Abstract
In this short paper, we compare the deterministic model for the nuclear reactor dynamic (Hetrick, 1993) with the stochastic model (Kinard and Allen, 2004). Our numerical results show coincidences between the deterministic model and the mean of the stochastic paths, although, as already observed by other authors, there is alarge amount of dispersion between the individual paths. Notably, we always observe that the neutron density approaches zero within a short time. In this paper, we investigate this question; more concretely, we study the mean-extinction of the neutron density. The technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using the finite-element method with FreeFem++. Our results confirm that in a very short time the neutrons disappear although later they recover probably due to the external source.
Highlights
We research the time-dependency of a nuclear reactor. Previous models in nuclear reactor dynamics are investigated in [1,2]
In this paper, we research the time-dependency of a nuclear reactor
In this short paper, we compare the deterministic model for the nuclear reactor dynamic (Hetrick, 1993) with the stochastic model (Kinard and Allen, 2004)
Summary
We research the time-dependency of a nuclear reactor. Previous models in nuclear reactor dynamics are investigated in [1,2]. Our numerical results show coincidences between the deterministic model and the mean of the stochastic paths, as already observed by other authors, there is alarge amount of dispersion between the individual paths. We always observe that the neutron density approaches zero within a short time.
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