In a previous work, we have presented an innovative theoretical model to describe the evolution of the life cycle of a new technology. We have proposed a mathematical approach based on a rate equation, similar to that used to describe quantum level transitions. The model is able to describe the hype curve evolution in many relevant conditions, which can be associated with various external parameters. In this article, we apply this model to describe the evolution of the number of publications in some different research fields that are very current and extremely advanced in terms of social impact. The applications have been chosen in the fields of biomolecular chemistry, genetics and superconducting nanoelectronics.