Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-08T14:12:47Z No. of bitstreams: 1 afonsoricardovaz.pdf: 1070446 bytes, checksum: c3e55ee918c4bb2fabde971d6aaeda6d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:27:36Z (GMT) No. of bitstreams: 1 afonsoricardovaz.pdf: 1070446 bytes, checksum: c3e55ee918c4bb2fabde971d6aaeda6d (MD5) / Made available in DSpace on 2016-07-13T13:27:36Z (GMT). No. of bitstreams: 1 afonsoricardovaz.pdf: 1070446 bytes, checksum: c3e55ee918c4bb2fabde971d6aaeda6d (MD5) Previous issue date: 2016-02-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Analisamos um modelo cosmológico clássico não-comutativo, através da formulação ADM, para um universo homogêneo e isotrópico com curvaturas constantes das seções espaciais (k) que podem ser positiva, negativa ou zero. A matéria é representada por um fluido perfeito de pressão negativa, fluido fantasma, que satisfaz a equação de estado p = , com < −1, onde p é a pressão e é a densidade do fluido. Este fluido é responsável pela expansão acelerada do universo. Usamos o formalismo de Schutz, o qual é capaz de fornecer uma hamiltoniana para o fluido perfeito, tendo como base as equações de movimento para potenciais de velocidade. Utilizamos a métrica de Friedmann-Robertson-Walker, onde a não-comutatividade foi introduzida através de parênteses de Poisson não triviais. Para recuperarmos as variáveis comutativas, introduzimos transformações entre as variáveis que dependem de um parâmetro não-comutativo ( ). A introdução da não-comutatividade tem por motivação explicar a presente expansão acelerada do universo e tentar contornar alguns problemas que são encontrados na abordagem comutativa, como a singularidade inicial e o Big Rip, comportamento previsto na literatura, que indica que o universo irá a um tempo finito a um fator escala infinito. Depois de obtermos as equações dinâmicas para esse modelo, comparamos a evolução do universo entre os casos comutativos e não-comutativos, buscando alterações nos comportamentos conhecidos. A análise dos dados para a dinâmica do universo obteve quatro fatores ajustáveis, o parâmetro , um parâmetro associado a energia inicial do fluido, o parâmetro k e o , além das condições iniciais presentes no modelo. Para cada novo valor de , obtivemos novas equações de movimento. Os resultados demonstraram que o parâmetro se mostrou muito útil para a descrição de um universo em expansão acelerada. Obtemos, ao fim deste trabalho, uma estimativa para o valor do parâmetro , nas condições atuais do universo. Depois disso, usamos esse valor estimado de , em um dos nossos modelos cosmológicos não-comutativos, para determinar o tempo que esse universo levará para atingir o Big Rip. / We have analyzed a non-commutative classic cosmological model using the ADM formulation for a homogeneous and isotropic universe with constant curvature of space sections (k) that can be positive, negative or zero. The matter is represented by a perfect fluid with negative pressure, phantom fluid, which satisfies the equation of state p = , with < −1, where p is pressure and is energy density. This fluid is responsible for the accelerating state of the universe. We use Schutz formalism, which is capable of providing a Hamiltonian for the perfect fluid, based on the equations of motion for velocity potentials. We use Friedmann-Robertson-Walker metric, and noncommutativity was introduced by nontrivial Poisson bracket. To recover the commutative variables, we introduced transformations between the variables that depend on a non-commutative parameter ( ). The main motivation for the introduction of noncommutativity is trying to explain the present accelerated state of the universe. We shall also try to solve some problems that are found in the commutative approach, as the initial singularity and the Big Rip, expected behavior in the literature, which indicates that the universe will go to an infinite scale factor, in a finite time. Once we obtained the dynamic equations for this model, we solved them and compared the evolution of the universe between commutative and non-commutative cases seeking changes in the known behavior. The solutions have four constants, the parameter , a parameter associated with initial energy of the fluid C, the parameter k and in addition to the initial conditions of the cosmological model. For each new value of , we obtained new equations of motion. The results showed that the parameter has proved to be very useful for describing an accelerating universe. We obtained at the end of this work an estimative for the value of the parameter , for the present conditions of the Universe. Then, using that value of , in one of our noncommutative cosmological models, we computed the amount of time this universe would take to reach the Big Rip.

Peripheral vascular grafts are used for the treatment of peripheral arterial disease and arteriovenous grafts for vascular access in end stage renal disease. The development of neo-intimal hyperplasia and thrombosis in the distal anastomosis remains the main reason for occlusion in that region. The local haemodynamics produced by a graft in the host vessel is believed to significantly affect endothelial function. Single spiral flow is a normal feature in medium and large sized vessels and it is induced by the anatomical structure and physiological function of the cardiovascular system. Grafts designed to generate a single spiral flow in the distal anastomosis have been introduced in clinical practice and are known as spiral grafts. In this work, spiral peripheral vascular and arteriovenous grafts were compared with conventional grafts using ultrasound and computational methods to identify their haemodynamic differences. Vascular-graft flow phantoms were developed to house the grafts in different surgical configurations. Mimicking components, with appropriate acoustic properties, were chosen to minimise ultrasound beam refraction and distortion. A dual-beam two-dimensional vector Doppler technique was developed to visualise and quantify vortical structures downstream of each graft outflow in the cross-flow direction. Vorticity mapping and measurements of circulation were acquired based on the vector Doppler data. The flow within the vascular-graft models was simulated with computed tomography based image-guided modelling for further understanding of secondary flow motions and comparison with the experimental results. The computational assessments provided a three-dimensional velocity field in the lumen of the models allowing a range of fluid dynamic parameters to be predicted. Single- or double-spiral flow patterns consisting of a dominant and a smaller vortex were detected in the outflow of the spiral grafts. A double- triple- or tetra-spiral flow pattern was found in the outflow of the conventional graft, depending on model configuration and Reynolds number. These multiple-spiral patterns were associated with increased flow stagnation, separation and instability, which are known to be detrimental for endothelial behaviour. Increased in-plane mixing and wall shear stress, which are considered atheroprotective in normal vessels, were found in the outflow of the spiral devices. The results from the experimental approach were in agreement with those from the computational approach. This study applied ultrasound and computational methods to vascular-graft phantoms in order to characterise the flow field induced by spiral and conventional peripheral vascular and arteriovenous grafts. The results suggest that spiral grafts are associated with advanced local haemodynamics that may protect endothelial function and thereby may prevent their outflow anastomosis from neo-intimal hyperplasia and thrombosis. Consequently this work supports the hypothesis that spiral grafts may decrease outflow stenosis and hence improve patency rates in patients.