A hybrid spectral/finite-difference to transient free-surface flow inside thin symmetric cavities of longitudinally varying thickness
Bibliographic record
Abstract
The lubrication theory is extended for transient free-surface flow of a viscous fluid inside three-dimensional symmetric thin cavities of thickness that varies in the flow direction. The problem is first formulated for a cavity of arbitrary shape. The moving domain is mapped onto a rectangular domain at each time step of the computation. The pressure, which in this case is governed by the modified Laplace's equation, is expanded in a Fourier series in the spanwise direction. The expansion coefficients are obtained using the finite-difference method. Only a few modes are usually needed to secure convergence. The flow behaviour is strongly influenced by the cavity thickness. The flows inside a straight, contracting, expanding, and modulated cavities are examined. It is found that while the evolution of the front is always monotonic with time, that of the velocity at the front can be oscillatory if the degree of contraction of the cavity (whether modulated or not) is significant. The velocity of the contact point along the lateral walls is usually larger than that at the front, leading to the straightening of the front. However, for modulated cavities, the front may advance at a faster rate, leading to its own undulation. Copyright © 2005 John Wiley & Sons, Ltd.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".