Free energy of a knotted polymer confined to narrow cylindrical and conical channels
Bibliographic record
Abstract
Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.001 | 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".