Category: Publications

A nonstiff solution for the stochastic neutron point kinetics equations

Introducing an approach that yields a nonstiff solution to solve the stochastic neutron point kinetics equations.

Title

A nonstiff solution for the stochastic neutron point kinetics equations

Author(s)

Milena Wollmann da Silva, Richard Vasques, Bardo E.J. Bodmann, Marco T. Vilhena

Publication

Annals of Nuclear Energy 97: 47-52

Description

We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation, allowing the calculation of the neutron and precursor densities at any time of interest without the need of using progressive time steps. We use Double-DDM to compute results for stochastic problems with constant, linear, and sinusoidal reactivities. We show that these results strongly agree with those obtained by other approaches established in the literature. We also compute and analyze the first four statistical moments of the solutions.

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Nonclassical particle transport in the 1-D diffusive limit

We provide computational results demonstrating for the first time that the solution of the nonclassical particle transport equation is well-approximated
by the solution of the nonclassical diffusion equation.

Title

Nonclassical particle transport in the 1-D diffusive limit

Author(s)

Richard Vasques, Rachel N. Slaybaugh, Kai Krycki

Publication

Transactions of the American Nuclear Society 114: 361-364

Description

In this paper, we investigate nonclassical particle transport taking place in a 1-D random periodic diffusive system. We provide computational results that validate the theoretical predictions, demonstrating for the first time that the solution of the nonclassical particle transport equation is well-approximated
by the solution of the nonclassical diffusion equation.

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The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation

Showing that the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium.

Title

The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation

Author(s)

Richard Vasques*

Publication

Applied Mathematics Letters 53: 63–68

Description

We show that, by correctly selecting the probability distribution function for a particle’s distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of probability distribution function preserves the true mean-squared free path of the system.

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