Universal scaling in bidirectional flows of self-avoiding agents

Abstract

The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has revealed recently the existence of a universal scaling in systems of pedestrians, provided the potential of interaction $V(\tau )$ is conveniently defined in the space of the times-to-collision $\tau$ [Phys. Rev. Lett. \textbf{113}, 238701 (2014)]. Here we significantly extend this result by comparing numerically the performance of completely different rules of self-avoidance in bidirectional systems and proving that all of them collapse to a common scaling both in the disordered phase ($V(\tau )\sim {\tau }^{-2}$) and in the lane-formation regime ($V(\tau )\sim {\tau }^{-1}$), so suggesting that these scalings represent actually a universal feature of any self-avoiding bidirectional flow.

10 pages, 6 figures