Saturn ring defect around a spherical particle immersed in nematic\n liquid crystal
Bibliographic record
Abstract
We consider a nematic liquid crystal occupying the three-dimensional domain\nin the exterior of a spherical colloid particle. The nematic is subject to\nDirichlet boundary conditions that enforce orthogonal attachment of nematic\nmolecules to the surface of the particle. Our main interest is to understand\nthe behavior of energy-critical configurations of the Landau-de Gennes\n$Q$-tensor model in the limit of vanishing correlation length. We demonstrate\nexistence of configurations with a single Saturn-ring defect approaching the\nequator of the particle and no other line or point defects. We show this by\nanalyzing asymptotics of energy minimizers under two symmetry constraints:\nrotational equivariance around the vertical axis and reflection across the\nhorizontal plane. Energy blow-up at the ring defect is a significant obstacle\nto constructing well-behaved comparison maps needed to eliminate the\npossibility of point defects. The boundary estimates we develop to address this\nissue are new and should be applicable to a wider class of problems.\n
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".