Simple and faithful nonlinear field equations for aligning self-propelled rods

TL;DR

This paper derives minimal nonlinear field equations from the Vicsek model to accurately describe the collective behavior of self-propelled rods, including density band formation, with good agreement to microscopic simulations.

Contribution

It introduces a simple, faithful set of nonlinear equations capturing the collective dynamics of self-propelled rods from a microscopic Vicsek model with nematic alignment.

Findings

Derived explicit expressions for density band fronts

Achieved good agreement with microscopic model dynamics

Provided a comprehensive nonlinear analytical framework

Abstract

We derive a set of minimal yet complete nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for the fronts forming density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.