Wake-mediated interaction between driven particles crossing a perpendicular flow

TL;DR

This paper investigates how particles crossing perpendicular flows create wakes that mediate interactions, leading to pattern formation such as chevrons, through a lattice model and analytical characterization of effective interactions.

Contribution

It introduces a microscopic lattice model to analyze wake-mediated interactions in crossing particle flows, providing analytical insights into pattern formation mechanisms.

Findings

Wakes created by crossing particles can localize other particles traveling in the same direction.

Effective interactions mediated by perpendicular flows can lead to spontaneous pattern formation.

The semi-deterministic model allows for analytical characterization of these interactions.

Abstract

Diagonal or chevron patterns are known to spontaneously emerge at the intersection of two perpendicular flows of self-propelled particles, e.g. pedestrians. The instability responsible for this pattern formation has been studied in previous work in the context of a mean-field approach. Here we investigate the microscopic mechanism yielding to this pattern. We present a lattice model study of the wake created by a particle crossing a perpendicular flow and show how this wake can localize other particles traveling in the same direction as a result of an effective interaction mediated by the perpendicular flow. The use of a semi-deterministic model allows us to characterize analytically the effective interaction between two particles.