  Sperm swimming at low Reynolds number have strong hydrodynamic interactions
when their concentration is high in vivo or near substrates in vitro. The
beating tails not only propel the sperm through a fluid, but also create flow
fields through which sperm interact with each other. We study the hydrodynamic
interaction and cooperation of sperm embedded in a two-dimensional fluid by
using a particle-based mesoscopic simulation method, multi-particle collision
dynamics (MPC). We analyze the sperm behavior by investigating the relationship
between the beating-phase difference and the relative sperm position, as well
as the energy consumption. Two effects of hydrodynamic interaction are found,
synchronization and attraction. With these hydrodynamic effects, a multi-sperm
system shows swarm behavior with a power-law dependence of the average cluster
size on the width of the distribution of beating frequencies.
