Perturbation Theory Based on the Method of Cyclic Characteristics
Bibliographic record
Abstract
Generalized perturbation theory (GPT) is a technique used for the estimation of small changes in performance functionals, such as linear reaction rate ratios, eigenvalues, power density, etc., affected by small variations in reactor core compositions. Here, a GPT algorithm is developed for the multigroup integral neutron transport problems in two-dimensional fuel assemblies with isotropic scattering. We then use the relationship between the generalized flux importance and generalized source importance functions to transform the generalized flux importance transport equations into the integrodifferential equations for the generalized adjoints. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup rebalance technique. After convergence is reached, the decontamination procedure extracts from the generalized adjoints the component parallel to the adjoint function. Three types of biasing/decontamination schemes are investigated in the study. To demonstrate the efficiency of our solution algorithms, calculations are performed on 17 × 17 pressurized water reactor and 37-pin Canada deuterium uranium reactor (CANDU) lattices. Numerical comparisons of the generalized adjoint functions and GPT estimates using the MOCC and collision probability method are presented as well as sensitivity coefficients of nuclide densities.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".