Collective motion with extended spatiotemporal coherence can be found in systems of self-propelled objects at almost every length scale, from flocking birds and fish schools, to bacterial swarming and cooperative behavior of molecular motors in the cell. This biologically originated phenomenon has been studied from perspectives of nonequilibrium statistical mechanics and nonlinear dynamics. The studies have used discrete-particle dynamics based on simple local-interaction laws, continuum ideas from liquid crystal physics, two-fluid models, and hydrodynamics, and have simulated numerically idealized swimmers.
We determine and relate the characteristic velocity, length, and time scales for bacterial motion in swarming colonies of Paenibacillus dendritiformis growing on semi-solid agar substrates. The bacteria swim within a thin fluid layer, and they form long-lived jets and vortices. These coherent structures lead to anisotropy in velocity spatial correlations and to a two-step relaxation in velocity temporal correlations. The mean squared displacement of passive tracers exhibits a short-time regime with nearly ballistic transport and a diffusive long-time regime. We find that various definitions of the correlation length all lead to length scales that are, surprisingly, essentially independent of the mean bacterial speed, while the correlation time is linearly proportional to the ratio of the correlation length to the mean speed.
 Zhang, H.P., A. Be’er, E.-L. Florin, and H.L. Swinney, 2010, Collective motion and density fluctuations in bacterial colonies, Proceedings of the National Academy of Sciences , 107 (31): 13626-13630.
 Zhang, H.P., A. Be’er, A., R.S. Smith, E.-L. Florin, and H.L. Swinney, 2009, Swarming dynamics in bacterial colonies, Europhysics Letters , 87:48011, doi: 10.1209/0295-5075/87/48011.