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Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Faculty Publications
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 nonlinear space-dependent problems. To complement these illustrative applications, this work illustrates the application of the nth-CASAM-N to a paradigm nonlinear time-dependent model chosen from the field of reactor dynamics/safety, namely the well-known Nordheim–Fuchs model. This phenomenological model describes a short-time self-limiting power transient 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 model is sufficiently complex to demonstrate all the …
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Illustrative Application Of The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems To The Nordheim–Fuchs Reactor Dynamics/Safety Model, Dan Gabriel Cacuci
Faculty Publications
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 nonlinear space-dependent problems. To complement these illustrative applications, this work illustrates the application of the nth-CASAM-N to a paradigm nonlinear time-dependent model chosen from the field of reactor dynamics/safety, namely the well-known Nordheim–Fuchs model. This phenomenological model describes a short-time self-limiting power transient 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 model is sufficiently complex to demonstrate all the …
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems (Nth-Casam-N): Mathematical Framework, Dan Gabriel Cacuci
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Nonlinear Systems (Nth-Casam-N): Mathematical Framework, Dan Gabriel Cacuci
Faculty Publications
This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the nth-CASAM-N is proven to be correct by using mathematical induction. The nth-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems.
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Response-Coupled Forward/Adjoint Linear Systems (NTh-Casam-L): Ii. Illustrative Application, Dan Gabriel Cacuci
The NTh-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Response-Coupled Forward/Adjoint Linear Systems (NTh-Casam-L): Ii. Illustrative Application, Dan Gabriel Cacuci
Faculty Publications
This work illustrates the application of the nth-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “nth-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the nth-CASAM-L. The results presented in this work underscore the fundamentally important role of the nth-CASAM-L in the quest …