Problemas diretos e inversos em cinética química e reconstrução de imagens

Abstract

Natural phenomena can be mathematically classified as direct or inverse problems. Direct problems are recommended to determine the effects, that is, the macroscopic properties of the system, and inverse problems involve the causes, the microscopic properties of the system. However, on most occasions, resolution of inverse problems involve poorly conditioned matrices, thus requiring robust and elaborate techniques like Singular Value Decomposition and artificial neural network, especially MLP and Hopfield. In this study, these methodologies are used to solve direct or inverse problems of chemical kinetics and image. This thesis is divided into three steps, with the first devoted to a brief discussion of this research, as well as the methods used in its resolution. At the second step, numerical and theoretical principles are applied in the chemical kinetics area through three works: 1) study of decomposition of drugs, in particular Efavirenz and Lamivudine in anti-HIV cocktail; 2) study of decomposition of rigid polyurethanes foams, with and without addition of alumina from industrial waste, which are used in construction as flame retardants. Both decomposition studies used experimental data of thermal analysis. 3) Study on the combustion of methane to recover rate constants from the modified Westbrook Dryer model, besides carrying out its certification. Finally, the third step discusses digital image processing, particularly image reconstruction treated as an inverse problem. Thus, this theoretical basis was applied in two image recovery work by the backprojection method, especially in CT and MRI medical imaging.