Spatiotemporal Control of Charge +1 Topological Defects in Polar Active Matter

TL;DR

This paper demonstrates a method to control +1 topological defects in active polar fluids confined to a disk, enabling precise defect motion through boundary and activity modulation, with potential applications in morphogenesis and material design.

Contribution

It introduces a novel control mechanism for topological defects in active matter using boundary conditions and localized activity, with real-time defect trajectory guidance.

Findings

Defect moves on a circular path when activity is localized in an annulus.

Angular speed and radius depend on boundary orientation and active annulus size.

Proportional integral control guides defect along complex trajectories.

Abstract

Topological defects are a conspicuous feature of active liquid crystals that have been associated with important morphogenetic transitions in organismal development. Robust development thus requires a tight control of the motion and placement of topological defects. In this manuscript, we study a mechanism to control +1 topological defects in an active polar fluid confined to a disk. If activity is localized in an annulus within the disk, the defect moves on a circular trajectory around the center of the disk. Using an ansatz for the polar field, we determine the dependence of the angular speed and the circle radius on the boundary orientation of the polar field and the active annulus. Using a proportional integral controller, we guide the defect along complex trajectories by changing the active annulus size and the boundary orientation.