An Eshelby inclusion in a nonlinearly coupled thermoelectric bi‐material and tri‐material
Bibliographic record
Abstract
Abstract We first derive an analytic solution to Eshelby's problem concerning a circular inclusion within one of two perfectly bonded nonlinearly coupled thermoelectric half‐planes. The inclusion undergoes a prescribed uniform electric current‐free thermoelectric potential gradient and a prescribed uniform energy flux‐free temperature gradient. Closed‐form expressions for the six analytic functions characterizing the thermoelectric fields of electric current density and energy flux in all three phases of the composite are obtained primarily with the aid of analytic continuation. A general method is then proposed for the analytic solution of Eshelby's problem of an inclusion of arbitrary shape in a nonlinearly coupled thermoelectric bi‐material. Finally, we extend our ideas to the case of a tri‐material by developing an analytic solution to the thermoelectric problem associated with a circular Eshelby inclusion in a nonlinearly coupled thermoelectric tri‐material composed of two semi‐infinite thermoelectric media bonded together through an intermediate thermoelectric layer of finite thickness.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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".