%0 Journal Article
%T Introducing the n<sup>th</sup>-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n<sup>th</sup>-FASAM-N): II. Illustrative Example
%A Dan Gabriel Cacuci
%J American Journal of Computational Mathematics
%P 43-95
%@ 2161-1211
%D 2024
%I Scientific Research Publishing
%R 10.4236/ajcm.2024.141003
%X <span style=\"font-family:&quot;\"><span style=\"font-family:Verdana;\">This work highlights the unparalleled efficiency of
the ˇ°n</span><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-Order Function/</span></span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\"><span style=\"font-family:Verdana;\">Feature Adjoint Sensitivity Analysis Methodology for
Nonlinear Systemsˇ± (n</span><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-FASAM-N) by considering the well-known
Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time
self-limiting power excursion in a nuclear reactor system having a negative
temperature coefficient in which a large amount of reactivity is suddenly
inserted, either intentionally or by accident. This nonlinear paradigm model is
sufficiently complex to model realistically self-limiting power excursions for
short times yet admits closed-form exact expressions for the time-dependent neutron
flux, temperature distribution and energy released during the transient power
burst. The n</span><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-FASAM-N methodology is compared to the extant ˇ°n</span><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-Order
Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systemsˇ±
(n</span><sup><span style=\"font-family:Verdana;\">th</span></sup><span style=\"font-family:Verdana;\">-CASAM-N) showing that: (i) the 1</span><sup><span style=\"font-family:Verdana;\">st</span></sup><span style=\"font-family:Verdana;\">-FASAM-N and the 1</span><sup><span style=\"font-family:Verdana;\">st</span></sup><span style=\"font-family:Verdana;\">-CASAM-N
methodologies are equally efficient for computing the first-order
sensitivities; each methodology requires a single large-scale computation for
solving the ˇ°First-Level Adjoint Sensitivity Systemˇ± (1</span><sup><span style=\"font-family:Verdana;\">st</span></sup><span style=\"font-family:Verdana;\">-LASS);
(ii) the 2</span><sup><span style=\"font-family:Verdana;\">nd</span></sup><span style=\"font-family:Verdana;\">-FASAM-N methodology is considerably more efficient than
the 2</span><sup><span style=\"font-family:Verdana;\">nd</span></sup><span style=\"font-family:Verdana;\">-CASAM-N methodology for computing the second-order
sensitivities since the number of feature-functions is much smaller than the
number of primary parameters;
%K Nordheim-Fuchs Reactor Safety Model
%K Feature Functions of Model Parameters
%K High-Order Response Sensitivities to Parameters
%K Adjoint Sensitivity Systems
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132066