The goal of this thesis is to present a comprehensive study of the parabolic and hyperbolic Anderson models with constant initial condition, driven by a Gaussian noise which is fractional in space with index H > 1/2 or H < 1/2, and is either white in time, or fractional in time with index H_0 > 1/2. As a preliminary step, we study the linear stochastic heat and wave equations with the same type of noise. In the case H_0 > 1/2 and H < 1/2, we present a new result, regarding the solution of the parabolic Anderson model with general initial condition given by a measure.

This thesis includes the work of Robert Allen Anderson for a Master of Fine Arts in Sculpture.

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Luck egalitarianism is the view that justice requires that we hold people accountable for the choices that they make but not the circumstances that they find themselves in. My aim in this thesis is to reject luck egalitarianism. My argument builds on the recent critique of luck egalitarianism by Elizabeth Anderson. Anderson rejects luck egalitarianism in favor of a view she calls "democratic equality." The aim of democratic equality is to create a community in which citizens relate to one another as equals. This requires, among other things, that we provide citizens with the necessary capabilities and functionings needed in order for them to function as free and equal citizens. In this thesis I argue that Anderson's critique of luck egalitarianism, although successful against the standard luck egalitarian view, does not undermine a weaker version of luck egalitarianism. This position — which I call moderate luck egalitarianism — claims that we ought to apply the choice/circumstance distinction always and only when doing so does not compromise the aims of democratic equality. This is because it is always unfair, according to luck egalitarians, when some people are worse off than others through no fault of their own. Since Anderson's view does not correct for this, we need to combine the aims of democratic equality and luck egalitarianism in the name of fairness. I argue, however, that this is not necessary. Not all inequalities that are the result of people's unchosen circumstances are unfair or unjust; inequalities in income and wealth are unfair only to the extent that they inhibit the ability of individuals to function as free and equal citizens. Thus, luck egalitarians have given us no reason to conjoin the aims of democratic equality and luck egalitarianism: democratic equality suffices. / Master of Arts

This thesis uses Benedict Anderson's theoretical contributions on the topic of national identity and Michel Foucault's contributions toward discourse analysis to perform a discursive analysis of Donald Trump's campaign speeches in which he exploits pre-existing anti-immigration sentiments among certain voters to gain political power. The research question addressed herein is: How has Donald Trump invoked the issue of national security to single out groups of immigrants as threats to U.S. national security, and what conditions exists so that he is able to do so in a way that enlists the support of a sizeable portion of the American public? First, this thesis works to put into context what drove post-World War II immigration in the U.S. to provide insight into what conditions lead to certain groups being encouraged or discouraged from immigrating. Second, I contrast Anderson's concept of nationalism with that of Samuel Huntington, whose idea of nationalism more closely aligns with Trump's nativist sense of national identity. Third, having put the history of U.S. immigration and the concept of national identity into context, I perform a discursive analysis of three of Trump's campaign speeches and tweets that focus on immigration and make problematic his racist, far-right ideology and its purpose toward the de-politicization and de-historicization of immigration as a national security and economic issue. I conclude by reminding the reader that allowing anti-immigrant discourse to become normalized without the burden of proof can lead to curbed freedoms under an authoritarian regime, a direction toward which Trump appears ready and willing to lead the American electorate. / Master of Arts / This thesis poses the question: How has Donald Trump invoked the issue of national security to single out groups of immigrants as threats to U.S. national security, and what conditions exists so that he is able to do so in a way that enlists the support of a sizeable portion of the American public? This question is answered through a discursive analysis of Trump’s campaign speeches, a discussion of how national identity is derived, and a brief consideration of a few policies that have impacted immigration to the U.S. and its political landscape. Ultimately, this thesis identifies a discursive apparatus that has been leveraged by Donald Trump and his supporters in order to gain political favor. If left unchecked, this discourse could have a damaging effect on the U.S. and its citizens by making it acceptable to cast certain groups as un-American.

