Phases and homogeneous ordered states in alignment-based self-propelled particle models

TL;DR

This study explores the phase behavior and homogeneous states of alignment-based self-propelled particle models, revealing new regimes and deviations from theoretical predictions across various parameters and interaction types.

Contribution

It provides a comprehensive analysis of phase diagrams and homogeneous states in self-propelled particle models, including comparisons with existing theories and identification of previously uncharacterized regimes.

Findings

Identified new regimes in phase diagrams with and without repulsion.

Compared homogeneous polarized states to theoretical predictions, noting deviations.

Analyzed effects of finite-size and inhomogeneity on model behavior.

Abstract

We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular for high coupling strengths. We compare the boundaries and representative states of all regions, identifying various regimes that had not been previously characterized. We analyze in detail three types of homogeneous polarized states, comparing them to existing theoretical and numerical results by computing their velocity and density correlations, giant number fluctuations, and local order-density coupling. We find that they all deviate in one way or another from the theoretical predictions, attributing these differences either to the remaining inhomogeneities or to finite-size effects. We discuss our results in terms of the universal or specific features of each model, their thermodynamic limit, and the high mixing and low mixing regimes. Our study provides a broad, overarching perspective on the multiple phases and states found in alignment-based self-propelled particle models.