# Tuning Self Organization Of Confined Active Particles By Steepness Of The Trap

## TL;DR

This study explores how the steepness of a confining trap influences the collective behavior and ordering of self-propelling particles, revealing a transition from boundary flocking to spatially ordered structures as the trap becomes less steep.

## Contribution

It demonstrates how tuning the trap steepness induces a transition from boundary flocking to hexagonal spatial order in confined active particles.

## Key findings

- Particles form boundary flocking in steep traps.
- Decreasing trap steepness leads to hexagonal order.
- Order stability persists after trap removal.

## Abstract

We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They are also interacting with each other by a soft, isotropic, excluded-volume interaction. Particles are confined in a circular trap. The steepness of the trap is tuneable. Their average packing fraction and strength of rotational fluctuation are low. When the trap is steep, particles flock along its boundary. They form polar cluster that spreads over the boundary. The cluster has no spatial or structural order. We show, when the steepness is decreased beyond a threshold value, the clusters become round, compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order within them. We investigate kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the clusters need to roll around their centre of mass, to be spatially ordered. We also discuss the stability of the order when the trap is suddenly switched off.