Mathematical modeling of spreading processes have been largely studied in the literature, and its presented a boom in the past few years. This is a fundamental task on the understanding and prediction of real spreading processes on top of a population and are subject to many structural and dynamical constraints. Aiming at a better understanding of this processes, we focused in two task: the modeling and the analysis of both dynamical and structural aspects of these processes. Initially, we proposed a new and general model that unifies epidemic and rumor spreading. Besides, regarding the analysis of these processes, we extended the classical formalism to multilayer networks, in which the theory was lacking. Interestingly, this study opened up new challenges concerning the understanding of multilayer networks. More specifically, regarding their spectral properties. In this thesis, we analyzed such processes on top of single and multilayer networks. Thus, throughout our analysis, we followed three complementary approaches: (i) analytical, (ii) numerical and (iii) simulations, mainly Monte Carlo simulations. Our main results are: (i) a new unifying model, enabling us to model and understand spreading processes on large systems, (ii) characterization of new phenomena on multilayer networks, such as layer-wise localization and the barrier effect and (iii) an spectral analysis of multilayer systems, suggesting a universal parameter and proposing a new analytical tool for its analysis. Our contributions enable further research on modeling of spreading processes, also emphasizing the importance of considering the complete multilayer structure instead of any coarse-graining. Additionally, it can be directly applied on the prediction and modeling real processes. Thus, aside from the theoretical interest and its mathematical implications, it also presents important social impact. / A modelagem matemática dos processos de disseminação tem sido amplamente estudada na literatura, sendo que o seu estudo apresentou um boom nos últimos anos. Esta é uma tarefa fundamental na compreensão e previsão de epidemias reais e propagação de rumores numa população, ademais, estas estão sujeitas a muitas restrições estruturais e dinâmicas. Com o objetivo de entender melhor esses processos, nos concentramos em duas tarefas: a de modelagem e a de análise de aspectos dinâmicos e estruturais. No primeiro, propomos um modelo novo e geral que une a epidemia e propagação de rumores. Também, no que diz respeito à análise desses processos, estendemos o formalismo clássico às redes multicamadas, onde tal teoria era inexistente. Curiosamente, este estudo abriu novos desafios relacionados à compreensão de redes multicamadas, mais especificamente em relação às suas propriedades espectrais. Nessa tese, analisamos esses processos em redes de uma e múltiplas camadas. Ao longo de nossas análises seguimos três abordagens complementares: (i) análises analíticas, (ii) experimentos numéricos e (iii) simulações de Monte Carlo. Assim, nossos principais resultados são: (i) um novo modelo que unifica as dinâmicas de rumor e epidemias, nos permitindo modelar e entender tais processos em grandes sistemas, (ii) caracterização de novos fenômenos em redes multicamadas, como a localização em camadas e o efeito barreira e (iii) uma análise espectral de sistemas multicamadas, sugerindo um parâmetro de escala universal e propondo uma nova ferramenta analítica para sua análise. Nossas contribuições permitem que novas pesquisas sobre modelagem de processos de propagação, enfatizando também a importância de se considerar a estrutura multicamada. Dessa forma, as nossas contribuições podem ser diretamente aplicadas à predição e modelagem de processos reais. Além do interesse teórico e matemático, nosso trabalho também apresenta implicações sociais importantes.

