The interaction effect between two neutron absorbers using Wallace's method
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Bibliographic record
Abstract
The dependence of Galanin's constant on fuel-plate separation is studied. Galanin's constant arises in the sourcesink method of lattice calculations and normally its value for an isolated fuel plate is used. Our calculations therefore enable the accuracy of that assumption to be assessed. To illustrate the problem, two absorbing and scattering plates, embedded in an infinite moderator and separated by a distance b are considered, with a source in the moderator region. The calculations are carried out via the integral form of the transport equation using the little-known method of Wallace. This approach enables the integral equation to be cast into a particularly useful form for evaluation of the flux and absorption rate in the plates. A variational method and a numerical solution provide results that show that there are significant deviations from the isolated plate approximation. Tables and figures are provided to illustrate these conclusions. In addition to the main result, we take the opportunity to show how Wallace's method can be used to simplify the transport equation for an infinitely reflected slab reactor. We also obtain results for the flux in a half-space in which there is a constant source, using a novel approximation procedure. Comparison with the exact result shows high accuracy.
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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)
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