Multiple-wavelength surface patterns in models of biological chiral liquid crystal membranes
Bibliographic record
Abstract
We present a model to investigate the formation of surface patterns in biological materials through the interaction of anisotropic interfacial tension, bending elasticity, and capillarity at their free surfaces. Focusing on the cholesteric liquid crystal (CLC) material model, the generalized shape equation for anisotropic interfaces using the Rapini-Papoular anchoring and Helfrich free energies is applied to understand the formation of multi-length scale patterns, such as those found in floral petals. The chiral liquid crystal-membrane model is shown to be analogous to a driven pendulum, a connection that enables generic pattern classification as a function of bending elasticity, liquid crystal chirality and anchoring strength. The unique pattern-formation mechanism emerging from the model here presented is based on the nonlinear interaction between bending-driven folding and anchoring-driven creasing. The predictions are shown to capture accurately the two-scale wrinkling of certain tulips. These new findings enable not only to establish a new paradigm for characterizing surface wrinkling in biological liquid crystals, but also to inspire the design of functional surface structures.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".