Harmonic Function for 3D Warped Transition Geometry and Its Practical Use
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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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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 | 0.001 |
| 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