Reynolds scaling analysis of the Landau–de Gennes equations for nematic liquid crystals
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Bibliographic record
Abstract
Using the Reynolds scaling analysis, we simplify the Landau-de Gennes (LdG) equations for the flow of liquid crystals (LCs) in thin gaps. Then, both the simplified LdG equations and the full LdG equations are applied to a Couette geometry and a slider bearing geometry for the evaluation and verification of the simplified LdG equations by comparing results. The use of the simplified LdG equations results in a large decrease in wall time, which has the potential to significantly reduce the computational resources needed for simulating LC flows in complex geometries.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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