Neste trabalho estudamos as propriedades estruturais e eletrônicas de defeitos e impurezas de hidrogênio em MgO. As investigações foram efetuadas através de simulações computacionais baseadas em métodos de primeiros princípios dentro do formalismo da teoria do funcional da densidade e utilizando o método FPLAPW (Full Potential - Linearized Augmented Plane Wave), implementado no código computacional WIEN2k, dentro do esquema de supercelula, com relaxações iônicas tratadas de modo apropriado. Os defeitos estudados foram as vacâncias de oxigênio e de magnésio e as impurezas de hidrogênio foram simuladas em sitos substitucionais e intersticiais da rede do MgO. Em termos de configurações iônicas, a maioria dos centros de defeito ou de impureza apresentam pequenas relaxações do tipo respiratórias, mantendo a simetria local do sito, com exceção de dois dos centros estudados. O primeiro deles é a vacância de magnésio, no estado de carga neutro, que apresenta uma pequena distorção iônica trigonal. O segundo é a impureza intersticial de hidrogênio, no estado de carga positivo, que apresenta uma grande distorção local na rede, com a impureza se deslocando na direção de um dos dois átomos de oxigênio primeiros vizinhos. Nossos resultados para as energias de formação dos defeitos e impurezas nos permitiu avaliar a estabilidade dos centros, em função dos estados de carga, e prever as posicoes energeticas, no gap do material, dos estados de transicao. Para a impureza substitucional de hidrogenio no stio do oxigenio observamos que o centro no estado de carga positivo é o mais estável para qualquer valor do nível de Fermi, indicando que a impureza substitucional de hidrogênio, no sítio do oxigênio, apresenta caráter doador e o MgO pode ser caracterizado como um material tipo-n. Estas características também foram obtidas para as impurezas intersticiais de hidrogênio, mas nestes casos elas são dependentes da posição do nível de Fermi no gap do MgO. / In this work we report the results of the structural and electronic properties of defects and hydrogen impurities in MgO. The investigations were carried by computational simulations using ab initio methods, based on the density functional theory and the FP-LAPW (Full Potential - Linearized Augmented Plane Wave) method, as implemented in the WIEN2k code, considering the supercell approach and atomic relaxations. The studies comprise the oxygen and vacancies and substitutional and interstitial hydrogen impurities. Almost all defects and impurities keeps the crystalline local symmetry, showing breath mode relaxations. The magnesium vacancy, in the neutral charge state conguration, has a very small trigonal, while one of the hydrogen interstitial impurity, in the positive charge state conguration, has a very large local distortion, where the impurity moves toward one of the oxygen next neighbour atom. We have also investigated the energetic stability of these defects, evaluating the transition states related to each defect center. We nd that the substitutional hydrogen impurity in the oxygen site, in the positive charge state conguration, is the most stable one, independent of the Fermi level energy, showing a donor behaviour. Therefore, this impurity can lead to an n-type MgO material. Those characteristics were also observed for the interstitial hydrogen impurities investigated here, but in those cases the donor behaviour are Fermi level dependent.

