Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2017-04-11T18:59:11Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) DissertaçãoOmar.pdf: 629619 bytes, checksum: f018416fe978f2e27de6abfe2542c60c (MD5) / Made available in DSpace on 2017-04-11T18:59:11Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) DissertaçãoOmar.pdf: 629619 bytes, checksum: f018416fe978f2e27de6abfe2542c60c (MD5) Previous issue date: 2016-02-19 / CNPQ / Estudamos aspectos teóricos de um sistema que modela o comportamento dos unidos micro polares incompressíveis num domínio limitado _ Rn (n = 2 ou 3). Especificamente, utilizamos o método espectral de Galerkin para mostrar a existência de soluções fortes e com determinadas condições mostramos a unicidade das soluções / We study theoretical aspects of a system that models the behavior of incompressible micropolar uids in a bounded domain _ Rn (n = 2 or 3). Speci cally, we use the spectral Galerkin method to show the existence of strong solutions and under certain conditions show the uniqueness of solutions.

This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions. In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice. Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method. In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available. Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.