Nonequilibrium dynamics of polymer translocation: a mean-field model

We analyse the dynamics of polymer translocation in the strong force regime by recasting the problem into solving a differential equation with a moving absorbing boundary. For the total translocation time, $\tau_{\rm tr}$, our simple mean-field model predicts that $\tau_{\rm tr}\sim$ (number of monomers)$^{1.5}$, which is in agreement with the exponent found in previous simulation results. Our model also predicts intricate dependencies of $\tau_{\rm tr}$ on the variations of the pulling force and of the temperature.