Hydrodynamics of the Kuramoto-Vicsek model of rotating self-propelled particles

TL;DR

This paper derives and analyzes hydrodynamic models for self-propelled particles that synchronize their rotation, combining the Kuramoto and Vicsek models, and explores different regimes of angular velocity.

Contribution

It introduces a new hydrodynamic model for rotating self-propelled particles and compares small and large angular velocity regimes within a unified framework.

Findings

In the small angular velocity regime, the model aligns with the existing Self-Organized Hydrodynamic model.

A novel hydrodynamic model is derived for the large angular velocity case.

Preliminary linear stability analysis is conducted for the new models.

Abstract

We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their rotation motion with their neighbors. It combines the Kuramoto model of synchronization and the Vicsek model of swarm formation. We study the mean-field kinetic and hydrodynamic limits of this system within two different scalings. In the small angular velocity regime, the resulting model is a slight modification of the 'Self-Organized Hydrodynamic' model which has been previously introduced by the first author. In the large angular velocity case, a new type of hydrodynamic model is obtained. A preliminary study of the linearized stability is proposed.