Elasticity of flexible polymers under cylindrical confinement: appreciating the blob scaling regime in computer simulations
Bibliographic record
Abstract
Despite much renewed interest in cylindrically confined polymers with linear or nonlinear topology, often considered as model chromosomes, their scaling predictions, especially on chain elasticity and relaxation, have not been reconciled with numerical data. Of particular interest is their “effective spring constant” given in the scaling form of keff ∼ N−αD−γ, where N is the number of monomers and D the diameter of the cylindrical space. If the blob-scaling approach produces α = 1 and γ = 2 − 1/ν = 1/3 with ν = 3/5 the Flory exponent, a series of numerical studies indicate α ≈ 0.75 and unexpectedly large γ ≈ 0.9. Using computer simulations, we show that there exists a crossover from the formerly called unexpected to blob-scaling regime at a certain value of D ≈ 10 (in units of monomer sizes) for sufficiently large N (>Ncr). Our results suggest that Ncr ≈ 1000, if the farthermost distance is used as the chain size: a quantity relevant in single-chain manipulations or for ring polymers (e.g., bacterial chromosomes). Accordingly, chain relaxation dynamics is expected to show a similar crossover. Our results imply that the applicability of the blob scaling approach depends on how confined chains are characterized.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".