  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 taking place in homogenized random media in which a particle's
distance-to-collision is not exponentially distributed. To solve the
nonclassical equation one needs to know the $s$-dependent ensemble-averaged
total cross section, $\Sigma_t(\mu,s)$, or its corresponding path-length
distribution function, $p(\mu,s)$. We consider a 1-D spatially periodic system
consisting of alternating solid and void layers, randomly placed in the
$x$-axis. We obtain an analytical expression for $p(\mu,s)$ and use this result
to compute the corresponding $\Sigma_t(\mu,s)$. Then, we proceed to numerically
solve the nonclassical equation for different test problems in rod geometry;
that is, particles can move only in the directions $\mu=\pm 1$. 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.
