Abstract. Biologically inspired models of self-propelled interacting agents display a wide variety of collective motion such as swarm migration and vortex formation. In these models, active interactions among agents are typically included such as velocity alignment and cohesive and repulsive forces that represent agents' short- and long-range 'sensing' capabilities of their environment. Here, we show that similar collective behaviors can emerge in a minimal model of isotropic agents solely due to a passive mechanism—inelastic collisions among agents. The model dynamics shows a gradual velocity correlation build-up into the collective motion state. The model displays a discontinuous transition of collective motion with respect to noise and exhibits several collective motion types such as vortex formation, swarm migration and also complex spatio-temporal group motion. This model can be regarded as a hybrid model, connecting granular materials and agent-based models.

GENERAL SCIENTIFIC SUMMARY
Introduction and background. Self propelled agents are widely used to investigate the behavior of animal groups such as flocks of birds or swarms of bacteria. In these models, an animal is described by an agent with active sensing and steering capabilities mediated by a set of simple rules. Taking advantage of insights from the field of granular materials (systems characterized by inanimate inelastically colliding particles such as sand or gravel), inelastic 'self propelled particles' (SPP) have been investigated. Such an SPP can be a grain of rice, for example, bouncing on a vibrating container (the tilt of the grain with respect to a vibrating bottom creates an effective self propulsion force). These SPP systems do not possess any kind of the active mechanisms utilized by living organisms; nevertheless surprising collective motion emerges. One of the fundamental questions arising in this context is what are the minimal interactions required and how crucial are the active mechanisms in the emergence of collective motion.

Main results. By simulating a system of isotropic self propelled grains, the emergence of large-scale vortices, coherent group migration, and complex group motions are observed. The model exhibits a gradual velocity correlation build-up into a dynamic collective state and a discontinuous transition into the collective motion with respect to noise—features typical of many active agents systems, and, in particular, to the minimal Vicsek model.

Wider implications. The model suggests that myriad instant inelastic collisions can reproduce the velocity alignment force, a critical ingredient of many active agent models. The results also suggest an alternate mechanism for explanation of the collective motion in animal groups, like swimming bacteria colonies, where the active biological mechanisms, e.g. chemotaxis, are not obvious. The model also expands our understanding of why granular materials (even isotropic ones) display such a plethora of phenomena—they appear to have 'a life of their own'....

Figure. Dynamics of a system of inelastically colliding self-propelled particles in periodic boundary conditions. Starting from random initial conditions (top left), the gradual build-up of velocity correlation due to collision forms local groups and vortices (top middle–top right) competing and annihilating (bottom left–bottom middle) until uniform motion is obtained (bottom right).

Received 24 November 2007
Published 25 February 2008