Geometric‐Bifurcation Methods for Dual Order‐Disorder Transitions: Applications to the Isotropic‐to‐Smectic A Phase Transformation
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Bibliographic record
Abstract
Herein, the focus is on equilibrium self‐assembly of smectic A liquid crystal (LC) phases, characterized by partial orientational and 1D positional order. This LC material organization is observed in the protein solution precursor phases of mussel byssus and its emergence is of importance to biological material science, biomimetics, and green manufacturing. A purely thermodynamic model is intrinsically complex due to proliferation of unknown parameters and computational predictions with low information content. This work extends previous work on smectic self‐assembly using an integrated theory and computational platform based on polynomial conservation laws, differential geometry of thermodynamic surfaces, and soft matter shape algebra. The predictions include two zones (nucleation and growth and spinodal decomposition), the stability predicted for single‐order states (nematic, plastic), and the birth and death of the possible phases under varying quenches. A systematic theory‐computation loop yields conservation laws for smectic ordering, the geometry description (shape and curvedness) of bifurcations, and the response functions to thermal quenches. The outputs of this study form the foundation for characterization of drop‐like spatial‐temporal self‐assembly and colloidal nonequilibrium self‐organization of rod‐like protein precursors into functional biological fibrous materials.
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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 | 0.001 |
| 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 | 0.000 |
| Open science | 0.000 | 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