Topological flocking models in spatially heterogeneous environments

Parisa Rahmani,Pawel Romanczuk,Fernando Peruani

doi:10.1038/s42005-021-00708-y

Abstract

Flocking models with metric and topological interactions are supposed to exhibit distinct features, as for instance the presence and absence of moving polar bands. On the other hand, quenched disorder (spatial heterogeneities) has been shown to dramatically affect large-scale properties of active systems with metric interactions, while the impact of quenched disorder on active systems with metric-free interactions has remained, until now, unexplored. Here, we show that topological flocking models recover several features of metric ones in homogeneous media, when placed in a heterogeneous environment. In particular, we find that order is long-ranged even in the presence of spatial heterogeneities, and that the heterogeneous environment induces an effective density-order coupling facilitating emergence of traveling bands, which are observed in wide regions of parameter space. We argue that such a coupling results from a fluctuation-induced rewiring of the topological interaction network, strongly enhanced by the presence of spatial heterogeneities.

Highlights

Flocking models with metric and topological interactions are supposed to exhibit distinct features, as for instance the presence and absence of moving polar bands
The impact of quenched disorder on the active matter with topological interactions has, so far, not been addressed. We address this open question in active matter theory by studying how the quenched disorder affects the emergent properties of topological flocking models using k-nearest neighbors and Voronoi tessellation[37]
We use two definitions of topological neighborhood (TN): (i) the first k-nearest neighbor objects, and (ii) all objects in the first shell by performing a Voronoi tessellation

Summary

Introduction

Flocking models with metric and topological interactions are supposed to exhibit distinct features, as for instance the presence and absence of moving polar bands. We find that order is long-ranged even in the presence of spatial heterogeneities, and that the heterogeneous environment induces an effective density-order coupling facilitating emergence of traveling bands, which are observed in wide regions of parameter space. We argue that such a coupling results from a fluctuation-induced rewiring of the topological interaction network, strongly enhanced by the presence of spatial heterogeneities. Our analysis extends our understanding of topological interactions in active matter systems by showing that topological flocking models in complex environments behave as metric ones in homogeneous media

Methods

Results

Discussion

Conclusion