Collective Behaviors in Two-Dimensional Systems of Interacting Particles

This article presents results of molecular dynamics simulations that show the emergence of collective behaviors in a two-dimensional system of particles (hard disks) interacting through a properly chosen collision rule. The particles, which are of finite size and are in free flight between collisions, are not self-propelled. They tumble randomly like bacteria and interact only when they collide, not through continuous potential forces. This work therefore indicates that interactions at the microscopic level, which occur only locally and discretely both in time and space, are sufficient to lead to large-scale macroscopic behaviors. Order parameters that capture and quantify the formation of collective behaviors are introduced and used to describe how the choice of collision rule affects the steady state dynamics of the system, by comparing the outcome to the standard case of elastic collisions. This work was motivated by recent results on the dynamics of bacterial colonies. Possible applications of the present approach to other systems are also discussed.