Periodic patterns displace active phase separation

TL;DR

This paper uncovers a new bifurcation in conserved systems that halts active phase separation, leading to stable, spatially periodic or hybrid patterns, with implications for various particle-conserving systems.

Contribution

It introduces a generic dissipative model revealing a secondary bifurcation that transitions systems from phase separation to periodic or hybrid states.

Findings

Identification of a secondary bifurcation stopping active phase separation.

Discovery of stable, multiscale spatial patterns beyond the bifurcation.

Hysteretic transition between phase separation and periodic patterns.

Abstract

In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially periodic pattern or, in a complementary parameter region, by a novel hybrid state with spatially alternating homogeneous and periodic states. The transition from phase separation to extended spatially periodic patterns is hysteretic. We show that the resulting patterns are multistable, as they show stability beyond the bifurcation for different wavenumbers belonging to a wavenumber band. The transition from active phase separation to the hybrid states is continuous. Both transition scenarios are systems-spanning phenomena in particle conserving systems. They are predicted with a generic dissipative model introduced in this work. Candidates for specific systems, in which these generic secondary transitions are likely to occur, are, for example, generalized models for motility-induced phase separation in active Brownian particles, models for cell division or chemotactic systems with conserved particle dynamics.