Bounds on double-diffusive convection
Bibliographic record
Abstract
We consider double-diffusive convection between two parallel plates and compute bounds on the flux of the unstably stratified species using the background method. The bound on the heat flux for Rayleigh–Bénard convection also serves as a bound on the double-diffusive problem (with the thermal Rayleigh number equal to that of the unstably stratified component). In order to incorporate a dependence of the bound on the stably stratified component, an additional constraint must be included, like that used by Joseph ( Stability of Fluid Motion , 1976, Springer) to improve the energy stability analysis of this system. Our bound extends Joseph's result beyond his energy stability boundary. At large Rayleigh number, the bound is found to behave like $R_T^{1/2}$ for fixed ratio $R_S/R_T$ , where $R_T$ and $R_S$ are the Rayleigh numbers of the unstably and stably stratified components, respectively.
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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".