Active pattern formation emergent from single-species nonreciprocity

TL;DR

This paper introduces a new continuum model called Active Model N for single-species nonreciprocal interactions, revealing complex pattern formation including self-traveling states and unique yarn-like structures, with implications for biological and artificial active matter.

Contribution

It derives a generic field theory for single-species nonreciprocal systems and uncovers novel pattern formation phenomena not previously studied in such systems.

Findings

Emergence of self-traveling active patterns.

Development of interwoven yarn-like structures.

Distinct scaling behaviors in droplet growth dynamics.

Abstract

Nonreciprocal interactions violating Newton's third law are common in a plethora of nonequilibrium situations ranging from predator-prey systems to the swarming of birds and effective colloidal interactions under flow. While many recent studies have focused on two species with nonreciprocal coupling, less is examined for the basic single-component system breaking the actio and reactio equality of force within the same species. Here, we systematically derive a field theory for the case of single-species nonreciprocal interactions from the microscopic particle dynamics, leading to a generic continuum model termed Active Model N (N denoting nonreciprocity). We explore the rich dynamics of pattern formation in this nonreciprocal system and the emergence of self-traveling states with persistent variation and flowing of active branched patterns. One particular new characteristic pattern is an interwoven self-knitting "yarn" structure with a unique feature of simultaneous development of micro- and bulk phase separations. The growth dynamics of a "ball-of-wool" active droplet towards these self-knitted yarn or branched states exhibits a crossover between different scaling behaviors. The mechanism underlying this distinct class of active phase separation is attributed to the interplay between nonreciprocity and competition of interparticle forces. Our predictions can be applied to various biological and artificial active matter systems controlled by single-species nonreciprocity.