Generalized extreme value analysis of efficient evaluation of extreme values in random media criticality calculations

Ueki, Taro  

The theme of this paper is how to efficiently analyse extreme realizations of neutron effective multiplication factor (keff) over random media replicas modelled by incomplete randomized Weierstrass function (IRWF). To this end, a new bounded amplification (BA) technique is applied to IRWF. Numerical results indicate that the BA-applied IRWF reduces a required number of random media replicas at least by an order of magnitude. To validate this efficiency gain, generalized extreme value (GEV) analysis is applied to a data set of keff values obtained without applying BA. It turns out that the extreme values of these keff values follow the Weibull distribution. Therefore, the theory of GEV guarantees the existence of the upper limit of these keff values, and the actually computed upper limit is indeed smaller than the top two keff values obtained from an order-of magnitude reduced number of BA-applied IRWF random media replicas. This means that the efficiency gain via BA has been confirmed by GEV analysis.