This thesis will present a new cosmic shear analysis pipeline SUNGLASS (Simulated UNiverses for Gravitational Lensing Analysis and Shear Surveys). SUNGLASS is a pipeline that rapidly generates simulated universes for weak lensing and cosmic shear analysis. The pipeline forms suites of cosmological N-body simulations and performs tomographic cosmic shear analysis using a novel line-of-sight integration through the simulations while saving the particle lightcone information. Galaxy shear and convergence catalogues with realistic 3-D galaxy redshift distributions are produced for the purposes of testing weak lensing analysis techniques and generating covariance matrices for data analysis and cosmological parameter estimation. This thesis presents a suite of fast medium-resolution simulations with shear and convergence maps for a generic 100 square degree survey out to a redshift of z = 1.5, with angular power spectra agreeing with the theoretical expectations to better than a few percent accuracy up to ℓ = 103 for all source redshifts up to z = 1.5 and wavenumbers up to ℓ = 2000 for source redshifts z ≥ 1.1. A two-parameter Gaussian likelihood analysis of Ωm and σ8 is also performed on the suite of simulations for a 2-D weak lensing survey, demonstrating that the cosmological parameters are recovered from the simulations and the covariance matrices are stable for data analysis, with negligible bias. An investigation into the accuracy of traditional Fisher matrix calculations is presented. Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this thesis, the loss of information is quantified by comparing näıve Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of the suite of mock weak lensing catalogues derived from the SUNGLASS pipeline, for 2-D and tomographic shear analyses of a Euclid-like survey. In both cases the 68% confidence area of the Ωm − σ8 plane is found to increase by a factor 5. However, the marginal errors increase by just 20 to 40%. A new method is proposed to model the effects of non-linear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. The findings in this thesis show that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Ωm − σ8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, three multi-parameter analyses of (Ωm, σ8, ns), (Ωm, σ8, ns, ΩΛ)and (Ωm, σ8, h, ns, w0, wa) are performed to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The multi-parameter volumes of the 1σ error contours for the six-parameter non-linear Fisher analysis are consistently larger than for the Gaussian case, and the shape of the 68% confidence volume is modified. These results strongly suggest that future Fisher Matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Student Number : 9908888R - MSc research report - School of Statistics and Actuarial Science - Faculty of Science / Much research has been devoted towards the understanding of population behaviour. Such understanding has often been furthered through the development of theoretical population models. This research report explores a variety of population models and their implications. The implications of the various models are explored using both analytical results and simulations. Specific aspects of population behaviour studied include gross fluctuation characteristics and extinction probabilities for a population. This research report starts with an overview of Deterministic Models. This is followed by a study of Birth and Death Processes, Branching Processes and Models that incorporate environmental variability. Finally, we study the maximum likelihood approach to population parameter estimation. The more notable theoretical results derived include: the development of models that incorporate the population’s history; models that incorporate discontinuous environmental changes and the development of a means of parameter estimation for a Stochastic Differential Equation.

Baroclinic tides play a significant role in driving deep-ocean mixing, which not only influences the transport of nutrients and other biological tracers, but also affects the large scale circulations. This thesis combines advanced numerical modeling techniques and available observations to investigate the characteristics of baroclinic tides in the Red Sea, and understand their formation and fate, and their influence on the circulation and ecosystem. Based on a validated 3D, non-hydrostatic and high-resolution MIT General Circulation Model (MITgcm), we first established four potential areas for the generation of baroclinic tide in the Red Sea: the Strait of Bab-el-Mandeb (BAM), the southern Red Sea, the Gulf of Suez, and the Strait of Tiran. These areas are consistently suggested by the spatial distribution of baroclinic tidal kinetic energy and energy fluxes. The majority of the baroclinic energy disappears within the basin; either dissipates due to friction and bottom drag or converts back into barotropic energy due to pressure. We next conducted 2D numerical simulations to investigate the generation mechanism behind the formation of the observed internal solitary waves(ISWs) in the southern Red Sea, revealing the dominant role of tide-topography interactions. Instead of evolving from the disturbed thermocline due to a locally impinging tidal beam ISWs are generated from the depression formed near the shelf. As this depression propagates out of the shelf, it gradually steepens and ultimately breaks into a group of ISWs. To further study the breaking and dissipation processes of the ISWs, we implemented a regional high-resolution MITgcm for the southern Red Sea with a realistic topography revealing that the breaking process is triggered by the fission mechanism. The associated particles transport is further quantitatively analyzed, revealing a significant transport, both vertically and horizontally. The thesis, finally examined the tidal influences on the basin-scale circulation of the Red Sea. Comparison experiments with and without tides show that, the intrusion of the Gulf of Aden Intermediate Water (GAIW) in summer is strongly influenced by the tides. It is suggested that tides enforce more turbulence and mixing at the strait, which significantly increase the diffusivity of heat and salinity.

