Curvature-Driven Coarsening — Allen-Cahn

Phase ordering dynamics: domains grow as interfaces move toward their center of curvature, obeying the t^(1/2) growth law.

t = 0 | Domain size ∝ t^0.50 | Interfaces: 0

Allen-Cahn equation: ∂φ/∂t = M[ε²∇²φ − f'(φ)], where f(φ) = (φ²−1)²/4 is a double-well potential. Interfaces move with velocity v = −Mκ (κ = mean curvature), giving L(t) ~ t^(1/2) coarsening.