Aplicação do método da Transformada de Laplace com representação matricial para modelagem computacional do fenômeno do decaimento radioativo

Abstract

Radioactive decay is a physical phenomenon that can be modeled by simple computational techniques, using aspects of the two main schools of mathematical modeling: the deterministic school and the probabilistic school. In this work, we focus on the deterministic school. The mathematical model is characterized by an initial value problem with a single or coupled chain of radioactive decays according to the history of an atomic nucleus to decay to a daughter-atomic nucleus, that is stable or not. In this dissertation we describe a computer software modeling simple radioactive decays, i.e., decays to stable nuclei and directly coupled decay chains that we developed on a free platform. To achieve this goal, we used a matrix formulation and a diagonalization technique by means of similarity transformation, where we introduced a general form of constructing the diagonalizer matrix and its inverse, that are needed. We present numerical results for three typical problems.