Defect-mediated dynamics of coherent structures in active nematics

The paper’s instantaneous Eulerian folding-rate formula (SI Eq. (2) and main-text Eq. (8)) includes a minus sign in front of the vorticity-gradient contribution, i.e., −(∇ω·n)/2. Under the stated perpendicular operator ∇⊥ = (−∂y, ∂x) and the standard 2D vorticity definition ω = ∂x v_y − ∂y v_x, the correct sign is plus. A simple check with v(x,y) = (0, (g/2)x^2) at (x,n)=(0,e1) shows the paper’s sign would predict zero curvature growth, whereas the correct plus sign gives κ̇ = g, matching the direct geometry of the advected parabola. The model’s derivation recovers κ̇(t,x,n) = [(∇D n)·n]·n⊥ + (1/2)(∇ω·n), agreeing with the sanity check. See the paper’s stated formulae in SI (Eq. (2)-(3)) and main text (Eq. (8)) for the sign used in the manuscript , and note their perpendicular operator definition ∇⊥ = (−∂y, ∂x) .