable under a finite range of applied stresses due to the lattice trapping effect. The present thesis proposes a novel approach to interpret the intrinsic mechanical behaviour of the two metallic systems under loading. In particular, the ductile or brittle response of a crystalline system can be determined by examining whether the lattice trapping barrier of a pre-existing crack is sufficient to cause the glide of pre-existing static dislocations on the available slip systems. Simulation results along with experimental data demonstrate that, according to the model proposed, aluminium and iron are ductile and brittle at T=0K, respectively.

The thesis is focused on finding the most appropriate method for constructing the yield curve which will meet the criteria of Solvency II and also the selected evaluation criteria. An overview of advantages of each method is obtained by comparing these methods. Yield curves are constructed using the Czech interest rate swap data from 2007 to 2013. The selection of the evaluated methods respects their public availability and their practical application in life insurance or central banks. This thesis is divided into two parts. The first part describes the theoretical background which is necessary to understand the examined issues. In the second part the analysis of selected methods was carried out with detailed evaluation.

With Ericsson’s goal to have optimal user experience at 5G’s 2020 release, it is very important to optimize transport protocols and techniques to manage the increasing amount of data traffic. Additionally, it will be important to manage handovers between very high speed 5G networks and older networks. Today most of the traffic is video on demand and the amount of this kind of traffic is expected to increase. Moreover, the current amount of data traffic will increase by an order of magnitude over the next few years. This thesis focuses on radio access networks and the difficulties they face in delivering high speed data traffic. This thesis analyzes one of the most used TCP protocols, CUBIC, as well as a new transport protocol developed by Aspera, called the Fast and Secure Protocol. Aspera’s FASP is a new transport protocol that promises full link utilization. FASP is built upon UDP and uses advanced round trip time measurements and queuing delay to detect the available bandwidth between two communicating hosts. This thesis project also provides methods to realize experiments to assess the limitations of transport protocols. These experiments are conducted in an environment that resembles the upcoming 5G radio access network. Results have shown that both delay and packet loss affect TCP more than we expected and that high packet loss is devastating. In contrast, Aspera’s FASP is very resistant to both delay and packet loss. These results and analysis provide a foundation upon which others can build. / Med Ericssons mål att ha optimal användarupplevelse vid släppet av 5G år 2020 är det oerhört viktigt att optimera transportprotokoll och tekniker för att hantera den ökande mängden datatrafik. En annan viktig aspekt kan vara att hantera överlämningar mellan 5G nätverk och äldre radionätverk. Idag är den största trafiken streamad video och prognoser visar att den sortens trafik bara kommer att öka. Prognoserna visar också att all trafik kommer att öka mångfaldigt de närmaste åren. Denna thesis kommer att fokusera på svårigheterna just inom radionätverk. Denna thesis kommer att analysera ett av vårt mest använda transportprotokoll CUBIC TCP, den kommer också att analysera ett helt nytt transportprotokoll utvecklat av Aspera, Fast and Secure Protocol. Aspera lovar fullt utnyttjande av den mellanliggande länken. FASP är byggt ovanpå UDP och använder avancerade tur- och returtidsmätningar för att använda all outnyttjad bandbredd. Denna thesis visar även hur man kan göra experiment för att hitta begränsningar i transportprotokoll. Alla dessa experiment kommer utförs i en miljö som efterliknar det nya 5G-nätverket. Resultatet visar att både förlora paket tillsammans med en hög fördröjning påverkar mycket mer än väntat och att frekvent förlora paket är förödande för TCP. Asperas FASP är i motsats mycket tålig mot både paketförlust och hög fördröjning. Detta resultat och denna analys lägger en grund var andra kan arbeta vidare.