A thermal analysis of a conventional vaporization source by finite difference methods, including experimental validation, is presented. Such a system is common to industries whose chief concern is the precipitation of inorganic coatings. Both the physical and the model systems are comprised of a number of layers, or strata, arranged in a rectangular configuration. The model strata represent the component and deposition materials of the physical vaporization source. The symmetry and simplistic geometry of the operational source permit the use of a two-dimensional model, thereby neglecting gradients in the third dimension. The production unit, as well as the numerical model, experience various modes of heat transfer, including radiation, convection, conduction, internal generation, and phase change. Moreover, the system inputs are time-dependent. The numerical model is subsequently compared to and validated against both simplistic case studies and the physical production system. Data collected from the operational deposition source is examined and analyzed in comparison to corresponding information generated by the numerical model. Sufficient agreement between the data sets encourages the utilization of the numerical model as a practical indicator of the subject system's behavior. Finally, recommendations for modifications to the physical vaporization source, yielding practical improvements in temperature uniformity, are evaluated based on the predictions of the validated numerical model. The goal is the attainment of an ideally uniform temperature distribution that would correspond to highly desirable performance of the process vaporization system. / Master of Science

Near shore hydrodynamics has been an important research area dealing with coastal processes. The nearshore coastal region is the region between the shoreline and a fictive offshore limit which usually is defined as the limit where the depth becomes so large that it no longer influences the waves. This spatially limited but highly energetic zone is where water waves shoal, break and transmit energy to the shoreline and are governed by highly dispersive and non-linear effects. An accurate understanding of this phenomena is extremely useful, especially in emergency situations during hurricanes and storms. While the shallow water assumption is valid in regions where the characteristic wavelength exceeds a typical depth by orders of magnitude, Boussinesq-type equations have been used to model near-shore wave motion. Unfortunately these equations are complex system of coupled non-linear and dispersive differential equations that have made the developement of numerical approximations extremely challenging. In this dissertation, a local discontinuous Galerkin method for Boussinesq-Green Naghdi Equations is presented and validated against experimental results. Currently Green-Naghdi equations have many variants. We develop a numerical method in one horizontal dimension for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations and a careful proof of linear stability of the numerical method is carried out. Verification is done against a linearized standing wave problem in flat bathymetry and h,p (denoted by K in this thesis) error rates are plotted. The numerical method is validated with experimental data from dispersive and non-linear test cases. / text

Transition in high-speed boundary layers is investigated using direct numerical simulation (DNS). A compressible Navier-Stokes code that is specifically tailored towards accurate and efficient simulations of boundary layer stability and boundary layer transition was developed and thoroughly validated. Particular emphasis was put into the adoption of a high-order accurate spatial discretization including a boundary closure with the same stencil width as the interior scheme. Oblique breakdown has been shown, using both temporal and spatial DNS, to be a viable route to transition for the boundary layer of the sharp 7° cone at Mach 3.5 investigated by Corke 2002. A 'wedge-shaped' transitional regime was observed to be characteristic for this type of breakdown on the cone geometry. Furthermore, it was shown that the dominance of the longitudinal mode in the nonlinear transition regime of oblique breakdown is due to a continuously nonlinear forced transient growth. That is the primary pair of oblique waves permanently 'seeds' disturbances into the longitudinal mode, where these disturbances exhibit non-modal unstable behavior. In addition to the simulations of controlled transition via oblique breakdown, six simulations have been conducted and analyzed where transition is initiated by multiple primary waves. Despite the broader spectrum of primary waves, typical features of oblique breakdown are still apparent in these simulations and therefore, it may be conjectured, that oblique breakdown initiated by one primary pair of waves is a good model for the nonlinear processes in natural transition. Furthermore, hypersonic boundary layer stability and transition for a flared and a straight cone at Mach 6 was investigated. In particular, a comparative investigation between both geometries regarding the K-type breakdown was performed in order to give some indications towards the open question how strong the nonlinear transition processis altered by the cone flare.

