New and improved channel cross section with piecewise linear or smooth sides
Bibliographic record
Abstract
This paper presents a new and improved channel cross section with m-segment linear sides and horizontal bottom (MSLS). For large m, the section sides become smooth curves, thus providing the designer with flexibility in using either piecewise linear or smooth channel sides with the same formulation. General simple formulas for the area and perimeter are presented for section sides with m linear segments. An optimization model, which implements the general formulas and minimizes the construction cost, is presented and applied using an example. For sections with piecewise linear sides, where the surface lining unit cost increases as the number of sides increases, the MSLS section was found to be more economical than a section with two-segment linear sides when the rate of increase in cost is not large. The smooth MSLS was found to be always more economical than the two-segment parabolic side section and the parabolic side section. The MSLS, which is more economical, yet simpler, than other section types is useful for a wide range of applications involving small and large channels.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".