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.

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.

Proton therapy facilities, as other industrial applications using ionizing radiations, are confronted to radioprotection problems and seek to mitigate the undesirable effects. The aim of this thesis is to study the IBA compact proton therapy center, the Proteus®One in this radioprotection context. The compactness of this system implies important radioprotection issues, mainly the concrete shielding activation where a model allowing to predict and characterize the impact of secondary radiations on the system is required. Numerical simulations using Monte Carlo methods are used and in particular, a benchmark between different existing software has been carried out to validate the use of the Geant4 software in this work. The first part of this thesis focuses on the design of the structural shielding taking into account neutron sources in the model. In particular, the concept of neutron-equivalent source is introduced. In this framework, the quantity and the localization of the generated nuclear waste in concrete are determined. The second part of the work investigates the beam properties and its interactions with matter along the transport beamline. After the analysis of the existing system, a new degrader, which is one of the critical elements for the emission of secondary radiations and for the performances of the device, is proposed. Comparisons between existing (aluminium, graphite, beryllium) and novel (boron carbide and diamond) degrader materials are provided and evaluated against semi-analytical models of multiple Coulomb scattering. The use of diamond with a geometry adaptation allows beam emittance reduction and beam transmission increase. The third part of this thesis considers a complete 3D model of the Proteus®One system. It contributes to acquire a detailed knowledge of the beam properties inside the beamline. This model is validated with experimental data and the assumption of neutron-equivalent source is verified. Finally, maps of proton and neutron interactions are generated to provide a complete mapping of the secondary radiations in the system. These maps can be used to determine dosimetric or radioprotection quantities. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not. / May 2009

Sea-ice ecosystem modelling is a novel field of research. In this thesis, the main organism studied is sea-ice algae. A basic introduction to algae and its importance in the aquatic food web is given first. An introduction to modeling and its purposes is presented, and this is followed by a brief description of ice algae models in practice with some physical conditions which influence ecosystem modelling. In the following Chapter, a simple mathematical model to represent the algae population is derived, and analyzed using pseudo spectral numerical methods implemented with MATLAB. The behaviour of the algae population and the boundary layers are discussed by examining the numerical results. Perturbation and asymptotic analysis is used for further analysis of the system using Maple. In the following Chapter a Nutrient Phytoplankton Zooplankton Detritus (or NPZD) model, which is a commonly used type of model in marine ecosystem modelling, is developed based on the framework of Soetaert and Herman. The model is examined under five different experimental setups (herein we mean numerical experiments) and the results are discussed. The NPZD model implemented is compared with a well-studied model in the literature. Our model can be considered somewhat simpler than other models in the literature (though it still has a much larger parameter space than the idealized model discussed in the previous Chapter). Finally we discuss future directions for research.

This dissertation describes a multidimensional relativistic hydrodynamic code which solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based on the total variation diminishing (TVD) scheme. Several standard tests and test simulations are presented to demonstrate the accuracy, robustness and flexibility of the code. Using this code we have studied three-dimensional hydrodynamic interactions of relativistic extragalactic jets with two-phase ambient media. The deflection angle of the jet is influenced more by the density contrast of the cloud than by the beam Mach number of the jet, and a relativistic jet with low relativistic beam Mach number can eventually be slightly bent after it crosses the dense cloud. Relativistic jet impacts on dense clouds do not necessarily destroy the clouds completely, and much of the cloud body can survive as a coherent blob due to the combination of the geometric influence of off-axis collisions and the lower rate of cloud fragmentation through the Kelvin-Helmholtz instability for relativistic flows. We find that relativistic jets interacting with clouds can produce synchrotron emission knots similar to structures observed in many VLBI-scale radio sources and the synchrotron emission peaks right before the jet passes through the cloud.

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.

This thesis presents a study of reduced-order models based on proper orthogonal decomposition applied to non-isothermal transport phenomena in °uidized beds. A numerical °ow solver called Multiphase Flow with Interphase eXchanges (MFIX) was used to generate a database of solution snapshots for proper orthogonal decomposi- tion (POD). Using POD, time independent basis functions were extracted from the data and the governing equations of the numerical solver were projected onto the basis functions to generate reduced-order models. A reduced-order model was constructed that simulates multi-phase isothermal and non-isothermal °ow. In the reduced-order models (ROMs) the large number of partial di®erential equations were replaced by a much smaller number of ordinary di®erential equations. These reduced-order models were applied to two reference cases, a time extrapolation case and a time-dependent period boundary condition case. Three additional acceleration techniques were devel- oped to further improve computational e±ciency of the POD based ROM: 1) Database splitting, 2) Freezing the matrix of the linear system and 3) Time step adjustment. Detailed numerical analysis of both the full-order model, MFIX and the POD-based ROM, including estimating the number of operations and the CPU time per iteration, was performed as part of this study. The results of this investigation show that the reduced-order models are capable of producing qualitatively accurate results with less than 5% error with a two-order of magnitude reduction of computational costs.

