English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We present a first numerical investigation of the accuracy of the recentlyproposed {\em non-classical transport equation}. This equation contains anextra independent variable (the path-length $s$), and models particle transporttaking place in random media in which a particle's distance-to-collision is{\em not} exponentially distributed. To solve the non-classical equation, oneneeds to know the $s$-dependent ensemble-averaged total cross section$\Sigma_t(s)$, or its corresponding path-length distribution function $p(s)$.We consider a 1-D spatially periodic system consisting of alternating solid andvoid layers, randomly placed in the infinite line. In this preliminary work, weassume transport in rod geometry: particles can move only in the directions$\mu=\pm 1$. We obtain an analytical expression for $p(s)$, and use this resultto compute the corresponding $\Sigma_t(s)$. Then, we proceed to solve thenon-classical equation for different test problems. To assess the accuracy ofthese solutions, we produce "benchmark" results obtained by (i) generating alarge number of physical realizations of the system, (ii) numerically solvingthe transport equation in each realization, and (iii) ensemble-averaging thesolutions over all physical realizations. We show that the results obtainedwith the non-classical equation accurately model the ensemble-averaged scalarflux in this 1-D random system, generally outperforming the widely-used atomicmix model. We conclude by discussing plans to extend the present work to slabgeometry, as well as to more general random mixtures.

On the Accuracy of the Non-Classical Transport Equation in 1-D Random Periodic Media