# Universal scaling in bidirectional flows of self-avoiding agents

## TL;DR

This paper demonstrates that various self-avoidance rules in bidirectional pedestrian flows exhibit a universal scaling behavior in their interaction potential, regardless of the specific rule or phase, indicating a fundamental property of such systems.

## Contribution

It extends previous findings by showing that different self-avoidance mechanisms in bidirectional flows share a universal scaling law in their interaction potential.

## Key findings

- All tested self-avoidance rules collapse to a common scaling in disordered phase ($V( au) o au^{-2}$).
- In lane-formation regime, all rules show a $V( au) o au^{-1}$ scaling.
- Universal scaling suggests a fundamental property of bidirectional self-avoiding flows.

## 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.