Collection of polar self-propelled particles with a modified alignment interaction

TL;DR

This paper investigates how a modified alignment interaction affects the collective behavior of polar self-propelled particles, revealing a transition from discontinuous to continuous phase change and instability near the classic Vicsek model.

Contribution

It introduces a distance-dependent alignment interaction in self-propelled particles and analyzes its impact on phase transition nature and stability.

Findings

Transition nature changes from discontinuous to continuous as interaction range decreases.

Critical noise strength varies with interaction decay parameter and matches mean-field predictions.

Homogeneous ordered state becomes unstable near the Vicsek limit, leading to phase separation.

Abstract

We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction, $a^{d}$ ($0<a<1$) decays with metric distance $d$ between particle pair, and the interaction is short range. At $a = 1.0$, our model reduces to the famous Vicsek model. For all ${\it a}>0$, the system shows a transition from a disordered to an ordered state as a function of noise strength. We calculate the critical noise strength, $\eta_c(a)$ for different $a$ and compare it with the mean-field result. Nature of the disorder-to-order transition continuously changes from discontinuous to continuous with decreasing $a$. We numerically estimate tri-critical point $a_{TCP}$ at which the nature of transition changes from discontinuous to continuous. The density phase separation is large for ${\it a}$ close to unity, and it decays with decreasing $a$. We also write the coarse-grained hydrodynamic equations of motion for general ${\it a}$, and find that the homogeneous ordered state is unstable to small perturbation as ${\it a}$ approaches to $1$. The instability in the homogeneous ordered state is consistent with the large density phase separation for ${\it a}$ close to unity.