Illustrative Application of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems to the Nordheim–Fuchs Reactor Dynamics/Safety Model

The application of the recently developed “nth-order comprehensive sensitivity analysis methodology for nonlinear systems” (abbreviated as “nth-CASAM-N”) has been previously illustrated on paradigm space-dependent problems. To complement these illustrative applications, this work illustrates nth-CASAM-N to a time-dependent model chosen from field reactor dynamics/safety, namely well-known Nordheim–Fuchs model. This phenomenological describes short-time self-limiting power transient in nuclear system having negative temperature coefficient which large amount reactivity is suddenly inserted, either intentionally or by accident. sufficiently complex demonstrate all important features applying yet admits exact closed-form solutions energy released transient, most response. All expressions first- and second-level adjoint functions and, subsequently, second-order sensitivities model’s parameters are obtained analytically closed form. principles underlying 3rd-CASAM-N computation third-order demonstrated both mixed unmixed sensitivities. For model, single suffices obtain six 1st-order sensitivities, while two computations suffice 36 (of 21 distinct). example demonstrates that number (large-scale) increases at linearly within methodology, opposed exponential increase parameter-dimensional space occurs when conventional statistical and/or finite difference schemes compute higher-order very models, only practical computing response comprehensively accurately, overcoming curse dimensionality systems.