Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material
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Bibliographic record
Abstract
Abstract We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux. A conformal mapping function for the coating and matrix is introduced, which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane. Using analytic continuation, we derive a general solution in terms of two auxiliary functions. The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface. Once the two auxiliary functions have been obtained in the elementary-form, the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined. The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition. Finally, the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.
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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 | 0.001 | 0.000 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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.
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