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arXiv · 1202.1246

Concentration phenomena for neutronic multigroup diffusion in random environments

Scott N. Armstrong·Panagiotis E. Souganidis
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Abstract

We study the asymptotic behavior of the principal eigenvalue of a weakly coupled, cooperative linear elliptic system in a stationary ergodic heterogeneous medium. The system arises as the so-called multigroup diffusion model for neutron flux in nuclear reactor cores, the principal eigenvalue determining the criticality of the reactor in a stationary state. Such systems have been well-studied in recent years in the periodic setting, and the purpose of this work is to obtain results in random media. Our approach connects the linear eigenvalue problem to a system of quasilinear viscous Hamilton-Jacobi equations. By homogenizing the latter, we characterize the asymptotic behavior of the eigenvalue of the linear problem and exhibit some concentration behavior of the eigenfunctions.

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Scott N. Armstrong, Panagiotis E. Souganidis. 2012-02-06. Concentration phenomena for neutronic multigroup diffusion in random environments. https://doi.org/10.1016/j.anihpc.2012.09.002

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