Collective motion of symmetric camphor papers in an annular water channel

We investigate the collective motion of symmetric self-propelled objects that are driven by a difference in the surface tension. The objects move around an annular water channel spontaneously and interact through the camphor layer that develops on the water surface. We found that two collective motion modes, discrete and continuous density waves, are generated depending on the number of self-propelled objects. The two modes are characterized by examining the local and global dynamics, and the collective motion mechanism is discussed in relation to the distribution of camphor concentration in the annular water channel. We conclude that the difference between these two modes originates from that of the driving mechanism that pushes a camphor paper away from a cluster, through which mechanism density waves are generated and maintained.