The aim of this thesis is to implement source terms to numerical model for curent sheet in solar atmosphere. The chapters are structured in the way that can present us with basic knowledge of the Sun and processes in its atmosphere. Than we present important equations for numerical solution and for the initial equilibrium of our simulation. One of the last chapters is dedicated to software we use for our numerical simulations called FLASH. In the end of the thesis we present results of our numerical simulations.

Nesse trabalho investigamos através de simulações numéricas a evolução da composição genética de uma população, dando atenção especial ao processo dinâmico conhecido como catraca de Muller, que é responsável pela degradação da população devido ao acúmulo de mutações deletérias em populações finitas. Consideramos também a genealogia dos indivíduos em uma população sob a ação da catraca de Muller. Ainda, investigamos analiticamente o limite determinístico do modelo, no qual o tamanho da população é infinito, onde o processo da catraca não atua. O relevo replicativo, ou seja, a função que mapeia a carga genética de um indivíduo com a sua probabilidade de reprodução utilizado nesse trabalho é uma generalização do relevo originalmente proposto por Muller para ilustrar o processo da catraca. Adicionamos a esse relevo um parâmetro de epistase que simula a interação entre os sítios das seqüências dos indivíduos. A escolha desse parâmetro determina três tipos possíveis de epistase: (i) sinergística, no qual as mutações ficam cada vez mais deletérias com o número de mutações já existentes; (ii) atenuante, no qual o efeito deletério de uma nova mutação é atenuado; e (iii) multiplicativa, no qual as novas mutações causam danos idênticos, independentemente do número anterior de mutações / In this work we investigate through numerical simulations the evolution of the genetic composition of a population, giving emphasis to the dynamic process termed Muller\'s ratchet, which is responsible for the degradation of the population due to the accumulation of deleterious mutations in finite populations. We consider also the genealogy of the individuals evolving in a population under the effect of the Muller\'s ratchet. In addition, we investigate analytically the deterministic limit of the model, in which the population size is infinite, where ratchet process does not act. The replication landscape, i.e., the function that maps the genetic load of an individual on its probability of reproduction used in this work is a generalization of that originally considered by Muller to illustrate the process of the ratchet. In particular, we add to that landscape a parameter of epistasis that models the interactions among the sites of the sequences of the individuals. The tunning of this parameter determines three different types of epistasis: (i) synergistic, where the mutations become more deleterious with the number of mutations already present; (ii) diminishing, where the deleterious effect of a new mutation is attenuated; and (iii) multiplicative, where the new mutations cause identical damages, independently of the previous number of mutations

A Tomografia por Emissão de Pósitrons (PET) está se definindo como um dos métodos preferidos para diagnóstico e seguimento de inúmeras doenças em Oncologia, Neurologia e Cardiologia. Esta modalidade é realizada com sistemas dedicados e sistemas baseados em câmaras de cintilação, que podem ser também usados em tomografia por emissão de fótons únicos (SPECT). Neste trabalho, efetuamos uma avaliação dos fatores que favorecem a quantificação em imagens PET com câmaras de cintilação em coincidência, caracterizadas por urna menor sensibilidade em relação a sistemas dedicados. Avaliamos as condições de quantificação de imagens sob os modos 2D e 3D de aquisição, obtidas por métodos de reconstrução 2D e 3D diversos e correções associadas. Dados de aquisição foram simulados por método de Monte Carlo empregando parâmetros realistas. Objetos de interesse diversos foram modelados. Imagens foram reconstruídas pelos métodos FBP, ART, MLEM e OSEM e consideramos correções de sensibilidade, normalização de detector, espalhamento e atenuação de radiação. Estabelecemos uma metodologia de avaliação de detectabilidade e recuperação de contrastes em imagens que contemplam, a partir de dois parâmetros mensuráveis, os aspectos mais relevantes em quantificação. Análises visuais também foram consideradas. Verificamos que o modo 3D é mais adequado que 2D na recuperação de baixos contrastes no objeto com a aplicação das correções selecionadas. A detectabilidade de pequenas estruturas está limitada pelos efeitos de volume parcial e pela resolução espacial finita dos sistemas de detecção. Os métodos ART, MLEM e, em particular, OSEM com 8 subconjuntos, apresentam-se adequados para estudos quantitativos no modo 3D. Os parâmetros definidos para avaliação podem ser empregados como indicadores de condições propícias a estudos quantitativos. / Volumetric reconstruction in gamma camera based PET imaging Positron Emission Tomography (PET) is considered as a very useful tool for diagnosing and following several diseases in Oncology, Neurology and Cardiology. Two types of systems are available for this imaging modality: the dedicated systems and those based on gamma camera technology. In this work, we assessed a number of factors affecting the quantitation of gamma camera based PET imaging, characterized by a lower sensitivity compared to those of dedicated systems. We also evaluated image quantitation conditions under 2D and 3D acquisition/reconstruction modes, for different reconstruction methods and associated corrections. Acquisition data were simulated by Monte Carla method, using realistic parameters. Several objects of interest were modelled. We reconstructed slices and volumes using FBP, ART, MLEM and OSEM and also included four corrections: detector sensitivity, detector normalization, scatter and attenuation of annihilation photons. We proposed a method to assess detectability and object contrast recovery by using two measurable parameters. Visual analysis was also considered. We found that 3D mode is more effective than 2D for low contrast recovery when the selected (J corrections are applied. Detectability of small structures is limited by partial volume effects and device finite spatial resolution. ART, MLEM and specially 8-subsets OSEM are the most adequate methods for quantitative studies in 3D mode. The parameter that we have defined may also be used as indicators of suitable conditions for quantitation in images.

