Chaos in eigenvalue search methods - CEA - Commissariat à l’énergie atomique et aux énergies alternatives Access content directly
Journal Articles Annals of Nuclear Energy Year : 2017

Chaos in eigenvalue search methods


Eigenvalue searches for multiplying systems emerge in several applications, encompassing the determination of the so-called alpha eigenvalues associated to the asymptotic reactor period and the adjustment of albedo boundary conditions or buckling in assembly calculations. Such problems are usually formulated by introducing a free parameter into a standard power iteration, and finding the value of the parameter that makes the system exactly critical. The corresponding parameter is supposed to converge to the sought eigenvalue. In this paper we show that the search for the critical value of the parameter might fail to converge for deep sub-critical systems: in this case, the search algorithm may undergo a series of period doubling bifurcations (leading to a multiplicity of solutions) instead of converging to a fixed point, or it may even crash. This anomalous behaviour is explained in terms of the mathematical structure of the search algorithm, which is shown to be closely related to the well-known logistic map for a few relevant applications illustrated in the context of the rod model. The impact of these findings for real-life applications is discussed, and possible remedies are finally suggested.
Fichier principal
Vignette du fichier
201700002701.pdf (1.28 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

cea-02421744 , version 1 (06-03-2020)



D. Mancusi, Andrea Zoia. Chaos in eigenvalue search methods. Annals of Nuclear Energy, 2017, 112, pp.354-363. ⟨10.1016/j.anucene.2017.10.022⟩. ⟨cea-02421744⟩


26 View
116 Download



Gmail Facebook Twitter LinkedIn More