Finite-size scaling in unbiased translocation dynamics. (English) Zbl 1456.82760
Summary: Finite-size scaling arguments naturally lead to the introduction of a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late-stage dynamics of unbiased polymer translocation through a membrane pore. The solution for the probability density function of the chemical coordinate matches the initial-stage subdiffusive regime and takes into account the equilibrium entropic drive. We find precise scaling relations connecting the subdiffusion exponent to the divergence with the polymer length of the translocation time, and also to the singularity of the probability density function at the absorbing boundaries. Quantitative comparisons with numerical simulation data in \(d = 2\) strongly support the validity of the model and of the predicted scalings.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 82D60 | Statistical mechanics of polymers |
Software:
GSLReferences:
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