The work in this thesis aims to gain fundamental understanding of several important types of disordered systems, including liquids, supercritical fluids and amorphous solids on the basis of extensive molecular dynamics simulations. I begin with studying the diffusion in amorphous zirconolite, a potential waste form to encapsulate highly radioactive nuclear waste. I find that amorphization has a dramatic effect for diffusion. Interestingly and differently from previous understanding, diffusion increases as a result of amorphization at constant density. Another interesting insight is related to different response of diffusion of different atomic species to structural disorder. I calculate activation energies and diffusion pre-factors which can be used to predict long-term diffusion properties in this system. This improves our understanding of how waste forms operate and provides a quantitative tool to predict their performance. I subsequently study the effects of phase coexistence and phase decomposition in Y-stabilized zirconia, the system of interest in many industrial applications including in encapsulating nuclear waste due to its exceptional resistance to radiation damage. For the first time I show how the microstructure emerges and evolves in this system and demonstrate its importance for self-diffusion and other properties. This has not been observed before and is important for better understanding of existing experiments and planning the new ones. I subsequently address dynamical properties of subcritical liquids and supercritical fluids. I start with developing a new empirical potential for CO2 with improved performance. Using this and other potentials, I simulate the properties of supercritical H2O, CO2 and CH4 and map their Frenkel lines in the supercritical region of the phase diagram. I observe that the Frenkel line for CO2 coincides with experimentally found maxima of solubility and explain this finding by noting that the Frenkel line corresponds to the optimal combination of density and temperature where the density is maximal and the diffusion is still in the fast gas-like regime. This can serve as a guide in future applications of supercritical fluids and will result in their more efficient use in dissolving and extracting applications. I extend my study to collective modes in liquids. Here, my simulations provide first direct evidence that a gap emerges and evolves in the reciprocal space in transverse spectra of liquids. I show that the gap increases with temperature and is inversely proportional to liquid relaxation time. Interestingly, the gap emerges and evolves not only in subcritical liquids but also in supercritical fluids as long as they are below the Frenkel line. Given the importance of phonons in condensed matter physics and other areas of physics, I propose that the discovery of the gap represents a paradigm change. There is an active interest in the dynamics of liquids and supercritical fluids, and I therefore hope that my results will quickly stimulate high-temperature and high-pressure experiments aimed at detecting and studying the gap in several important systems.

This diploma thesis deals with the practical use of simulation models. It is divided into theoretical and practical part. The theoretical part is intended to acquaint the reader with the history of simulation, possibilities of their use and basic starting points for creating simulation models. The content of the practical part is usage of simulation models to solve real problem in a particular company. That is a finding of mobile tariffs to four central office employees of the Executive Board of the Czech Union for Nature Conservation, which would minimize their costs of telephone calls. The data required to create a model was obtained on the basis of previous observations. The entire model was created in the program product Microsoft Excel using the Crystal Ball software addon.

An antibody microarray consists of antibody bound to a surface. Antibody microarrays have great potential in many fields, particularly as a tool to detect antigens. Unfortunately, antibodies suffer from poor performance. A greater understanding of how antibodies interact with surfaces would improve microarray design and performance, but experimental methods fall short of being able to observe these interactions. Therefore molecular simulation has emerged as the primary method to study protein/surface interactions.The simulations here were coarse grain simulations performed using the model of Karanicolas and Brooks. Additionally, an advanced surface model was used that allows for different surface chemistries. PyMBAR analysis was used to find heat capacities and determine relative stabilities of different linkers and tethering sites for the antibody/surface system.The actual work looked at how 24 different tethering sites affect antibody stability on two different surfaces and examined nine linkers varying in length and rigidity. Ultimately the findings were that antibody stability is a function of tethering position when tethered to a hydrophobic surface, but not when tethered to a hydrophilic surface. Furthermore, the length and rigidity of the linkers do not have a significant impact on stability.