O objetivo deste trabalho foi propor, caracterizar e avaliar, por meio de simulações computacionais, um sistema de detecção de um tomógrafo PET (Positron Emission Tomography) dedicado para pequenas regiões. Os principais fatores considerados para a modelagem do sistema foram: resolução energética, resolução espacial, sensibilidade de detecção e custo do sistema. O pacote GATE (Geant4 Application for Tomographic Emission), baseado no código de transporte de radiação Geant4, foi escolhido para as simulações. Como forma de acompanhar os avanços da tecnologia PET, o tomógrafo Q-PEM/DoPET, da Universidade de Pisa - Itália, foi simulado e um modelo óptico analítico foi proposto para comparação entre os resultados simulados e experimentais. Assim, a utilidade do modelo óptico foi demonstrada, pois o mesmo evita o tempo de computação excessivamente longo de uma simulação com os processos ópticos do GATE ativados. Foi feita a caracterização de um bloco detector que consiste de um cristal cintilador monolítico acoplado a uma matriz de fotodetectores, baseados na tecnologia das fotomultiplicadoras de silício. A posição da interação do fóton gama dentro do cristal foi determinada usando um método baseado na estimativa de parâmetros de um modelo que descreve a distribuição da intensidade dos sinais dos fótons ópticos coletados pela matriz de fotodetectores, de acordo com o local da interação. O método possui a capacidade de determinação da profundidade da interação dentro do cristal, o que diminui consideravelmente os erros de paralaxe. O bloco detector proposto também pode ter aplicação em outras áreas da física e afins que fazem uso da instrumentação nuclear e que necessitam de detectores sensíveis à posição. Foi proposto um sistema de detecção para um tomógrafo PET com aplicação na Mamografia por Emissão de Pósitrons - PEM (Positron Emission Mammography). O conceito proposto tem o potencial para aperfeiçoar a capacidade da tecnologia PET de visualizar, quantificar e caracterizar tumores de mama. O tomógrafo foi avaliado, onde os parâmetros de desempenho para uma fonte pontual de 22Na no centro do campo de visão e distância entre planos detectores de 10 cm foram: resolução energética em 511 keV de 12,1(3)%, resolução espacial 3D de 1;34(1) x 1;26(1) x 2;04(2)mm3 e sensibilidade de detecção de 8(1)%. Os resultados mostram que o conceito proposto possui desempenho compatível aos tomógrafos já existentes, além de ter um custo menor, por ser baseado em cristais cintiladores monolíticos. / The aim of this work was to propose, to characterize and to evaluate, by means of computational simulations, a detection system of a dedicated PET (Positron Emission Tomography) tomograph. The main factors considered for the system modeling were: energetic resolution, spatial resolution, detection sensitivity and system cost. The package GATE (Geant4 Application for Tomographic Emission), based on Geant4 radiation transport code, was chosen for the simulations. To follow the advances on PET technology, the Q-PEM/DoPET tomograph, from University of Pisa - Italy, was simulated and an analytical optical model was proposed for comparison between simulated and experimental results. Thus, the usefulness of the optical model was demonstrated, since it avoids the excessively long computation time when activating the optical processes in GATE. A block detector made of a monolithic scintillator crystal coupled to a photodetector array based on silicon photomultiplier technology was characterized. The interaction position of gamma radiation inside the crystal was determined using a method based on estimating parameters of a model which describes the signal distribution of the optical photons collected by the photodectetor array. The method has the ability of determining the depth of interaction inside the crystal, which decreases considerably parallax errors. The proposed block detector also can be used in other applications of nuclear instrumentation that require sensitive position detectors. A detection system of a PET tomograph was proposed to be applied in Positron Emission Mammography - PEM. The proposed design has the potential to improve the PET ability to visualize, quantify and characterize breast tumors. The tomograph performance was evaluated and the following parameters were obtained from an acquisition of a 22Na point source in the center of the field view and for a distance of 10 cm between the detector planes: energy resolution at 511 keV of 12,1(3)%, 3D spatial resolution of 1;34(1) x 1;26(1) x 2;04(2)mm3 and detection sensitivity of 8(1)%. The results show that the performance of the proposed design is similar to existing tomographs, in addition to have a lower cost due to the employment of monolithic crystals.

The decline of Moore's law has catalyzed a significant effort to identify beyond-CMOS devices and architectures for the coming decades. A multitude of classical and quantum systems have been proposed to address this challenge, and spintronics has emerged as a promising approach for these post-Moore systems. Many of these architectures are tailored specifically for applications in combinatorial optimization and machine learning. Here we propose the use of spintronics for such applications by exploring two distinct but related computing paradigms. First, the use of spin-currents to manipulate and control quantum information is investigated with demonstrated high-fidelity gate operation. This control is accomplished through repeated entanglement and measurement of a stationary qubit with a flying-spin through spin-torque like effects. Secondly, by transitioning from single-spin quantum bits to larger spin ensembles, we then explore the use of stochastic nanomagnets to realize a probabilistic system that is intrinsically governed by Boltzmann statistics. The nanomagnets explore the search space at rapid speeds and can be used in a wide-range of applications including optimization and quantum emulation by encoding the solution to a given problem as the ground state of the equivalent Boltzmann machine. These applications are demonstrated through hardware emulation using an all-digital autonomous probabilistic circuit.

