  We investigate the sedimentation of knotted polymers by means of stochastic
rotation dynamics, a molecular dynamics algorithm that takes hydrodynamics
fully into account. We show that the sedimentation coefficient s, related to
the terminal velocity of the knotted polymers, increases linearly with the
average crossing number n_c of the corresponding ideal knot. To the best of our
knowledge, this provides the first direct computational confirmation of this
relation, postulated on the basis of experiments in "The effect of ionic
conditions on the conformations of supercoiled DNA. I. sedimentation analysis"
by Rybenkov et al., for the case of sedimentation. Such a relation was
previously shown to hold with simulations for knot electrophoresis. We also
show that there is an accurate linear dependence of s on the inverse of the
radius of gyration R_g^-1, more specifically with the inverse of the R_g
component that is perpendicular to the direction along which the polymer
sediments. When the polymer sediments in a slab, the walls affect the results
appreciably. However, R_g^-1 remains to a good precision linearly dependent on
n_c. Therefore, R_g^-1 is a good measure of a knot's complexity.
