Plot of the entropic barrier for polymer sizes N = 102,103,104,105 for γ = 0.50.
Schematic of the one-dimensional biased random walk model of translocation. Here, N = 15 and s = 4.
t 0 vs |Δs| for N = 500, 1000, 2000 generated by the exact method. The inset shows the rescaled data yielding a universal curve. The rescaled analytic solution is also plotted in the inset to demonstrate the agreement between the analytic and exact numerical results.
t 0 vs |Δs| for all polymer lengths. The inset highlights the endpoint behavior for N = 500, 1000, 2000.
Second derivative of t 0 with respect to Δs for N = 1000 at three γ values: 0.10 (inner curve), 0.50, and 0.69 (outer curve). The inset displays the first derivative for the same data.
t 0 vs |Δs| for N = 500,1000,2000 at γ = 0.5. The inset shows the corresponding universal curves calculated for N = 100,1000,10 000.
dt 0/ds at N = 1000 for both boundary conditions at the γ values: γ = 0.1, 0.5, 0.69. The three upper curves correspond to the reflective boundary condition while the three lower curves correspond to the selective boundary condition.
Critical value Δs* for different polymer models obtained from the data and from Eq. (17). The last column shows the prefactor for the scaling of τ with N 2.
Prefactor for the τ ~ N 2 scaling.
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