Over the last two decades, advanced fabrication techniques have enabled the fabrication of materials and devices at sub-micron length scales. For heat conduction, the conventional Fourier model for predicting energy transport has been shown to yield erroneous results on such length scales. In semiconductors and dielectrics, energy transport occurs through phonons, which are quanta of lattice vibrations. When phase coherence effects can be ignored, phonon transport may be modeled using the semi-classical phonon Boltzmann transport equation (BTE). The objective of this thesis is to develop an efficient computational method to solve the BTE, both for single-material and multi-material systems, where transport across heterogeneous interfaces is expected to play a critical role. The resulting solver will find application in the design of microelectronic circuits and thermoelectric devices. The primary source of computational difficulties in solving the phonon BTE lies in the scattering term, which redistributes phonon energies in wave-vector space. In its complete form, the scattering term is non-linear, and is non-zero only when energy and momentum conservation rules are satisfied. To reduce complexity, scattering interactions are often approximated by the single mode relaxation time (SMRT) approximation, which couples different phonon groups to each other through a thermal bath at the equilibrium temperature. The most common methods for solving the BTE in the SMRT approximation employ sequential solution techniques which solve for the spatial distribution of the phonon energy of each phonon group one after another. Coupling between phonons is treated explicitly and updated after all phonon groups have been solved individually. When the domain length is small compared to the phonon mean free path, corresponding to a high Knudsen number ([mathematical equation]), this sequential procedure works well. At low Knudsen number, however, this procedure suffers long convergence times because the coupling between phonon groups is very strong for an explicit treatment of coupling to suffice. In problems of practical interest, such as silicon-based microelectronics, for example, phonon groups have a very large spread in mean free paths, resulting in a combination of high and low Knudsen number; in these problems, it is virtually impossible to obtain solutions using sequential solution techniques. In this thesis, a new computational procedure for solving the non-gray phonon BTE under the SMRT approximation is developed. This procedure, called the coupled ordinates method (COMET), is shown to achieve significant solution acceleration over the sequential solution technique for a wide range of Knudsen numbers. Its success lies in treating phonon-phonon coupling implicitly through a direct solution of all equations in wave vector space at a particular spatial location. To increase coupling in the spatial domain, this procedure is embedded as a relaxation sweep in a geometric multigrid. Due to the heavy computational load at each spatial location, COMET exhibits excellent scaling on parallel platforms using domain decomposition. On serial platforms, COMET is shown to achieve accelerations of 60 times over the sequential procedure for Kn<1.0 for gray phonon transport problems, and accelerations of 233 times for non-gray problems. COMET is then extended to include phonon transport across heterogeneous material interfaces using the diffuse mismatch model (DMM). Here, coupling between phonon groups occurs because of reflection and transmission. Efficient algorithms, based on heuristics, are developed for interface agglomeration in creating coarse multigrid levels. COMET is tested for phonon transport problems with multiple interfaces and shown to outperform the sequential technique. Finally, the utility of COMET is demonstrated by simulating phonon transport in a nanoparticle composite of silicon and germanium. A realistic geometry constructed from x-ray CT scans is employed. This composite is typical of those which are used to reduce lattice thermal conductivity in thermoelectric materials. The effective thermal conductivity of the composite is computed for two different domain sizes over a range of temperatures. It is found that for low temperatures, the thermal conductivity increases with temperature because interface scattering dominates, and is insensitive to temperature; the increase of thermal conductivity is primarily a result of the increase in phonon population with temperature consistent with Bose-Einstein statistics. At higher temperatures, Umklapp scattering begins to take over, causing a peak in thermal conductivity and a subsequent decrease with temperature. However, unlike bulk materials, the peak is shallow, consistent with the strong role of interface scattering. The interaction of phonon mean free path with the particulate length scale is examined. The results also suggest that materials with very dissimilar cutoff frequencies would yield a thermal conductivity which is closest to the lowest possible value for the given geometry. / text