Cahn–Hoffman capillarity vector thermodynamics for curved liquid crystal interfaces with applications to fiber instabilities
Bibliographic record
Abstract
The Cahn–Hoffman capillarity vector thermodynamics for curved anisotropic interfaces is adapted to soft liquid crystalline interfaces. The formalism is used to derive Herring’s capillary pressure equation for anisotropic surfaces, where the role of anchoring energy of liquid crystals is made explicity. It is shown in detail that liquid crystal interfaces have three distinct contributions to capillary pressure: (i) area reduction, (ii) area rotation, and (iii) orientation curvature. General expressions representing these three mechanisms in terms of isotropic and anisotropic surface tensions are derived and used to analyze the Rayleigh capillary instability in thin fibers. It is shown that liquid crystal fibers and filaments are unstable to peristaltic and chiral surface ripple modes. The peristaltic mode leads to droplet formation, while chiral modes produce ripples in the curvature of the fiber. The role of liquid crystal orientation and anchoring energy on mode selection is elucidated and quantified.
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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 | 0.000 |
| 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) | 0.000 | 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".