Dans cette thèse nous avons montré que l'on peut on peut synthétiser des nanocristaux de silicium en utilisant des plasmas pulsés de silane dilué dans l'hydrogène. Dans nos conditions de dépôt, en changeant le temps de croissance entre 100 msec et 1 seconde, nous avons pu contrôler la taille des nanocristaux (de 4 nm à 12 nm). A partir de la mesure de la taille des nanocristaux sur les images MET, nous avons pu calculer la vitesse de croissance radiale. Cette vitesse est proportionnelle à la pression partielle de silane dans le mélange gazeux. Nous avons également montré le rôle important de l'hydrogène atomique pour le processus de cristallisation des nanoparticules dans le plasma. La maîtrise de la synthèse des nanocristaux de silicium ouvre la voie à deux champs d'applications : (i) la fabrication de diodes électroluminescences et (ii) la réalisation de transistors à un électron. Pour la première application, une étude préalable de photoluminescence a montré un déplacement vers le bleu du pic de photoluminescence lorsque la taille des nanocristaux diminue. Cela est interprété à la fois comme un effet de confinement quantique et de passivation de la surface des nanocristaux par une coquille de SiOx. Nous avons également élaboré des diodes électroluminescence PIN basées sur les nanocristaux de silicium. Après une optimisation de la structure PIN et des conditions de dépôt de la couche intrinsèque, nous avons obtenu une électroluminescence dans la gamme infrarouge-visible à température ambiante. En vue de l'application aux transistors, nous avons fait des expériences préalables d'injection de charge dans les nanocristaux par AFM/KFM. L'observation qualitative des charges injectées a été réalisée. L'estimation quantitative de ces charges ainsi que l'étude de charges résiduelles dans des nanocristaux dopés est un domaine qui mérite d'être exploré dans l'avenir.

<p> </p><p>The interaction between light and organometallic chromophores has been investigated theoretically in a strive for fast optical filters. The main emphasis is on two-photon absorption and excited state absorption as illustrated in the Jablonski diagram. We stress the need for relativistic calculations and have developed methods to address this issue. Furthermore, we present how quantum chemical calculations can be combined with Maxwell's equations in order to simulate propagation of laser pulses through a materials doped with chromophores with high two-photon absorption cross sections. Finally, we also discuss how fast agile filters using spin-transition materials can be modeled in order to accomplish theoretical material design.</p> / Report code: LIU-TEK-LIC-2006:55. On the day of the defence date the status on article III was Manuscript, article IV was Accepted and article V was Submitted.

<p>The solid oxide fuel cell (SOFC) technology has been under research since thelate 1950s, and most of the research has been on designs utilizing yttria stabilized zirconia (YSZ) as the electrolyte of choice. However, the SOFC technology has the major drawback of requiring high operation temperatures (up to 1000 degrees Celcius), so research of alternative materials have come into interest that would possibly require a lower working temperature without any significant loss of conductivity.One such material of interest for the electrolyte is compounds of ceriumdioxide (ceria). Ceria is well known for its ability to release oxygen by formingoxygen vacancies under oxygen-poor conditions, which increases its oxygen ionconductivity, and works at a lower temperature than the YSZ compounds whenproperly doped. Conversely, ceria is also able to absorb oxygen under oxygen-rich conditions, and those two abilities make it a very good material to use in catalytic converters for reduction of carbon monoxide and nitrogen oxide emission. The ability for the oxygen ions to easily relocate inbetween the different lattice sites is likely the key property of oxygen ion transportation in ceria. Also, in oxygen-rich conditions, the absorbed oxygen atom is assumed to join the structure at either the roomy octrahedral sites, or the vacant tetrahedral sites. Following that, the oxygen atom may relocate to other vacant locations, given it can overcome a possible potential barrier.</p><p>This thesis studies how those interstitial oxygen vacancies (defects) affect theenergy profile of ceria-based supercells by first principles calculations. The system is modeled within the density functional theory (DFT) with aid of (extended) local density approximation (LDA+U) using the software VASP. Furthermore, it is studied how those vacancies affect neighbouring oxygen atoms, and wether or not it is energetically benificial for the neighbouring atoms to readjust their positions closer or further away from the vacancy. The purpose of this thesis is to analyze wether or not it is theoretically possible that interstitial oxygen vacancies may cause neighbouring oxygen atoms to naturally relocate to the octahedral site in ceria, and how this affects the overall energy profile of the material.</p>