This thesis is concerned with the design of numerical methods for quantum simulation and the development of improved models for quantum relaxation. Analysis is presented for the treatment of quantum systems using the density matrix formalism. This approach has been developed from the early days of quantum mechanics as a tool to describe from a statistical point of view a large number of identical quantum ensembles. Traditional methods are well established and reliable, but they perform poorly for practical simulation as the system size is scaled up. Ad hoc schemes for nuclear spin dynamics appearing in the literature can be shown to fail in certain situations. The challenge is therefore to identify efficient reduction methods for the quantum system which are also based on a rigorous foundation. The method presented in the thesis, for the time–independent Hamiltonian case, combines a quantum density matrix formalism with a procedure based on Chebyshev polynomials; application of the method to Nuclear Magnetic Resonance (NMR) spectroscopy is considered, and it is shown that the new technique outperforms existing alternatives in term of computational costs. The case of a time–dependent Hamiltonian in NMR simulation is studied as well and some splitting methods are presented. To the author’s knowledge this is the first time such methods have been applied within the NMR framework, and the numerical results show a better error–to–cost rate than traditional methods. In a separate strand of research, formulations for open quantum systems are studied and new dynamical systems approaches are considered for this problem. Motivations This thesis work is mainly focused on nuclear spin dynamics. Nuclear spin dynamics constitutes the basis for NMR, which is a very powerful spectroscopy technique that exploits the interaction between nuclear spins and magnetic fields. The same technique is used to reveal the presence of hydrogen atoms in the blood for Magnetic Resonance Imaging (MRI). Within this framework the role of simulations is extremely important, as it provides a benchmark for studies of new materials, and the development of new magnetic fields. The main computational issue is that with current software for NMR simulation it is extremely expensive to deal with systems made of more than few (7–10) spins. There is therefore a strong need to develop new algorithms capable of simulating larger systems. In recent years NMR simulations have been found to be one of the most favorable candidates for quantum computing. There are two reasons for this: nuclear quantum states maintain extremely long coherences, and it is possible to attain a very strong control on the quantum state via the application of sequences of pulses. In order to develop a proper quantum computer it is fundamental to understand how the entangled states lose coherence and relax back to equilibrium by means of external interactions. This process is described as relaxation in an open quantum system. The theory for such systems has been available for 50 years but there are still substantial limitations in the two main approaches. There are also relatively few numerical approaches for the simulation of such systems, for this reason it is important to develop numerical alternatives for the description of open quantum systems. Thesis Outline The thesis is organized as follow: the first two chapters provide background material to familiarize the reader with fundamental concepts of both quantum mechanics and nuclear spin dynamics; in this part of the thesis no new results are presented. The first chapter introduces the concept of quantum systems and the mathematical environment with which we describe those systems. We also present the main equations we need to solve to determine the dynamics of a quantum system in a statistical framework. In the second chapter we introduce the nuclear spin system, that is the physical system that has been the main reference frame in this work, for both tests and practical applications of the new algorithms. We describe how nuclear spin systems are at the basis of very important applications like NMR spectroscopy and MRI. We present in some detail the physical features of the NMR technique and the equations we need to solve to describe the dynamics of a spin system; we also focus on the relevance of numerical simulations for these systems, and consequently which must be the interest in developing new algorithms, and the major obstacles which must be overcome. In the third chapter we investigate the numerical challenges that arise in simulation of quantum systems, we describe some of the methods that have been developed in the literature, focusing on the performances and the computational costs of them, setting the new developments of this thesis in the proper research frame. We discuss one of the major issues: the evaluation of the matrix exponential. We also present the analysis we have done of a recent method called Zero Track Elimination (ZTE) that has been developed specifically for NMR simulations. This analysis shows the limitations of this method but also gives a mathematical explanation of why–and in which cases–it works. In the fourth chapter we present the main result of the thesis, the development of a new method that directly evaluates the expectation values for a quantum simulation via a different application of the well known Chebyshev expansion. We have proved that this new method can provide an excellent boost in terms of performance, with computational costs that can be reduced by a factor ten in common cases. (The results of this chapter and the new method have been presented in international conferences and recently they have been submitted for publication). We also present some attempts we have made in the application of splitting methods for the evolution of the system in a time dependent environment. To our knowledge this is the first time splitting methods have been used for NMR simulations. The results of this approach are as follows: for a particular splitting technique combined with a Lanczos iteration method it is possible to speed up the calculation by a third if compared with a Lanczos type method whilst keeping the error below a critical threshold. This last approach is still a work in progress especially in terms of developing clever ways to split the Hamiltonian. The last chapter of this thesis deals with simulation of quantum systems interacting with an external environment. After presenting the main theoretical approaches for the description of such systems we then survey several the techniques that are currently used for the numerical implementation of such theories. As a work in progress we present a considerably different new approach we have been developing aiming to overcome some of the issues that arise when treating this kind of system within usual frameworks. This is somewhat speculative work that gives rise to some new directions in the development of a numerical description for open quantum systems. We also present some numerical results. (The main core of this chapter has been presented in international conferences).

