Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (N) of the average translocation time \u3c tau \u3e, the average velocity of the center of mass \u3c upsilon(CM) \u3e , and the effective radius of gyration \u3c R-g \u3e during the translocation process defined as \u3c tau \u3e similar to N-alpha, \u3c upsilon(CM) \u3e similar to N-delta, and R-g similar to N-(nu) over bar. respectively, and the exponent of the translocation coordinate (s-coordinate) as a function of the translocation time \u3c s(2)(t) \u3e similar to t(beta). We find alpha = 1.36 +/- 0.01, beta = 1.60 +/- 0.01 for \u3c s(2)(t) \u3e similar to tau(beta) and (beta) over bar = 1.44 +/- 0.02 for \u3c Delta s(2)(t) \u3e similar to tau((beta) over bar), delta = 0.81 +/- 0.04, and (nu) over bar similar or equal to nu = 0.59 +/- 0.01, where nu is the equilibrium Flory exponent in 3D. Therefore, we find that \u3c tau \u3e similar to N-1.36 is consistent with the estimate of \u3c tau \u3e similar to \u3c R-g \u3e / \u3c upsilon(CM) \u3e . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent alpha = 1.36 +/- 0.01 \u3c 1 + nu. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the cis and trans parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here