Estudamos o calor específico de um sistema formado por duas impurezas adsorvidas, sem spin, em meio fermiônico (banda de condução do metal) e que contém um buraco (elétron) tunelando entre elas. Modelamos esse sistema por dois níveis acoplados e que sofrem interação Coulombiana com a banda de condução. Através da análise das curvas de calor específico, investigamos a alteração (renormalização) da taxa de tunelamento em função da interação eletrostática entre os elétrons da banda de condução e o buraco tunelante e da separação entre as impurezas. Utilizamos o Hamiltoniano de Kondo de tunelamento para representar esse modelo e usamos o Grupo de Renormalização Numérico para diagonalizá-lo. Analisamos a influência de cada termo do Hamiltoniano na renormalização da taxa de tunelamento e verificamos que a troca de paridade das funções de onda do buraco tunelante e dos elétrons da banda desempenha papel essencial. Encontramos uma expressão que combina a distância entre as impurezas e a interação Coulombiana em um único parâmetro (a), de tal forma que sistemas diferentes mas que apresentam o mesmo a e a mesma taxa de tunelamento livre têm a mesma curva de calor específico. / We calculate the specific heat of the two-spinless impurity coupled to a fermionic bath. The model takes into account the tunneling of a hole between the impurities. The two-level system representing the impurities is coupled electrostatically with the conduction electrons. Through the specific heat curves, we analyse the renormalization of the tunneling rate as a function of the Coulomb interaction and distance between impurities. The Numerical Renormalization Group is used to diagonalize the tunneling Hamiltonian proposed by Kondo. We analyse the role of each term of the Hamiltonian in the renormalization of the bare tunneling rate and we stress the importance of the exchange parity between impurity states and conduction states. Finally, a parameter a, is found which combines the distance between impurities and Coulomb interaction in such a way that every curve is specified only by a and the bare tunneling rate.

Nesta dissertação, apresentamos uma aplicação simples de RMN de 1H no domínio do tempo (TD-NMR) de baixo campo para caracterização de dinâmica molecular variando do regime intermediário ao rápido. O método se baseia no filtro dipolar seguido da aplicação do Mixed Magic Sandwich Echo(MSE), o qual denominamos DF-MSE. O filtro dipolar suprime os sinais oriundo de segmentos com mobilidade abaixo de kHz, de modo que somente segmentos móveis sejam detectados. Assim, a dependência com a temperatura da intensidade do sinal mostra diretamente a temperatura em que movimentos moleculares ocorrem ao atingirem taxas maiores que kHz. Para que não ocorra variação da intensidade com a temperatura, mas somente pelos movimentos moleculares, os sinais são normalizados por uma intensidade de referência obtida pela aquisição de DF-MSE sem aplicação do filtro dipolar. A intensidade normalizada DF-MSE pode ser descrita adequadamente por uma expressão analítica baseada na aproximação de Anderson-Weiss, de forma a permitir que parâmetros de ativação de movimentos sejam avaliados. Ademais, também propomos um método baseado na diferença entre sinais DF-MSE normalizados adquiridos com tempos de filtro distintos, permitindo assim quantificar a largura da ditribuição de tempos de correlação de uma forma independente. A aplicação geral foi testada de forma bem sucedida em polímeros monofásicos e multifásicos. De fato, o método apresentado é um prosseguimento da análise feita pelo MSE já presente na literatura, porém sondando movimentos mais rápidos e com uma forma aprimorada para avaliação de heterogeneidades de movimento. / In this dissertation, we present a simple NMR approach for characterizing intermediate to fast regime molecular dynamics using 1H time-domain NMR (TD-NMR) at low magnetic field. The method is based on a dipolar filter followed by a Mixed Magic Sandwich Echo and FID acquisition, which is symbolized DF-MSE. The dipolar filter suppresses the signals of segments presenting sub kHz mobility, so only signals from mobile segments are detected. Thus, the temperature dependence of the signal intensities directly evidences the onset of molecular motions with rates higher than kHz. In order to avoid temperature variation of the signal intensities other than that due to motions, the signals are normalized by a reference intensity obtained in a DF-MSE acquisition without the dipolar filter. The normalized DF-MSE intensity can be well described by an analytical function based on the Anderson-Weiss approach, so the activation parameters of the motion can be evaluated. Furthermore, we also propose a method based on the difference between normalized DF-MSE signals acquired with different dipolar filter times, which provide evaluation of the width of the distribution of correlation times in an independent fashion. The general approach was successfully tested in single and multiphase polymer systems. Indeed, the presented method is a follow up of the MSE analysis previously reported, but probing faster motions and with an improved way of evaluating the motion heterogeneities.

