Hybrid Dealiased Convolutions

This paper proposes a practical and efficient solution for computing convolutions using hybrid dealiasing. It offers an alternative to explicit or implicit dealiasing and includes an optimized hyperparameter tuning algorithm that uses experience to find the optimal parameters. Machine learning algorithms and efficient heuristics are also developed to estimate optimal parameters for larger convolution problems using only small squares/rectangles.Comment: Undergraduate Thesi

Cosmological structure formation using spectral methods

Numerical simulations are becoming an increasingly important tool for understanding the growth and development of structure in the universe. Common practice is to discretize the space-time using physical variables. The discreteness is embodied by considering the dynamical variables as fields on a fixed spatial and time resolution, or by constructing the matter fields by a large number of particles which interact gravitationally (N-body methods). Recognizing that the physical quantities of interest are related to the spectrum of perturbations, we propose an alternate discretization in the frequency domain, using standard spectral methods. This approach is further aided by periodic boundary conditions which allows a straightforward decomposition of variables in a Fourier basis. Fixed resources require a high-frequency cut-off which lead to aliasing effects in non-linear equations, such as the ones considered here. This thesis describes the implementation of a 3D cosmological model based on Newtonian hydrodynamic equations in an expanding background. Initial data is constructed as a spectrum of perturbations, and evolved in the frequency domain using a pseudo-spectral evolution scheme and an explicit Runge-Kutta time integrator. The code is found to converge for both linear and non-linear evolutions, and the convergence rate is determined. The correct growth rates expected from analytical calculations are recovered in the linear case. In the non-linear model, we observe close correspondence with linear growth and are able to monitor the growth on features associated with the non-linearity. High-frequency aliasing effects were evident in the non-linear evolutions, leading to a study of two potential resolutions to this problem: a boxcar filter which adheres to“Orszag’s two thirds rule” and an exponential window function, the exponential filter suggested by Hou and Li [1], and a shifted version of the exponential filter suggested, which has the potential to alleviate high frequency- ripples resulting from the Gibbs’ phenomenon. We found that the filters were somewhat successful at reducing aliasing effects but that the Gibbs’ phenomenon could not be entirely removed by the choice of filters

Particle motion and gradient dynamics in turbulent flows: Theory and Numerical Simulations

L'abstract è presente nell'allegato / the abstract is in the attachmen

X-ray images and microtomography using scattering and phase contrast

Orientador: Carlos Manuel Giles Antunez de MayoloTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: O escopo desta tese foi o estudo, implementação, caracterização e aplicação das técnicas de imagens de raios X por contraste de fase e contraste de espalhamento. Este trabalho inicialmente descreve a formação das imagens por contraste de fase pelo método da propagação. Apresenta simulações de primeiros princípios para esta técnica comparando estes com a literatura. Em seguida reporta o desenvolvimento da instrumentação para uma estação experimental de microtomografias de raios X bem como os métodos de processamento de dados para reconstruções tomográficas. Microtomografias com alta resolução foram obtidas e são apresentadas com o intuito de caracterizar a instrumentação e suas aplicações. Essa técnica de instrumentação foi aplicada, em particular, no estudo da histomorfometria óssea em ratos Sprague-Dawley com o objetivo de quantificar os efeitos da dieta alimentar na estrutura óssea trabecular e compacta. Argumenta-se que ocorre uma ligeira tendência a diferenciação nesses tecidos em função da dieta alimentar. Além disso, neste trabalho foi implementado, caracterizado e aplicado a técnica de imagens harmônicas por espalhamento em amostras biológicas, detecção de fraturas e espalhamento anisotrópico. Também são descritos os esforços na melhoria da qualidade sinal-ruído dessa técnicaAbstract: The main scope of this work was the study, implementation, characterization and application of x-ray phase contrast and scattering constrast imaging techniques. First we describe the production of phase constrast images and early attempts to simulate phase contrast phenomena following the known literature. We also report efforts toward development of an experimental x-ray microtomography station as well as imaging processing techniques for tomography reconstruction. We present results on high resolution x-ray microtomography. This technique was applied in the study of Sprague-Dawley bone morphometric properties aiming quantification of high-fat diet effects on compact and trabecular bone structuture. It is argued about a tendency to differentiation on these tissues according to the diet. We also implemented, characterized and applied harmonic scattering imaging in biological samples, fracture detection and anisotropic scattering describing efforts to enhance signal to noise ratio in this techniqueDoutoradoFísicaDoutor em Ciências142800/2010-4CNP

Studying the Evolution of Polydisperse Droplet Size Distributions Using Large Eddy Simulations

We develop a Large Eddy Simulation (LES) model that can predict the turbulent transport and evolution of droplet size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, at low volume fraction. We use a population dynamics model for polydisperse droplets specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. Existing breakup models assume the scale of droplet--eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. The LES model is applied to a three-dimensional turbulent jet subjected to a uniform crossflow and droplet size distributions downstream of the injection are compared with experimental data with good agreement. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behaviour. Further applications with smaller nozzles require an inlet conditions for coarse LES. We develop a hybrid approach where the inlet condition is prescribed using a one dimensional (1D) parcel model that accounts for the evolution of the dispersed phase along the jet centerline due to the combined effects of advection, radial turbulent transport and droplet breakup. We examine the statistics of the velocity field and the concentration profiles of the polydisperse oil droplet plumes for two droplet Weber numbers. We find that the centerline decay rate of the droplet concentration is modified in the breakup dominated zone. Additionally due to trajectory crossing effects the dispersion of larger droplets is suppressed