We explore the effects of surface plasmon hybridization in graphene nanostructures and silver nanoparticles as applied to novel plasmonic phenomena. The analysis is based on the theory of surface plasmon hybridization under the boundary charges method. This method, which is based in the electrostatic approximation, has been largely used to predict the resonant frequencies in strongly coupled nanoparticle clusters. Here, we extend this formalism to analyze novel plasmonic phenomena such as the blueshift of modes in graphene plasmonics, near-field radiation, thermal transport and plasmon-induced hot carrier generation in silver nanoparticles. Furthermore, we develop analytical solutions for graphene nanodisks and metallic spheres that allow for fast and accurate modeling. The analytic models provide the basis to derive a large number of results, including prediction of hybrid eigenmodes and bandstructures, far-field response, and near-field response under thermally induced fluctuations. We predict that the strong near-filed coupling in graphene nanodisk stacks can induce a blueshift in the resonant frequencies up to the near-infrared part of the spectrum. We find that the strong near-filed coupling between disks can also lead to large values of radiative thermal conductance when thermally induced fluctuations are included. In this regard, an enhancement over the blackbody limit of up to two and four orders of magnitude was observed for co-planar and co-axial disk configurations. The strong coupling between coplanar disks was also explored for the development of plasmonic waveguides by considering long co-planar disk arrays. It was observed that the array posseses great potential for plasmonic waveguiding, with a strong degree of confinement for disks smaller than 200 nm. Thermal activation of the guided modes showed a thermal conductivity of up to 4.5 W/m K and thermal diffusivity of up to 1:4 x 10-3 m2/s. The large values of thermal diffusivity suggest the potential of graphene disk waveguides for thermotronic interconnects. The plasmon-induced hot carrier generation in silver nanosphere dimers was also studied. The modeling considered analytical solution for metallic nanospheres, from which the electrostatic potential of each sphere was obtained. Using these results, the hot carrier generation was explored under the basis of the Fermi golden rule. The results show a large number of hot carriers at the low frequency modes. This values exceed the number of generated hot carriers on a single sphere. The energy distribution of photogenerated electrons and holes showed a large energy gap that can be explored in photocatalysis and photovoltaic energy conversion.