Neste trabalho, realizamos o estudo da transição metal-isolante e da localização de Anderson na liga de Pb1-xEuxTe do tipo p para x variando de 0 até 0.1. As propriedades de transporte nessa liga (mobilidade, concentração de portadores e resistividade elétrica) foram obtidas utilizando o método de caracterização elétrica por efeito Hall entre as temperaturas de 300 K e 10 K. Nessa região de temperatura, foi possível observar uma transição metal-isolante para x > 0.05. Verificamos que a transição é do tipo Anderson e ocorre devido à desordem presente na liga. Para baixas temperaturas (T < 10 K) e em amostras com x > 0.01, verificamos a presença de magnetorresistência positiva e negativa aplicando campos magnéticos de até 11T. Nas amostras metálicas, a presença de magnetorresistência negativa é causada pelo efeito conhecido como localização de Anderson (efeito de interferência quântica construtiva entre as funções de onda) e a presença de magnetorresistência positiva é causada, principalmente, pelo acoplamento spin-órbita, e é chamada de antilocalização. Nas amostras isolantes, a magnetorresistência negativa é originada pelo efeito Zeeman enquanto que a magnetoresistência positiva é causada pela redução do comprimento de localização. Assim, os valores positivos e negativos da magnetoresistência têm origens diferentes dependendo do regime de condução (metálicoou isolante). Por esse motivo, o estudo dos resultados experimentais apresentados nesse trabalho foi dividido em duas partes: uma parte que trata as amostras metálicas (região de desordem fraca) e outra parte para as amostras isolantes (região de desordem forte). A partir dessa divisão, e utilizando os modelos teóricos disponíveis na literatura, foi possível fazer uma análise das medidas experimentais de magnetotransporte. Como resultado, identificamos os principais mecanismos de interação (espalhamento inelástico, efeito Zeeman, acoplamento spin-órbita, etc.) que interferem no transporte e nos efeitos de localização e antilocalização. / In this work, we investigated Anderson localization and the metal-insulator transition in p-type films of Pb1-xEuxTe for x varying from 0 up to 0.1. The transport properties of this alloy (mobility, carrier concentration and electrical resistivity) were obtained using the Hall method of electrical caracterization for temperatures ranging from 300 K down to 10 K. In this temperature range, it was possible to observe a metal-insulator transition for x > 0:05. The transition is of the Anderson type and is due to the disorder present in the alloy. For low temperatures (T < 10 K) and for samples with x > 0.01, we observed positive and negative magnetoresistance for magnetic fields up to 11 T. For metallic samples, the negative magnetoresistance originates from Anderson’s localization (constructive quantum interference effect between the wave functions) while positive magnetoresistence is caused, mainly, by the spin-orbit scattering, and it is called antilocalization. For insulating samples, negative magnetoresistance is originated from the Zeeman effect while positive magnetoresistance is caused by the localization length reduction. Therefore, positive and negative magnetoresistance values have different origins depending on the conduction regime (metallic or insulating). For this reason, our experimental investigation, presented in this work, was separated into two parts: the first one treats the metallic samples (weak-disorder regime) and the other treats the insulating samples (strong-disorder regime). From this division, and using available theoretical models, it was possible to analyze the magnetotransport experimental measurements. As a result, we identify the main interaction mechanisms (inelastic scattering, Zeeman effect, spin-orbit coupling, etc.) that interfere on the transport and localization and antilocalization effects.

Este trabalho se dedica à paralelização de um programa para cálculos de propriedades físicas de ligas magnéticas diluídas. O método do grupo de renormalização aplicado ao modelo de Anderson de duas impurezas se mostrou particularmente adequado ao processamento paralelo visto que grande parte dos cálculos pode ser executada simultaneamente, assim como variações nos conjuntos de dados requeridas pelo método. Para tal reescrevemos o programa seqüencial usado anteriormente pelo Grupo de Física Teórica do IFSC e implementamos três versões paralelas. Essas versões diferem entre si em relação à abordagem dada à paralelização. O uso de clusters de computadores se revelou uma opção conveniente pois verificamos que o limitante no desempenho é o tempo tomado pelos cálculos e não pela comunicação. Os resultados mostram uma grande redução no tempo total de execução, porém deficiências no speedup e escalabilidade devido a problemas de balanceamento de carga. Analisamos esses problemas e sugerimos alternativas para solucioná-los. / This dissertation discuss the parallelization of a program that calculates physical properties of dilute magnetic alloys. The renormalization group method applied to Anderson's two impurities model showed to be specially suitable to parallel processing because a large amount of calculations as well as variations of data entries required by the method can be performed simultaneously. To achieve this we rewrote the sequential program previously used by the Theoretical Physics Group of the IFSC and wrote three parallel versions. These versions differ from each other by the parallelization approach. The use of computer clusters revealed to be an appropriate option because the calculation time is the limiting factor on performance instead of communication time. The results show a good reduction of execution time, but speedup and scalability lack due to load balancing problems. We analyze these problems and suggest possible solutions.