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The focus of this thesis is to investigate the impact of the boundary conditions on configurations in the Abelian sandpile model. We have two main results to present in this thesis. Firstly we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest to recurrent sandpiles. In the special case of $Z^d$, $d \geq 2$, we show how these bijections yield a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $Z^d$. Secondly we consider the Abelian sandpile on ladder graphs. For the ladder sandpile measure, $\nu$, a recurrent configuration on the boundary, I, and a cylinder event, E, we provide an upper bound for $\nu(E|I) − \nu(E)$.

No description available.

The Region of Waterloo relies mainly (75 %) on local groundwater resources for its drinking water supply. The water demand is increasing with the growth of the population and there is a need to enhance the present water supplies. The Regional Municipality of Waterloo (RMOW), which is the governing body in charge of providing the drinking water supply, is conducting an extensive program to protect the groundwater resources of the Waterloo Moraine aquifer. The focus of that work is defining the wellhead protection areas of the existing production wells as well as the investigation of potential further water supply. The main goal of the work presented here is to delineate the capture zones for the major well fields of the Region. To achieve that goal, the flow for the expected pumping conditions is simulated using a fully 3D finite element model (WATFLOW) which has been proven to be highly flexible to represent the natural boundaries and the highly irregular stratigraphy by previous researchers and scholars. The modified version of this model which includes a pseudo-unsaturated module is used for the solution of flow equation. For the delineation of capture zones, a new particle tracking code (WATRAC) as well as two advective-dispersive transport models are used by using a probabilistic approach presented by Neupauer and Wilson [1999]. For the probabilistic approach (Wilson's method), two transport models, a conventional time-marching code (WTC) and a time-continuous code (LTG) are usedand their results are compared. The LTG is computationally more efficient than the WTC, but it gives oscillatory results close to the steady state condition. A combined used of LTG and WTC istherefore recommended to obtain the steady state capture zones. The 0. 25 probability contour agrees very well with the particle tracks, except for somewhat greater transverse spreading due tothe dispersion which is not considered by the particle tracking algorithm. Both methods, backward particle tracking and probabilistic advective-dispersive modelling are clearly more informative and give better insight when considered together than each by itself.

INTRODUÇÃO: A doença de Wilson é um distúrbio autossômico recessivo, decorrente de mutações no gene ATP7B, resultando em acúmulo tóxico de cobre no organismo. Devido a sua raridade, séries com grande casuística e longo seguimento são escassas na literatura. Nesse estudo relatamos a experiência do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (HC-FMUSP) com os pacientes diagnosticados com doença de Wilson entre o período de 1946 a 2010. MÉTODOS: Realizamos análise retrospectiva de 262 casos, descrevendo as formas de apresentação clínica, os achados dos exames diagnósticos, os padrões de resposta terapêutica e a evolução clínica da doença. RESULTADOS: A idade média do início dos sintomas foi 17,4 anos (7-49 anos). Os pacientes foram acompanhados em média 9,6 anos (0-45 anos). As apresentações clínicas mais frequentes foram hepática (36,3%), neurológica (34,7%), assintomática (16,8%), neuro-psiquiátrica (8,3%) e hematológica (1,9%). Outras formas menos comuns foram renal, neuro-hepática, e osteoarticular. Disartria e manifestações clínicas de cirrose hepática descompensada foram as principais características neurológicas e hepáticas, respectivamente. Os parâmetros diagnósticos observados foram anéis de Kayser-Fleisher 78,3%, reduzidos níveis séricos de ceruloplasmina 98,3%, níveis elevados de cuprúria basal de 24 horas 73,0%, teste da D-penicilamina positivo em 54,0% e comprometimento nos dois alelos do gene ATP7B 84,4%. O exame de ressonância magnética encefálica mostrou alterações nos núcleos da base em 77,7% dos examinados. D-penicilamina foi prescrita inicialmente em 93,6% dos 245 casos tratados, e 53% relataram efeitos adversos. Houve necessidade de substituição em 50 indivíduos. Outras medicações utilizadas foram os sais de zinco e trientina. Não evidenciamos diferença significativa entre os resultados terapêuticos dessas três drogas (p=0,2). Os casos de má aderência à terapia evoluiram com pior desfecho quando comparados aos usuários regulares (p <0,0001). Nove pacientes realizaram transplante hepático. Durante o seguimento 82 casos faleceram. As principais causas dos óbitos foram descompensação hepática 41,5% (hemorragia digestiva, peritonite bacteriana espontânea, encefalopatia) e pneumonia 20,7%. Três pacientes cometeram suicídio. CONCLUSÕES: Não existe um exame padrão ouro ou achado patognomônico da doença. Todo paciente jovem com manifestações hepáticas, neurológicas, neuropsiquiátricas, hematológicas, renais ou osteoarticulares de causa indefinida deverá ser investigado para doença de Wilson. Além da farmacoterapia específica é necessária a avaliação psiquiátrica para detectar precocemente sintomas depressivos. / INTRODUCTION: Wilson\'s disease is an autosomal recessive disorder, caused by mutations in the gene ATP7B, leading to toxic copper accumulation in the body. Because it is a rare disease, large series with long-term follow-up are limited in literature. We reported the experience of Hospital das Clínicas of Sao Paulo University School of Medicine (HC-FMUSP) with Wilson\'s disease patients diagnosed between 1946 and 2010. METHODS: A retrospective analysis of 262 cases was performed describing the clinical presentation, the results of diagnostic tests, the patterns of treatment response and outcome. RESULTS: The mean age at the onset of symptoms was 17.4 years (7- 49 years). Patients were followed for a mean of 9.6 years (0-45 years). The most frequent clinical presentations were hepatic (36.3%), neurological (34.7%), asymptomatic (16.8%), neuro-psychiatric (8.3%) and hematologic (1.9%). Other less common forms were renal, neurological-hepatic, and musculoskeletal. Dysarthria and clinical manifestations of decompensated liver cirrhosis were the main neurological and liver features, respectively. The diagnostic parameters observed in this cohort of patients were Kayser-Fleischer rings in 78.3%, low serum ceruloplasmin in 98.3%, high 24-h urinary excretion of copper in 73.0%, positive challenge test with d-pencillamine in 54.0% and detection of two mutations of ATP7B gene in 84.4%. The magnetic resonance of brain showed abnormalities in the basal ganglia in 77.7% of those examined. D-penicillamine was prescribed in 93.6% of 245 cases as the first drug, and 53% reported adverse effects. It was need to replace it in 50 individuals. Other drugs used were salts of zinc and trientine. There was no significant difference between the therapeutic results of these three drugs (p = 0.2). The cases with poor adherence to therapy evolved with a worse outcome when compared to regular users (p <0.0001). Nine patients underwent liver transplantation. During the follow-up 82 patients died. The main causes of death were hepatic decompensation 41.5% (variceal hemorrhage, spontaneous bacterial peritonitis, encephalopathy) and pneumonia 20.7%. Three patients committed suicide. CONCLUSIONS: There is no gold standard or pathognomonic test for diagnosing this disease. Any young patient with hepatic, neurological, neuropsychiatric, hematologic, renal, or osteoarticular manifestations of unknown cause should be investigated for Wilson\'s disease. In addition to the classical pharmacotherapy, specific psychiatric evaluation is necessary to detect early symptoms of depression.

