Bibliographic record
Abstract
The Landau-de Gennes model for nematic liquid crystal bulk and interfaces has been extended to nematic triple lines involving the intersection of two isotropic fluids and one nematic liquid crystalline phase. A complete set of bulk, interface, and triple line force and torque balance equations has been formulated. The triple line force and torque balance equations have linear, interfacial, and bulk contributions. The bulk contributions appear as junction integrals, the surface contributions as junctions sums, and the line contributions as gradients of stresses. Reduction of dimensionality from three to one dimensional creates the following effects: (a) bulk terms enter interfacial balances as surface jumps and line balances as junction integrals, and (b) surface terms enter linear balances as junction sums. Line stress and torque equations are derived using classical liquid crystal models. The correspondence between line stress and line torque and their surface and bulk analogs is established. The triple line force and torque balance equations are use to analyze the contact angle in a nematic lens lying at the interface between two isotropic fluids, when the preferred surface orientation is tangential. The effect of anisotropy and long range elasticity on triple line phases is established. Under weak anchoring the contact angle is shown to be a function of the anchoring energy at the nematic-isotropic interface, while under strong anchoring conditions the contact angle is a function of the Peach-Koehler force that originates from bulk long range elasticity and acts on the triple line. The use of the complete set of balance equations removes the classical inconsistency in force balances at a contact line by properly taking into account long range (bulk gradient elasticity) and anisotropic (interfacial anchoring elasticity) effects.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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".