Design rules for controlling active topological defects

TL;DR

This paper introduces a symmetry-based method for controlling active topological defects in materials, enabling their creation, movement, and braiding through designed activity patterns, with potential applications in programmable active materials.

Contribution

It presents a novel additive framework combining theory and simulations to manipulate active defects using elementary activity patterns as active topological tweezers.

Findings

Spatial activity gradients induce defect polarization similar to electric fields.

Strong activity gradients can invert defect polarization, acting like negative susceptibility dielectric.

The framework allows programmable control of defect transport and patterning in active materials.

Abstract

Topological defects play a central role in the physics of many materials, including magnets, superconductors and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory and logic.