Dynamical scaling exponents for polymer translocation through a nanopore
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Bibliographic record
Abstract
We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to $N=800$ in some cases. We focus on the scaling of the average PT time $\ensuremath{\tau}\ensuremath{\sim}{N}^{\ensuremath{\alpha}}$ and the mean-square change of the PT coordinate, $⟨{s}^{2}(t)⟩\ensuremath{\sim}{t}^{\ensuremath{\beta}}$. We find $\ensuremath{\alpha}=1+2\ensuremath{\nu}$ and $\ensuremath{\beta}=2∕\ensuremath{\alpha}$ for unbiased PT in two dimensions (2D) and three dimensions (3D). The relation $\ensuremath{\alpha}\ensuremath{\beta}=2$ holds for driven PT in 2D, with a crossover from $\ensuremath{\alpha}\ensuremath{\approx}2\ensuremath{\nu}$ for short chains to $\ensuremath{\alpha}\ensuremath{\approx}1+\ensuremath{\nu}$ for long chains. This crossover is, however, absent in 3D where $\ensuremath{\alpha}=1.42\ifmmode\pm\else\textpm\fi{}0.01$ and $\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\approx}2.2$ for $N\ensuremath{\approx}40\ensuremath{-}800$.
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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 | 0.000 | 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) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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