On obtaining effective orthotropic elasticity tensors
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Bibliographic record
Abstract
We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; herein, by ‘effective’, we mean the closest in the sense of the Frobenius norm, without a priori assuming the orientation of the orthotropic tensor. It is difficult to find the absolute minimum of the distance function since the minimization process is nonlinear, exhibiting several local minima. To find the effective orthotropic tensor, the minimization process must be performed on a three-dimensional manifold SO(3). In the case of monoclinic and transversely isotropic tensors, it can be performed on a two-dimensional sphere, which lends itself to an insightful plot that allows us to guide a numerical method. We use the orientation of the symmetry-plane normal of the effective monoclinic tensor to guide the method and obtain the effective orthotropic tensor—a two-step process.
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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