Hydrodynamic Equations for Flocking Models without Velocity Alignment

TL;DR

This paper derives hydrodynamic equations for flocking models that lack velocity alignment, revealing three distinct collective behaviors and highlighting their fundamental differences from traditional active systems.

Contribution

It introduces a hydrodynamic framework for position-based flocking models without velocity alignment, extending previous results and identifying new collective behaviors.

Findings

Identification of three macroscopic behaviors: coarsening, nematic bands, and moving worms.

Hydrodynamic equations show these systems form a distinct class of active matter.

Position-based interactions lead to fundamentally different collective dynamics.

Abstract

The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been shown recently that several flocking behaviors can emerge in the absence of velocity alignment and as a result of short-range, position-based, attractive forces that act inside a vision cone. Here, we derive the corresponding hydrodynamic equations of a microscopic position-based flocking model, reviewing and extending previously reported results. In particular, we show that three distinct macroscopic collective behaviors can be observed: i) the coarsening of aggregates with no orientational order, ii) the emergence of static, elongated nematic bands, and iii) the formation of moving, locally polar structures, which we call worms. The derived hydrodynamic equations indicate that active particles interacting via position-based interactions belong to a distinct class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems.