The Second-Order Adjoint Sensitivity Analysis Methodology (2 nd-ASAM) recently conceived by Cacuci is the only practical method that enables the exact computation of the large number of 2 nd-order sensitivities arising in large-scale problems comprising many parameters. The second- and higher-order sensitivities could not be computed, except for very simple models comprising a handful of parameters, so these sensitivities were ignored. e., uncertain) parameters have been considered when assessing the uncertainties induced in the respective responses by the parameter uncertainties. e., quantities of interest) to the respective model’s imprecisely known ( i. e., functional derivatives) of a computational model’s responses ( i. Until recently, only the first-order sensitivities ( i. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross section and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response. This finding has motivated the development of the original 4 th-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4 th-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. It turned out that some of these 3 rd-order cross sections were far larger than the corresponding 2 nd-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. These works showed that largest response sensitivities involve the total microscopic cross sections, which motivated the recent computation of all of the (180) 3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 7477 first-order and 27,956,503 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters. These parameters are as follows: 180 microscopic total cross sections 7101 microscopic scattering sections 60 microscopic fission cross sections 60 parameters that characterize the average number of neutrons per fission 60 parameters that characterize the fission spectrum 10 parameters that characterize the fission source and 6 parameters that characterize the isotope number densities. The PERP benchmark comprises 7477 imprecisely known (uncertain) model parameters which have nonzero values. This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a poly ethylene- reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark.
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