Fig. 3.

Computer simulations suggested D ₀ and speed as two major parameters that affect directionality wave propagation. a Effect of repulsive threshold D ₀ (24, 36 or 40 µm) on directionality wave propagation. Speed is set at 37.3 µm/h. D ₀ is the threshold of repulsive interactions. The value ranges from 24 to 40 µm. Decreasing D ₀ accelerated wave propagation. b Effect of speed (50, 100, 150% of the control speed of 37.3 µm/h) on directionality wave propagation. Repulsive threshold D ₀ = 24 µm. The value ranges from 0 to 150% (12–55 µm/h). Increasing speed accelerates wave propagation. c, d The rate of directionality wave propagation depends on D ₀ and particle speed. R is the normalized rate of directionality wave propagation. R was set as 1 when D ₀ = 24 µm and speed = 37.3 µm/h. D ₀ negatively correlated with the rate, whereas the rate was positively correlated with speed