<p>The absorption spectra of a recently designed low-bandgap conjugated polymer has been studied using the semi-empirical method ZINDO and TDDFT/B3LYP/6-31G. The vertical excitation energies have been calculated for monomer up to hexamer. Two main absorption peaks can be seen, the one largest in wavelength corresponding to a HOMO to LUMO transition, and one involving higher order excitations. TDDFT results are red-shifted compared to the ZINDO results. Comparison with experiment yields that short conjugation lengths are dominating. This is possibly due to steric interactions between polymer chains, breaking the conjugation length. Such effects are also studied.</p>

<p>In this thesis we explore in particular the dynamics of a special type of quasi-particle in pi-conjugated materials termed polaron, the origin of which is intimately related to the strong interactions between the electronic and the vibrational degrees of freedom within these systems. In order to conduct such studies with the particular focus of each appended paper, we simultaneously solve the time-dependent Schrödinger equation and the lattice equation of motion with a three-dimensional extension of the famous Su-Schrieffer-Heeger (SSH) model Hamiltonian. In particular, we demonstrate in Paper I the applicability of the method to model transport dynamics in molecular crystals in a region were neither band theory nor perturbative treatments such as the Holstein model and extended Marcus theory apply. In Paper II we expand the model Hamiltonian to treat the revolution of phenylene rings around the sigma-bonds and demonstrate the great impact of stochastic ring torsion on the intra-chain mobility in conjugated polymers using poly[phenylene vinylene] (PPV) as a model system. Finally, in Paper III we go beyond the original purpose of the methodology and utilize its great flexibility to study radiationless relaxations of hot excitons.</p> / Report code: LiU-TEK-LIC-2007:4.

The solid oxide fuel cell (SOFC) technology has been under research since thelate 1950s, and most of the research has been on designs utilizing yttria stabilized zirconia (YSZ) as the electrolyte of choice. However, the SOFC technology has the major drawback of requiring high operation temperatures (up to 1000 degrees Celcius), so research of alternative materials have come into interest that would possibly require a lower working temperature without any significant loss of conductivity.One such material of interest for the electrolyte is compounds of ceriumdioxide (ceria). Ceria is well known for its ability to release oxygen by formingoxygen vacancies under oxygen-poor conditions, which increases its oxygen ionconductivity, and works at a lower temperature than the YSZ compounds whenproperly doped. Conversely, ceria is also able to absorb oxygen under oxygen-rich conditions, and those two abilities make it a very good material to use in catalytic converters for reduction of carbon monoxide and nitrogen oxide emission. The ability for the oxygen ions to easily relocate inbetween the different lattice sites is likely the key property of oxygen ion transportation in ceria. Also, in oxygen-rich conditions, the absorbed oxygen atom is assumed to join the structure at either the roomy octrahedral sites, or the vacant tetrahedral sites. Following that, the oxygen atom may relocate to other vacant locations, given it can overcome a possible potential barrier. This thesis studies how those interstitial oxygen vacancies (defects) affect theenergy profile of ceria-based supercells by first principles calculations. The system is modeled within the density functional theory (DFT) with aid of (extended) local density approximation (LDA+U) using the software VASP. Furthermore, it is studied how those vacancies affect neighbouring oxygen atoms, and wether or not it is energetically benificial for the neighbouring atoms to readjust their positions closer or further away from the vacancy. The purpose of this thesis is to analyze wether or not it is theoretically possible that interstitial oxygen vacancies may cause neighbouring oxygen atoms to naturally relocate to the octahedral site in ceria, and how this affects the overall energy profile of the material.