Two non-elliptical inhomogeneities with internal uniform stresses interacting with a mode-III crack
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Bibliographic record
Abstract
We use the method of Green's functions to analyze an inverse problem in which we aim to identify the shapes of two non-elliptical elastic inhomogeneities, embedded in an infinite matrix subjected to uniform remote stress, which enclose uniform stress distributions despite their interaction with a finite mode-III crack. The problem is reduced to an equivalent Cauchy singular integral equation, which is solved numerically using the Gauss–Chebyshev integration formula. The shapes of the two inhomogeneities and the corresponding location of the crack can then be determined by identifying a conformal mapping composed in part of a real density function obtained from the solution of the aforementioned singular integral equation. Several examples are given to demonstrate the solution.
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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