A Mathematical Theory of Motion of Researchers between Research Organizations

Abstract

We discuss a mathematical model of motion of substance in a node of a network which has a structure consisting of a chain of cells. An exact solution for the model equations is obtained in the case when the structure of the node is a chain of two cells. The obtained general results are applied to the construction of a theory for the specific case of motion of young and experienced researchers between research organizations. For this case, we obtain analytical relationships for the time dependence of the number of two kinds of researchers in the studied research organization. These relationships are based on a specific choice of the time-dependent parameters of the model. The obtained analytical results show that the changes in the numbers of young and experienced researchers in a research organization may depend on the ratio between the initial numbers of the two kinds of researchers as well as on the parameters regulating the exchange of researchers between the research organization and the rest of the research environment.