High-Order Linear Discontinuous and Diamond Differencing Schemes Along Cyclic Characteristics
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Bibliographic record
Abstract
We are investigating a new class of linear characteristics schemes along cyclic tracks for solving the transport equation for neutral particles with scattering anisotropy. These algorithms rely on linear discontinuous exact integration and diamond differencing, as implemented with the method of discrete ordinates. These schemes are based on linear discontinuous coefficients that are derived through the application of approximations describing the mesh-averaged spatial flux moments in terms of spatial source moments and of the beginning-of-segment and end-of-segment flux values. The linear discontinuous characteristics (LDC) and quadratic-order diamond differencing (DD1) schemes are inherently conservative. In this technical note, we intend to continue the development of the LDC and DD1 schemes by extending their application to cyclic trackings. This extension will make possible the representation of reflective or general albedo boundary conditions. We will present an improved and much shorter derivation of the LDC and DD1 schemes, compared to a previous presentation. Finally, we will implement the new schemes as Matlab scripts for solving a one-dimensional slab benchmark and in the DRAGON5 lattice code for solving a more representative two-dimensional eight-symmetry pressurized water reactor assembly mock-up.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it