  We present numerical results for the dynamics of a single chain in steady
shear flow. The chain is represented by a bead-spring model, and the smoothed
profile method is used to accurately account for the effects of thermal
fluctuations and hydrodynamic interactions acting on beads due to host fluids.
It is observed that the chain undergoes tumbling motions and that its
dimensionless frequency F depends only on the Peclet number Pe with a power
law. The exponent of Pe clearly changes from 2/3 to 1 around the critical
Peclet number, indicating that the crossover reflects the competition of
thermal fluctuation and shear flow. The presented numerical results agree well
with our theoretical analysis based on Jeffery's work.
