A phenomenological model for self-rippling energy of free graphene monolayers
Bibliographic record
Abstract
Several candidate phenomenological expressions are studied for self-rippling energy that drives ripple formation of free single-layer graphene sheets. One phenomenological expression is admitted, while all others are rejected because they cannot admit stable periodic ripple mode. The admitted phenomenological expression contains two terms: one quadratic term which acts like a compressive force and has a destabilizing effect, and another fourth-order term which acts like a nonlinear elastic foundation and has a stabilizing effect. The two associated coefficients depend on specific mechanism of self-rippling and can be determined based on observed wavelength and amplitude of ripple mode. Based on the admitted expression, the effect of an applied force on ripple formation is studied. The present model predicts that the rippling can be controlled or even suppressed with an applied tensile force or collapsed into narrow wrinkles (of deformed wavelengths down to around 2 nm) under an applied compressive force, and the estimated minimum tensile strain to suppress rippling is in remarkable agreement with some known data. Our results show that self-rippling energy dominates ripple formation of sufficiently long free graphene ribbons, although it cannot drive self-rippling of sufficiently short free graphene ribbons. Consequently, a critical length is estimated so that self-rippling occurs only when the length of free single-layer graphene ribbons is much longer than the critical length. The estimated critical length is reasonably consistent with the known fact that self-rippling cannot occur in shorter free graphene sheets (say, of length below 20 nm).
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.003 | 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".