Ascending Series Analysis of the Transition Layer
Bibliographic record
Abstract
This work considers existing formulation of a recent problem introduced in the literature and involves flow through a transition porous layer, whose solution has been found in terms of Airy’s functions and evaluated using asymptotic series. Ascending series expressions are derived in this work and used in the computations of the solution, namely the computations of Airy’s functions and the recently introduced Nield-Kuznetsov function that arises in the solution to inhomogeneous Airy’s equation. Ascending series expressions developed in this work represent a viable methodology in analyzing flow through the variable permeability transition layer, and are shown to produce results as accurate as the asymptotic series results available in the literature. Both thin and fat transition layers are considered in this work which compares friction factors, velocity profiles, and mean velocities in the two types of layers, Flow through a channel over a Darcy porous layer is also considered in this work and the computed results agree with known results.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".