L'objectif de cette thèse est de comprendre la dynamique des grandes populations de neurones interconnectées. La méthode utilisée pour atteindre cet objectif est un mélange de modèles mésoscopiques et calculs de haute performance. Le premier permet de réduire la complexité du réseau neuronale et le second de réaliser des simulations à grandes échelles. Dans la première partie de cette thèse une nouvelle approche du champ moyen est utilisée pour étudier numériquement les effets du bruit sur un groupe extrêmement grand de neurones. La même approche a été utilisée pour créer un modèle d' hypercolonne du premier cortex visuel d'où l'unité basique, est des grandes populations de neurones au lieu d'une seule cellule. Les simulations sont réalisées en résolvant un système d'équation différentielle partielle qui décrit l'évolution de la fonction de densité de probabilité du réseau. Dans la deuxième partie de cette thèse est présentée une étude numérique de deux modèles de champs neuronaux du premier cortex visuel. Le principal objectif est de déterminer comment les contours sont sélectionnés dans le cortex visuel. La différence entre les deux modèles est la manière de représenter des préférences d'orientations des neurones. Pour l'un des modèles, l'orientation est une caractéristique de l'équation et la connectivité dépend d'elle. Dans l'autre, il existe une carte d'orientation qui définit une fonction d'entrée. Toutes les simulations sont réalisées sur un cluster de processeurs graphiques. Cette thèse propose des techniques pour simuler rapidement les modèles proposés sur ce type de machine. La vitesse atteinte est équivalente à un cluster standard très grand. / The aim of this thesis is to understand the dynamics of large interconnected populations of neurons. The method we use to reach this objective is a mixture of mesoscopic modeling and high performance computing. The rst allows us to reduce the complexity of the network and the second to perform large scale simulations. In the rst part of this thesis a new mean eld approach for conductance based neurons is used to study numerically the eects of noise on extremely large ensembles of neurons. Also, the same approach is used to create a model of one hypercolumn from the primary visual cortex where the basic computational units are large populations of neurons instead of simple cells. All of these simulations are done by solving a set of partial dierential equations that describe the evolution of the probability density function of the network. In the second part of this thesis a numerical study of two neural eld models of the primary visual cortex is presented. The main focus in both cases is to determine how edge selection and continuation can be computed in the primary visual cortex. The dierence between the two models is in how they represent the orientation preference of neurons, in one this is a feature of the equations and the connectivity depends on it, while in the other there is an underlying map which denes an input function. All the simulations are performed on a Graphic Processing Unit cluster. Thethesis proposes a set of techniques to simulate the models fast enough on this kind of hardware. The speedup obtained is equivalent to that of a huge standard cluster.

In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation in an open sphere around the origin, with constant internal and external damping coefficients and nonlinear term of the form G' (w) = w ^p, with p an odd number greater than 1. We prove that our scheme is consistent of quadratic order, and provide a necessary condition for it to be stable order n. Part of our study will be devoted to study the effects of internal and external damping.

Neste trabalho é apresentada a solução das equações que regem o escoamento unidimensional não permanente em dutos sob pressão por meio do esquema numérico de MacCormack, esquema este, já empregado nos escoamentos transientes em condutos livres. É apresentada, também, a comparação dos resultados obtidos com a aplicação do esquema de MacCormack em relação aos obtidos através do método das características, na solução de transientes hidráulicos em condutos forçados. / This dissertation introduces the MacCormack numerical scheme for the solution of the one-dimensional unsteady pressurized flow equations, this scheme is already employed for solving open-channel transient flows. It is presented, also, the comparison of the results obtained from the application of the MacCormack numerical scheme with the obtained using the Method of the Characteristics, in the solution of hydraulic transient in pressurized flow.

