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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. 

The vertex model of epithelia describes the apical surface of a tissue as a tiling of elastic polygonal cells. We show how non-affine deformations allow the tissue to have a softer mechanical response under strain, such as a vanishing shear modulus. 

We study the active flow around isolated defects and the self-propulsion velocity of + 1 / 2 defects in an active nematic film with both viscous dissipation (with viscosity η ) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓ d = η / Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R . In the presence of friction that leads to a finite value of ℓ d , the vorticity field decays to zero on the lengthscales larger than ℓ d . We show that the self-propulsion velocity of + 1 / 2 defects grows with R in small systems where R < ℓ d , while in the infinite system limit or when R ≫ ℓ d , it approaches a constant value determined by ℓ d . 

The name active matter refers to any collection of entities that individually use free energy to generate their own motion and forces. Through interactions, active particles spontaneously organize in emergent large-scale structures with a rich range of materials properties. The active matter paradigm has been applied to living and non-living systems over a vast dynamic range, from the organization of subnuclear structures in the cell to collective motion at the human scale. The diverse phenomena exhibited by these systems all stem from the defining property of active matter as an assembly of components that individually and dissipatively break time-reversal symmetry. This article outlines a selection of current and emerging directions in active matter research. It aims at providing a pedagogical and forward looking introduction for researchers new to the field and a roadmap of open challenges and future directions that may appeal to those established in the area. 

Abstract We adapt the Halperin–Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that ±1/2 defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it is not possible to eliminate the fluid velocity in favor of the local defect polarization alone. For the case of two defects with opposite charge, the non-local hydrodynamic interaction is mediated by non-reciprocal pressure-gradient forces. Finally, we derive continuum equations for a defect gas coupled to an arbitrary (compressible or incompressible) fluid flow. 

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.