Active Nematic Defects

Topological defects ±½ in active liquid crystals — self-propelled +½ defects drive active turbulence

Activity α 1.5 Elastic K 1.0 Damping γ 0.5 Grid size N 60

+½ defects: --

-½ defects: --

Total charge: --

Activity: --

Color: director angle θ
▲ red = +½ defect
● blue = -½ defect

Q-tensor: Qᵢⱼ = S(nᵢnⱼ - δᵢⱼ/2) order parameter for nematic orientation

Active stress: σᵃᵢⱼ = -αQᵢⱼ extensile (α>0) or contractile (α<0)

+½ defect: self-propelled, velocity v ~ α/γ in head direction (comet-like)

-½ defect: passive, immobile without activity; charge conservation: Σq = 0