Coarsening — Allen-Cahn Domain Growth

Allen-Cahn equation ∂φ/∂t = M[ε²∇²φ − f'(φ)], with double-well potential f(φ) = ¼(φ²−1)². Phase-ordering kinetics: domains grow as L(t) ~ t^(1/2) after a quench into the miscibility gap. Watch the characteristic length scale grow over time.

Step: 0
L(t) ~ t^0.5
Domains: —