Harmonic circular inclusions for non-uniform fields through the use of multi-coating
Why this work is in the frame
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Bibliographic record
Abstract
We propose a novel method for rendering a circular inclusion harmonic even in the presence of non-uniform loading. Most significantly, the condition that the inclusion be harmonic is shown to be <italic>independent</italic> of the specific form of the loading. In addition, we demonstrate that the harmonicity condition obtained actually leads to the stronger property of neutrality when the loading takes a particular form. Our method is based on the idea of ‘multi-coating’ (surrounding the inclusion with a specified number of coatings each with its own separate elastic properties) used in the design of cloaking structures for the conductivity problem. Consequently, the harmonic inclusions designed here can also be thought of as special kinds of ‘near-cloaking’ structures in plane elasticity (in the sense that they are invisible to any changes in mean stress in the structure).
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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