Nonlinear model for the isotropic/smectic a phase transition
Why this work is in the frame
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Bibliographic record
Abstract
We present both solution and coefficient determination methods for a Landau-de Gennes type phenomenological phase transition model. A homogeneous-volume form of the model is analyzed and shown to be valid for the isotropic/smectic-A transition sequence. A method is presented for the direct linking to experimental observations through coefficient determination in the form of a nonlinear programming problem. A minimization analysis is utilized to simplify the nonlinear model. A computationally efficient and deterministic phase diagram generation method is presented based upon the single-variable form of the model. Phenomenological coefficients and the resulting phase diagram for the liquid crystal 12CB (dodecylcyanobiphenyl) are presented and compared to experimental data. The results show good agreement with experimental data, validating the coefficient determination method. In addition to this the determined constants are applicable for use in the full heterogeneous form of the model. Extensions to the simulation of free-standing smectic films are discussed.
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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 | 0.000 |
| 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 it