Bibliographic record
Abstract
Stokes flows of a Maxwell fluid produced by the motion of a wall are analyzed under the slip condition at the boundary. The wall is assumed to be translated in its plane with a given velocity. The relative velocity between the fluid at the wall and the wall is assumed to be proportional to the shear rate at the wall. The exact expressions for the velocity and shear stress are determined by means of a Laplace transform. The velocity fields corresponding to both slip and nonslip conditions for Maxwell and viscous Newtonian fluids are obtained. Two particular cases, namely sinusoidal oscillations and translation with a constant velocity of the wall, are studied. In the case of flows of a Maxwell fluid with a nonslip boundary condition, the velocity is discontinuous across a vortex sheet; this situation does not appear for flows with slip conditions. In this case, the velocity is always continuous. Because the exact expression for the velocity is rather complicated, two small-time and large-time expressions of the velocity are derived. Results for Maxwell fluids are compared with those of viscous Newtonian fluids in both cases of the flow with slip and nonslip conditions. Also, the exact and approximate solutions are compared and good agreement is found. In addition, the influence of the slip coefficient on the velocity and on the relative velocity is studied.
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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".