摘要

we investigate velocityfluctuations in two systems exhibiting collective motion. In Bacillus subtilis colonies, motile bacteria move collectively, spontaneously forming dynamicclusters. For a range of cell density and cluster size, the correlation length of fluctuations is shown to be 30% of the spatial size of clusters, and the correlationfunctions collapse onto a master curve after rescaling the separation with correlation length. These results demonstrate that correlations of fluctuations are scale-invariant in dynamic bacterial clusters. To further understand the origin and consequences of scale-invariant fluctuations, we carry out systematic simulations using Viscek-type numerical models. In simulations, scale-invariant fluctuations are found to emerge in a robust manor with a wide range of parameters. We also show that scale-invariant fluctuations facilitate motion coordination and help the system to respond coherently to external stimuli.