Monte Carlo Treatment of Fundamental-Mode Neutron Leakage in the Presence of Voids

Gelbard, E.M.; Lell, R. M.

doi:10.13182/nse77-a26999

Cited by 18 publications

(7 citation statements)

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“…The true dominant α eigenvalue has been determined numerically by setting γ = −1/2 in the update rule and is displayed as red dots. treatment of fundamental-mode neutron leakage in the presence of voids (Gelbard and Lell, 1976) and have also inspired recent work concerning complexweight Monte Carlo schemes (Yamamoto, 2012a,b;Rouchon, 2017). For the rod model, only the positive or negative directions are allowed: by taking B oriented in the positive direction Ω = +, the resulting eigenvalue equa-335 tions read…”

Section: Buckling Eigenvalue Equationmentioning

confidence: 97%

Chaos in eigenvalue search methods

Mancusi

Zoia

2018

Annals of Nuclear Energy

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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.

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Section: Buckling Eigenvalue Equationmentioning

confidence: 97%

Chaos in eigenvalue search methods

Mancusi

Zoia

2018

Annals of Nuclear Energy

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“…In order to check the validity of the above considerations, we use the simple slab (1D) unit cells, with 2 energy groups, described in Section 3.1: an asymmetric one, taken from (Gelbard and Lell, 1977), and a symmetric variant. The symmetry properties of such unit cells and of the solutions (U,k) of Eq.…”

Section: Numerical Testsmentioning

confidence: 99%

“…The asymmetric unit test cell used in (Gelbard and Lell, 1977) is a 3-region 1D (slab) cell consisting in 0.5 cm moderator + 0.1 cm absorber + 0.1 cm fuel (see Fig. 2).…”

Section: The 2-group 1d Test Casesmentioning

confidence: 99%

“…2. The asymmetric unit cell (Gelbard and Lell, 1977). Table 2 2-Group cross-sections for the unit cells.…”

Section: Expected Symmetry Featuresmentioning

confidence: 99%

“…However, (Gelbard and Lell, 1977) show, using a first-order perturbation formula, that Dk ¼ kðBÞ À kð0Þ remains, at 1st order, real in the vicinity ofB ¼ 0 if the cell has three orthogonal reflection planes. Furthermore, they give an example of a 1D slab core made of repeating dissymmetric unit cells where a sinusoidal macroscopic flux shape cannot be established.…”

Section: Introductionmentioning

confidence: 97%

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