Why this work is in the frame
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Bibliographic record
Abstract
For a fluid layer heated and cooled differentially at its surface, we use a variational approach to place bounds on the viscous dissipation rate and a horizontal Nusselt measure based on the entropy production. With a general temperature distribution imposed at the top of the layer and a variety of thermal boundary conditions at the base of the layer, the horizontal Nusselt number is bounded by $cR_H^{1/3}$ as the horizontal Rayleigh number $R_H \,{\rightarrow}\, \infty$ , for some constant $c.$ The analysis suggests that the ultimate regime for this so-called ‘horizontal convection’ is one in which the temperature field develops a boundary layer of width $O(R_H^{-1/3})$ at the surface, but has no variation in the interior. Although this scenario resonates with results of dimensional scaling theory and numerical computations, the bounds differ in the dependence of the Nusselt measure on $R_H$ . Numerical solutions for steady convection appear to confirm Rossby's result that the horizontal Nusselt number scales like $R_H^{1/5}$ , suggesting either that the bound is not tight or that the numerics have yet to reach the asymptotic regime.
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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 | 0.000 |
| 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 it