Concentration phenomena for neutronic multigroup diffusion in random environments

Scott N. Armstrong, Panagiotis E. Souganidis

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)419-439
Number of pages21
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume30
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Multigroup diffusion model
  • Stochastic homogenization
  • Viscous Hamilton-Jacobi system

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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