# [J11] Nonclassical particle transport in one-dimensional random periodic media

### Journal article

Richard Vasques, Kai Krycki, Rachel N. Slaybaugh

Nuclear Science and Engineering, vol. 185(1), 2017, pp. 78-106

Nuclear Science and Engineering, vol. 185(1), 2017, pp. 78-106

DOI:
10.13182/NSE16-35

Cite

*close*

### Cite

**APA**

Vasques, R., Krycki, K., & Slaybaugh, R. N. (2017). [J11] Nonclassical particle transport in one-dimensional random periodic media. Nuclear Science and Engineering, 185(1), 78–106.

**Chicago/Turabian**

Vasques, Richard, Kai Krycki, and Rachel N. Slaybaugh. “[J11] Nonclassical Particle Transport in One-Dimensional Random Periodic Media.” Nuclear Science and Engineering 185, no. 1 (2017): 78–106.

**MLA**

Vasques, Richard, et al. “[J11] Nonclassical Particle Transport in One-Dimensional Random Periodic Media.” Nuclear Science and Engineering, vol. 185, no. 1, 2017, pp. 78–106.

**ABSTRACT:**We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path length

*s*), and models particle transport in homogenized random media in which the distance to collision of a particle is not exponentially distributed. To solve the nonclassical equation, one needs to know the

*s*-dependent ensemble-averaged total cross section Σ

*t*(μ, s) or its corresponding path-length distribution function

*p*(μ, s). We consider a one-dimensional (1-D) spatially periodic system consisting of alternating solid and void layers, randomly placed along the

*x*-axis. We obtain an analytical expression for

*p*(μ,

*s*) and use this result to compute the corresponding Σ

*t*(μ, s). Then, we proceed to solve numerically the nonclassical equation for different test problems in rod geometry; that is, particles can move only in the directions μ = ±1. To assess the accuracy of these solutions, we produce benchmark results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. We show that the numerical results validate the nonclassical model; the solutions obtained with the nonclassical equation accurately estimate the ensemble-averaged scalar flux in this 1-D random periodic system, greatly outperforming the widely used atomic mix model in most problems.