Self-Propelled Collective Motion with Multiplicative Scalar Noise

TL;DR

This paper introduces a modified Vicsek model with multiplicative scalar noise that better captures individual behavior in sparse conditions, demonstrating a first order phase transition in collective motion.

Contribution

The paper presents a novel multiplicative scalar noise model that improves upon the Vicsek model by accurately representing behavior in low-density regimes, revealing a first order phase transition.

Findings

The model exhibits a first order phase transition in both high and low velocity/density regimes.

It better predicts the onset of collective motion in sparse populations.

The model aligns with observed behaviors in real self-propelled particle systems.

Abstract

The emergence of order from initial disordered movement in self-propelled collective motion is an instance of nonequilibrium phase transition, which is known to be first order in the thermodynamic limit. Here, we introduce a multiplicative scalar noise model of collective motion as a modification of the original Vicsek model, which more closely mimics the particles' behavior. We allow for more individual movement in sparsely populated neighborhoods, the mechanism of which is not incorporated in the original Vicsek model. This is especially important in the low velocity and density regime where the probability of a clear neighborhood is relatively high. The modification, thus, removes the shortcoming of the Vicsek model in predicting continuous phase transition in this regime. The onset of collective motion in the proposed model is numerically studied in detail, indicating a first order phase transition in both high and low velocity/density regimes for systems with comparatively smaller size which is computationally desirable.