# Traveling band formation in feedback-driven colloids

## TL;DR

This paper demonstrates how time-delayed feedback in colloidal suspensions induces self-organized traveling bands, with properties tunable by feedback parameters, supported by simulations and theoretical analysis.

## Contribution

It introduces a novel feedback mechanism causing traveling band formation in colloids, combining simulation and theory to analyze the phenomenon.

## Key findings

- Traveling bands form due to feedback in colloids.
- Band width and speed are tunable by delay and potential range.
- Traveling bands persist in finite and confined systems.

## Abstract

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory (DDFT). Traveling band formation also persists in systems of finite size leading, in the case of circularly confined systems, to rotating traveling waves.