The criticality of multiplicative processes

Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving particle creation) both in particle generations and in time. This framework allows us to obtain, within a same formalism, two corresponding estimates of the multiplication factor which describes the growth of particle numbers at large times. We obtain the relative positions of both estimates with respect to each other and to criticality. These relations may show particularly useful when simulating in a realistic way the monitoring of nuclear cores in subcritical states, such as is the case for Accelerator Driven Systems (ADS). More generally, this study applies to various multiplicative processes which can be found in nature.