A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $\left(\eta \right)$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_a|=0\mathrm{}$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_a|$ is found to scale as $({\eta }_c-\eta {)}^{\beta }$ with $\beta \simeq 0.45$.

Depending on the environmental conditions bacterial colonies growing on agar surfaces can exhibit complex colony formation and various types of collective motion. Experimental results are presented concerning the hydrodynamics (vortices, migration of bacteria in clusters) and colony formation of a morphotype of Bacillus subtilis. Some of these features are not specific to this morphotype but also have been observed in several other bacterial strains, suggesting the presence of universal effects. A simple model of self-propelled particles is proposed, which is capable of describing the hydrodynamics on the intermediate level, including the experimentally observed rotating disks of bacteria. The colony formation is captured by a complex generic model taking into account nutrient diffusion, reproduction, and sporulation of bacteria, extracellular slime deposition, chemoregulation, and inhomogeneous population. Our model also sheds light on some possible biological benefits of this ‘‘multicellular behavior.’’ © 1996 The American Physical Society.

We demonstrate that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a new continuum theory that can account for the development of the symmetry broken state and belongs to the same universality class as the discrete self-propelled particle model.