The Region of Waterloo relies mainly (75 %) on local groundwater resources for its drinking water supply. The water demand is increasing with the growth of the population and there is a need to enhance the present water supplies. The Regional Municipality of Waterloo (RMOW), which is the governing body in charge of providing the drinking water supply, is conducting an extensive program to protect the groundwater resources of the Waterloo Moraine aquifer. The focus of that work is defining the wellhead protection areas of the existing production wells as well as the investigation of potential further water supply. The main goal of the work presented here is to delineate the capture zones for the major well fields of the Region. To achieve that goal, the flow for the expected pumping conditions is simulated using a fully 3D finite element model (WATFLOW) which has been proven to be highly flexible to represent the natural boundaries and the highly irregular stratigraphy by previous researchers and scholars. The modified version of this model which includes a pseudo-unsaturated module is used for the solution of flow equation. For the delineation of capture zones, a new particle tracking code (WATRAC) as well as two advective-dispersive transport models are used by using a probabilistic approach presented by Neupauer and Wilson [1999]. For the probabilistic approach (Wilson's method), two transport models, a conventional time-marching code (WTC) and a time-continuous code (LTG) are usedand their results are compared. The LTG is computationally more efficient than the WTC, but it gives oscillatory results close to the steady state condition. A combined used of LTG and WTC istherefore recommended to obtain the steady state capture zones. The 0. 25 probability contour agrees very well with the particle tracks, except for somewhat greater transverse spreading due tothe dispersion which is not considered by the particle tracking algorithm. Both methods, backward particle tracking and probabilistic advective-dispersive modelling are clearly more informative and give better insight when considered together than each by itself.

The thesis explores the new expansions of eigenvalues for -£Gu =£f£lu in S with the Dirichlet boundary condition u=0 on $partial S$ by two conforming elements: the linear element $P_1$ and the bilinear element $Q_1$, and three non-conforming elements: the rotated bilinear element (denoted $Q_1^{rot}$), the extension of $Q_1^{rot}$ (denoted $EQ_1^{rot}$) and Wilson's element. The expansions indicate that $P_1$, $Q_1$ and $Q_1^{rot}$ provide the upper bounds of the eigenvalues, and $EQ_1^{rot}$ and Wilson's elements provide the lower bounds of the eigenvalues. Comparing the five finite elements, the $Q_1^{rot}$ element is more accurate. By the extrapolation, the superconvergence $O(h^4)$ can be obtained where $h$ is the boundary length of uniform squares. Numerical experiment are carried to verify the theoretical analysis made. (°Ñ·Ó¹q¤lÀÉp.4)