Em muitas simulações eletromagnéticas utilizando o método FDTD, é desejado que os campos radiados pelas estruturas em análise sejam transmitidos para fora do domínio computacional. Infelizmente isto não é possível de ser realizado através do método FDTD em sua forma original. Para resolver este problema, deve-se implementar, nas superfícies limítrofes dos domínios computacionais, condições especiais denominadas na literatura técnica de Condições de Fronteiras de Absorção, ou, em inglês, \"Absorbing Boundary Conditions\" (ABC´s). Essas Condições de Fronteiras de Absorção impedem que os campos radiados sejam refletidos nas superfícies limítrofes dos domínios computacionais, retornando para o interior do domínio e interferindo no resultado final das simulações. Não existe uma técnica de absorção ideal, ou seja, que elimine totalmente a reflexão. As técnicas atualmente existentes possuem vantagens e desvantagens, podendo ser mais ou menos eficientes, o que faz com que esse tema ainda seja motivo de extensivos estudos. O objetivo deste trabalho consiste no estudo, implementação e comparação de Condições de Fronteiras de Absorção e na indicação de uma possível melhoria nessa área. São realizadas simulações em domínios bidimensionais e tridimensionais para se determinar vantagens e desvantagens de cada técnica de absorção. A análise dos resultados das simulações está focalizada no grau de atenuação que as ABCs possuem e na carga computacional despendidas por elas. Este trabalho é concluído com simulações empregando as condições de fronteiras analisadas para três estruturas clássicas. As vantagens e desvantagens de cada ABC são apresentadas e uma melhoria proposta na técnica de Auto Teleportação de Campos, ou, em inglês, \"Self Teleportation of Fields\" é validada. As estruturas analisadas são uma microlinha de transmissão, um filtro planar e um cilindro metálico iluminado por uma onda plana uniforme. / In many electromagnetic computational simulations using the FDTD method, it is desired that the electromagnetic fields radiated by the structures under analysis can be transmitted outwards the computational domain. Unfortunately, this is impossible to be done by the FDTD method in its original form. To mitigate this problem, one must apply special conditions to the computational domain boundaries, known in the technical literature as Absorbing Boundary Conditions (ABCs) These Absorbing Boundaries Conditions prevent the radiated fields to be reflected by boundaries back into the computational domain. Without them, these fields would interfere with the final simulation results. However, there is no ideal technique that completely eliminates the reflections. The existing techniques have advantages and disadvantages, which make them more or less efficient, still making this subject a theme of extensive studies. This work is aimed at studying, implementing and comparing these Absorbing Boundary Conditions and at indicating a possible improvement in this field. Simulations in bi-dimensional and three-dimensional domains were made to evaluate advantages and disadvantages of each absorption technique. The analysis of the simulation results was focused in the attenuation degree of the ABCs and their computational burden. The work is concluded with simulations using the analyzed ABCs for three classic structures. The advantages and disadvantages of each ABC are presented and a proposed improvement on the \"Self Teleportation of Fields\" technique is validated. The analyzed structures are a microstrip line, a planar filter and a metallic cylinder illuminated by a uniform plane wave.

The proposed research is essentially concerned on numerical simulation of materials and structures commonly used in the aerospace industry. The work is primarily focused on the study of the fracture mechanics with emphasis to composite materials, which are widely employed in the aerospace and automotive industry. Since human lives are involved, it is highly important to know how such structures react in case of failure and, possibly, how to prevent them with an adequate design. It has become of primary importance to simulate the material response in composite, especially considering that even a crack, which could be invisible from the outside, can propagate throughout the structure with small external loads and lead to unrecoverable fracture of the structure. In addition, structures made in composite often present a complex behaviour, due to their unconventional elastic properties. A numerical simulation is then a starting point of an innovative and safe design. Conventional techniques (nite elements for example) are not su-cient or simply not ecient in providing a satisfactory description of these phenomena. In fact, being based on the continuum assumption, mesh-based techniques suer of a native incapacity of simulating discontinuities. Novel numerical methods, known as Meshless Methods or Meshfree Methods (MM) and, in a wider perspective, Partition of Unity Methods (PUM), promise to overcome all the disadvantages of the traditional finite element techniques. The absence of a mesh makes MM very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, MM still have signicant limitations that prevent their acceptance among researchers and engineers. Because of the infancy of these methods, more efforts should be made in order to improve their performances, with particular attention to the computational time. In summary, the proposed research will look at the attractive possibilities offered by these methods for the study of failure in composite materials and the subsequent propagation of cracks.