Boids in a loop: Self-propelled particles within a flexible boundary

Abstract

We numerically explore the behavior of repelling and aligning self-propelled polar particles (boids) in two dimensions enclosed by a damped flexible and elastic loop-shaped boundary. We observe disordered, polar ordered, jammed, and circulating states. The latter produce a rich variety of boundary shapes, including circles, ovals, irregulars, ruffles, or sprockets, depending upon the bending moment of the boundary and the boundary to particle mass ratio. With the exception of the circulating states with nonround boundaries, states resemble those exhibited by attracting self-propelled particles, but here the confining boundary acts in place of a cohesive force. We attribute the formation of ruffles to instability mediated by pressure on the boundary when the speed of waves on the boundary approximately matches the self-propelled particle's swim speed.