On the Zero-Neutron Density in Stochastic Nuclear Dynamics

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.

Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics

“…. , j k is equal to zero (the corresponding integral is called the mixed-type iterated stochastic integral), then the integral (3) can be reduced to a linear combination of integrals (5) with a smaller multiplicity and the additional condition [20]…”

“…For irregular random functions -such as white noise -the classical theory is not applicable, and, in its development, the theory of stochastic differential equations appeared [1][2][3]. Stochastic differential equations are used to describe stochastic dynamical systems in many fields [4][5][6][7].…”