Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the crowding of monomers on the {it trans} - side of the membrane which counterbalance the driving force acti
ng in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $alpha$ in the translocation time - vs. - chain length scaling law, $tau propto N^{alpha}$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $alpha$ values which were found in experiments and computer simulations.
We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of
which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.
