Assembly along lines in boundary-driven dynamical system

TL;DR

This paper presents a novel boundary-driven dynamical system where particles self-organize into lines and slices, revealing a new pattern of assembly driven by particles on the system boundary.

Contribution

The study introduces a simple rule leading to boundary-driven line formation, contrasting with traditional local clustering mechanisms in particle systems.

Findings

Particles form lines along the system boundary in 2D and 3D.

Lines are created by zigzag motion towards nearly equidistant attractors.

The pattern differs from local clustering, emphasizing boundary effects.

Abstract

We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual dynamical patterns: during the process of assembly the system self-organizes into slices of low particle density separated by lines of increasingly high particle density along which most particles move. As the process proceeds, pairs of lines meet and merge with each other until a single line remains and particles move along it towards the zone of assembly. We show that this pattern is governed by particles (attractors) situated on the instantaneous outer boundary of the system and that both in two and in three dimensions the lines are formed by zigzag motion of a particle towards a pair of nearly equidistant attractors. This novel line-dominated assembly is very different from the local assembly in which particles that move towards their nearest neighbors produce point-like clusters that coalesce into new point-like clusters, etc.