Harmonic Function for 3D Warped Transition Geometry and Its Practical Use
Bibliographic record
Abstract
A transition is typically required in irrigation canals, laboratory flumes and many other waterways. The warped type transition (WTT) is the preferred link structure between a small rectangular and relatively large trapezoidal channel section. However, the best method of determining the WTT geometry still requires evaluation. This paper provides an analytical function for the three-dimensional (3D) WTT geometry. This was achieved by solving a Dirichlet problem for Laplace’s equation. The boundary conditions in the problem were chosen based on guidelines and recommendations from earlier studies of transitions. Solving the problem analytically yields a harmonic function. The geometry given by this function guarantees a streamlined rectangular-trapezoidal link and avoids sharp corners. The streamlined transition would work to reduce flow separation and head loss. This paper contributes to the development of a new method for fabricating WTT with precision and repeatability. The harmonic function can generate geometrical data as essential input for laboratory-scale and field-scale WTTs and can aid in the construction of a three-dimensional model for use in computational fluid dynamic models.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".