A non-circular Eshelby inclusion near a non-parabolic inhomogeneity admitting internal uniform stresses
Bibliographic record
Abstract
With the aid of conformal mapping and analytic continuation, we prove that within the framework of anti-plane elasticity, a non-parabolic open elastic inhomogeneity can still admit an internal uniform stress field despite the presence of a nearby non-circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding elastic matrix is subjected to uniform remote stresses. The non-circular inclusion can take the form of a Booth’s lemniscate inclusion, a generalized Booth’s lemniscate inclusion or a cardioid inclusion. Our analysis indicates that the uniform stress field within the non-parabolic inhomogeneity is independent of the specific open shape of the inhomogeneity and is also unaffected by the existence of the nearby non-circular inclusion. On the other hand, the non-parabolic shape of the inhomogeneity is caused solely by the presence of the non-circular inclusion.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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".