Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems: self-propelled rods interacting via volume exclusion and sinusoidally beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are Gaussian distributed with a nonzero average. These systems are studied by Brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are varied. By distinguishing three types of cluster-size probability density functions, we obtain a phase diagram of different swarm behaviors. The properties of clusters such as their configuration, lifetime, and average size are analyzed. We find that the swarm behavior of the two systems, characterized by several effective power laws, is very similar. However, a more careful analysis reveals several differences. Clusters of self-propelled rods form due to partially blocked forward motion and are therefore typically wedge shaped. At higher rod density and low noise, a giant mobile cluster appears, in which most rods are mostly oriented toward the center. In contrast, flagella become hydrodynamically synchronized and attract each other; their clusters are therefore more elongated. Furthermore, the lifetime of flagella clusters decays more quickly with cluster size than of rod clusters.

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, multiparticle collision dynamics. 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 multisperm system shows swarm behavior with a power-law dependence of the average cluster size on the width of the distribution of beating frequencies.

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D<

We consider an inextensible, semiflexible polymer or wormlike chain, with persistence length P and contour length L, fluctuating in a cylindrical channel of diameter D. In the regime D Ӷ P Ӷ L, corresponding to a long, tightly confined polymer, the average length of the channel ͗R ʈ ͘ occupied by the polymer and the mean-square deviation from the average vary as ͗R ʈ ͘ = ͓1−␣ ‫ؠ‬ ͑D / P͒ 2/3 ͔L and ͗⌬R ʈ 2 ͘ = ␤ ‫ؠ‬ ͑D 2 / P͒L, respectively, where ␣ ‫ؠ‬ and ␤ ‫ؠ‬ are dimensionless amplitudes. In earlier work we determined ␣ ‫ؠ‬ and the analogous amplitude ␣ ᮀ for a channel with a rectangular cross section from simulations of very long chains. In this paper, we estimate ␤ ‫ؠ‬ and ␤ ᮀ from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of R ʈ or radial distribution function, which is asymptotically exact for large L and has the skewed shape seen experimentally.