The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely used in the analysis of transients, where the numerical solutions of the equations are limited by the stiffness problem that results from the different time scales of the instantaneous and delayed neutrons. Its derivation can be done directly from the neutron transport equation, from the neutron diffusion equation or through a heuristics procedure. All of them lead to the same functional form of the system of differential equations for point kinetics, but with different coefficients. However, the solution of the neutron transport equation is of little practical use as it requires the change of the existent core design systems, as used to calculate the design of the cores of nuclear reactors for different operating cycles. Several approximations can be made for the said derivation. One of them consists of disregarding the time derivative for neutron density in comparison with the remaining terms of the equation resulting from the P1 approximation of the transport equation. In this paper, we consider that the time derivative for neutron current density is not negligible in the P1 equation. Thus being, we obtained a new system of equations of point kinetics that we named as modified. The innovation of the method presented in the manuscript consists in adopting arising from the P1 equations, without neglecting the derivative of the current neutrons, to derive the modified point kinetics equations instead of adopting the Fick's law which results in the classic point kinetics equations. The results of the comparison between the point kinetics equations, modified and classical, indicate that the time derivative for the neutron current density should not be disregarded in several of transient analysis situations.

No abstract

No abstract

Nowadays, in 2020, we live during the most dangerous global pandemic that has been reported since the Spanish Flu, which occurred between 1918 and 1920. According to World Health Organization (WHO) records, the pandemic caused by the Sars-Cov-2 virus began in December 2019 and is present in all continents and almost all countries, surpassing more than 79 million infected and 1.7 million deaths by December 2020. Several mathematical models applied to Epidemiology have been adopted over time. One of the most widely adopted is the Susceptible-Infected-Recovered (SIR), developed in India by Kermack and Mckendrick in 1927. In our research, a comprehensive collection of data on the SARS-Cov-2 pandemic was made from reports by WHO, Dadax Limited (Chinese data company), and Johns Hopkins University in the United States of America (USA). Facts were collected from many different countries, regarding the number of confirmed, recovered, and death cases. In this article, we constructed a mathematical model that describes the evolution of the pandemic from the similarity with models already adopted in the field of nuclear physics. For the validation of the mathematical model, we chose information from Germany due to the reliability of the available information. Thus, a statistical analysis was executed to qualify the performance of the method and the predictive character of the mathematical model. To date, 11,716 raw data have been collected, of which we performed data mining relevant to use in this research.