Numerical Quenching for a System of Heat Equations Under Nonlinear Coupled Boundary Conditions
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Bibliographic record
Abstract
This research work deals with numerical quenching for a system of heat equations under nonlinear coupled boundary conditions. This problem models a heat transfer through two different materials. We obtain some conditions under which the solution of a semi-discrete form of the continuous problem quenches in finite time and estimate its semi-discrete quenching time. We also prove that the semi-discrete quenching time converges to real one, when the mesh size tends to zero. From fully discretized schemes, we have developed algorithms that have allowed us to obtain good approximations of the quenching time and other numerical results to illustrate our analysis.
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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 | 0.007 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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