  During polymer translocation driven by e.g. voltage drop across a nanopore,
the segments in the cis-side is incessantly pulled into the pore, which are
then pushed out of it into the trans-side. This pulling and pushing polymer
segments are described in the continuum level by nonlinear transport processes
known, respectively, as fast and slow diffusions. By matching solutions of both
sides through the mass conservation across the pore, we provide a physical
basis for the cis and trans dynamical asymmetry, a feature repeatedly reported
in recent numerical simulations. We then predict how the total driving force is
dynamically allocated between cis (pulling) and trans (pushing) sides,
demonstrating that the trans-side event adds a finite-chain length effect to
the dynamical scaling, which may become substantial for weak force and/or high
pore friction cases.
