Emergence of edge state in suspension of self-propelled particles

TL;DR

This paper investigates how self-propelled particle suspensions develop localized edge states and bistable convection patterns, revealing nonlinear behaviors beyond classical convection models through numerical and stability analyses.

Contribution

It introduces the concept of an edge state in self-propelled particle suspensions, connecting wall-bounded flow theories to bioconvection phenomena.

Findings

Identification of a nonlinear convection state despite stable nonconvection

Discovery of an edge state acting as a basin boundary in the system

Stabilization of the nonconvection state by increased vertical self-propulsion

Abstract

We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--B\'{e}nard convection. Linear stability analysis of the model system reveals that the trivial noncovection state is stabilized by an increase of self-propelled speed in the vertical direction. Through numerical simulations, we found a nonlinear convection state even when the nonconvection state is stable. Applying ideas and tools developed in wall-bounded flows, we numerically identified an edge state, which is an unstable solution on a basin boundary in the model dynamical systems.