  We use numerical simulations of a bead-spring model chain to investigate the
evolution of the conformation of long and flexible elastic fibers in a steady
shear flow. In particular, for rather open initial configurations, and by
varying a dimensionless elastic parameter, we identify two distinct
conformational modes with different final size, shape, and orientation. Through
further analysis we identify slipknots in the chain. Finally, we provide
examples of initial configurations of an "open" trefoil knot that the flow
unknots and then knots again, sometimes repeating several times. These changes
in topology should be reflected in changes in bulk rheological and/or transport
properties.
